0s autopkgtest [20:23:09]: starting date and time: 2024-03-16 20:23:09+0000 0s autopkgtest [20:23:09]: git checkout: b506e79c ssh-setup/nova: fix ARCH having two lines of data 0s autopkgtest [20:23:09]: host juju-7f2275-prod-proposed-migration-environment-3; command line: /home/ubuntu/autopkgtest/runner/autopkgtest --output-dir /tmp/autopkgtest-work.9fzk4ybl/out --timeout-copy=6000 --setup-commands /home/ubuntu/autopkgtest-cloud/worker-config-production/setup-canonical.sh --setup-commands /home/ubuntu/autopkgtest/setup-commands/setup-testbed --apt-pocket=proposed=src:r-base,src:curl,src:glib2.0,src:libpng1.6,src:libpsl,src:libtirpc,src:libxt,src:openssl,src:orthanc-python,src:readline,src:wp2latex --apt-upgrade r-cran-tensora --timeout-short=300 --timeout-copy=20000 --timeout-build=20000 '--env=ADT_TEST_TRIGGERS=r-base/4.3.3-2build1 curl/8.5.0-2ubuntu7 glib2.0/2.79.3-3ubuntu5 libpng1.6/1.6.43-3 libpsl/0.21.2-1.1 libtirpc/1.3.4+ds-1.1 libxt/1:1.2.1-1.2 openssl/3.0.13-0ubuntu1 orthanc-python/4.1+ds-2build3 readline/8.2-3.1 wp2latex/4.4~ds-1build1' -- ssh -s /home/ubuntu/autopkgtest/ssh-setup/nova -- --flavor autopkgtest --security-groups autopkgtest-juju-7f2275-prod-proposed-migration-environment-3@bos03-arm64-25.secgroup --name adt-noble-arm64-r-cran-tensora-20240316-202309-juju-7f2275-prod-proposed-migration-environment-3 --image adt/ubuntu-noble-arm64-server --keyname testbed-juju-7f2275-prod-proposed-migration-environment-3 --net-id=net_prod-proposed-migration -e TERM=linux -e ''"'"'http_proxy=http://squid.internal:3128'"'"'' -e ''"'"'https_proxy=http://squid.internal:3128'"'"'' -e ''"'"'no_proxy=127.0.0.1,127.0.1.1,login.ubuntu.com,localhost,localdomain,novalocal,internal,archive.ubuntu.com,ports.ubuntu.com,security.ubuntu.com,ddebs.ubuntu.com,changelogs.ubuntu.com,launchpadlibrarian.net,launchpadcontent.net,launchpad.net,10.24.0.0/24,keystone.ps5.canonical.com,objectstorage.prodstack5.canonical.com'"'"'' --mirror=http://ftpmaster.internal/ubuntu/ 137s autopkgtest [20:25:26]: testbed dpkg architecture: arm64 137s autopkgtest [20:25:26]: testbed apt version: 2.7.12 137s autopkgtest [20:25:26]: @@@@@@@@@@@@@@@@@@@@ test bed setup 137s Get:1 http://ftpmaster.internal/ubuntu noble-proposed InRelease [117 kB] 138s Get:2 http://ftpmaster.internal/ubuntu noble-proposed/multiverse Sources [51.4 kB] 138s Get:3 http://ftpmaster.internal/ubuntu noble-proposed/universe Sources [3704 kB] 138s Get:4 http://ftpmaster.internal/ubuntu noble-proposed/restricted Sources [6540 B] 138s Get:5 http://ftpmaster.internal/ubuntu noble-proposed/main Sources [474 kB] 138s Get:6 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 Packages [646 kB] 138s Get:7 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 c-n-f Metadata [3144 B] 138s Get:8 http://ftpmaster.internal/ubuntu noble-proposed/restricted arm64 Packages [33.6 kB] 138s Get:9 http://ftpmaster.internal/ubuntu noble-proposed/restricted arm64 c-n-f Metadata [116 B] 138s Get:10 http://ftpmaster.internal/ubuntu noble-proposed/universe arm64 Packages [4012 kB] 138s Get:11 http://ftpmaster.internal/ubuntu noble-proposed/universe arm64 c-n-f Metadata [8528 B] 138s Get:12 http://ftpmaster.internal/ubuntu noble-proposed/multiverse arm64 Packages [55.5 kB] 138s Get:13 http://ftpmaster.internal/ubuntu noble-proposed/multiverse arm64 c-n-f Metadata [116 B] 140s Fetched 9112 kB in 2s (5183 kB/s) 140s Reading package lists... 143s Reading package lists... 143s Building dependency tree... 143s Reading state information... 143s Calculating upgrade... 144s The following packages will be REMOVED: 144s libglib2.0-0 libssl3 144s The following NEW packages will be installed: 144s libglib2.0-0t64 libssl3t64 xdg-user-dirs 144s The following packages have been kept back: 144s curl 144s The following packages will be upgraded: 144s gir1.2-glib-2.0 libglib2.0-data libtirpc-common openssl readline-common 144s ubuntu-minimal ubuntu-standard 144s 7 upgraded, 3 newly installed, 2 to remove and 1 not upgraded. 144s Need to get 4613 kB of archives. 144s After this operation, 211 kB of additional disk space will be used. 144s Get:1 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 gir1.2-glib-2.0 arm64 2.79.3-3ubuntu5 [182 kB] 144s Get:2 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libglib2.0-0t64 arm64 2.79.3-3ubuntu5 [1527 kB] 144s Get:3 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 openssl arm64 3.0.13-0ubuntu1 [983 kB] 144s Get:4 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libssl3t64 arm64 3.0.13-0ubuntu1 [1770 kB] 145s Get:5 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libglib2.0-data all 2.79.3-3ubuntu5 [46.6 kB] 145s Get:6 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libtirpc-common all 1.3.4+ds-1.1 [8018 B] 145s Get:7 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 readline-common all 8.2-3.1 [56.4 kB] 145s Get:8 http://ftpmaster.internal/ubuntu noble/main arm64 ubuntu-minimal arm64 1.536 [10.7 kB] 145s Get:9 http://ftpmaster.internal/ubuntu noble/main arm64 xdg-user-dirs arm64 0.18-1 [18.1 kB] 145s Get:10 http://ftpmaster.internal/ubuntu noble/main arm64 ubuntu-standard arm64 1.536 [10.7 kB] 145s Fetched 4613 kB in 1s (6158 kB/s) 145s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74758 files and directories currently installed.) 145s Preparing to unpack .../gir1.2-glib-2.0_2.79.3-3ubuntu5_arm64.deb ... 145s Unpacking gir1.2-glib-2.0:arm64 (2.79.3-3ubuntu5) over (2.79.2-1~ubuntu1) ... 145s dpkg: libglib2.0-0:arm64: dependency problems, but removing anyway as you requested: 145s udisks2 depends on libglib2.0-0 (>= 2.77.0). 145s shared-mime-info depends on libglib2.0-0 (>= 2.75.3). 145s python3-gi depends on libglib2.0-0 (>= 2.77.0). 145s python3-dbus depends on libglib2.0-0 (>= 2.16.0). 145s netplan.io depends on libglib2.0-0 (>= 2.70.0). 145s netplan-generator depends on libglib2.0-0 (>= 2.70.0). 145s libxmlb2:arm64 depends on libglib2.0-0 (>= 2.54.0). 145s libvolume-key1:arm64 depends on libglib2.0-0 (>= 2.18.0). 145s libudisks2-0:arm64 depends on libglib2.0-0 (>= 2.75.3). 145s libqrtr-glib0:arm64 depends on libglib2.0-0 (>= 2.56). 145s libqmi-proxy depends on libglib2.0-0 (>= 2.30.0). 145s libqmi-glib5:arm64 depends on libglib2.0-0 (>= 2.54.0). 145s libpolkit-gobject-1-0:arm64 depends on libglib2.0-0 (>= 2.38.0). 145s libpolkit-agent-1-0:arm64 depends on libglib2.0-0 (>= 2.38.0). 145s libnetplan0:arm64 depends on libglib2.0-0 (>= 2.75.3). 145s libmm-glib0:arm64 depends on libglib2.0-0 (>= 2.62.0). 145s libmbim-proxy depends on libglib2.0-0 (>= 2.56). 145s libmbim-glib4:arm64 depends on libglib2.0-0 (>= 2.56). 145s libjson-glib-1.0-0:arm64 depends on libglib2.0-0 (>= 2.75.3). 145s libjcat1:arm64 depends on libglib2.0-0 (>= 2.75.3). 145s libgusb2:arm64 depends on libglib2.0-0 (>= 2.75.3). 145s libgudev-1.0-0:arm64 depends on libglib2.0-0 (>= 2.38.0). 145s libgirepository-1.0-1:arm64 depends on libglib2.0-0 (>= 2.79.0). 145s libfwupd2:arm64 depends on libglib2.0-0 (>= 2.79.0). 145s libblockdev3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-utils3:arm64 depends on libglib2.0-0 (>= 2.75.3). 145s libblockdev-swap3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-part3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-nvme3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-mdraid3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-loop3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-fs3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s libblockdev-crypto3:arm64 depends on libglib2.0-0 (>= 2.42.2). 145s fwupd depends on libglib2.0-0 (>= 2.79.0). 145s bolt depends on libglib2.0-0 (>= 2.56.0). 145s 145s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74758 files and directories currently installed.) 145s Removing libglib2.0-0:arm64 (2.79.2-1~ubuntu1) ... 145s Selecting previously unselected package libglib2.0-0t64:arm64. 145s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74733 files and directories currently installed.) 145s Preparing to unpack .../libglib2.0-0t64_2.79.3-3ubuntu5_arm64.deb ... 145s libglib2.0-0t64.preinst: Removing /var/lib/dpkg/info/libglib2.0-0:arm64.postrm to avoid loss of /usr/share/glib-2.0/schemas/gschemas.compiled... 145s removed '/var/lib/dpkg/info/libglib2.0-0:arm64.postrm' 145s Unpacking libglib2.0-0t64:arm64 (2.79.3-3ubuntu5) ... 146s Preparing to unpack .../openssl_3.0.13-0ubuntu1_arm64.deb ... 146s Unpacking openssl (3.0.13-0ubuntu1) over (3.0.10-1ubuntu4) ... 146s dpkg: libssl3:arm64: dependency problems, but removing anyway as you requested: 146s wget depends on libssl3 (>= 3.0.0). 146s u-boot-tools depends on libssl3 (>= 3.0.0). 146s tnftp depends on libssl3 (>= 3.0.0). 146s tcpdump depends on libssl3 (>= 3.0.0). 146s systemd-resolved depends on libssl3 (>= 3.0.0). 146s systemd depends on libssl3 (>= 3.0.0). 146s sudo depends on libssl3 (>= 3.0.0). 146s sbsigntool depends on libssl3 (>= 3.0.0). 146s rsync depends on libssl3 (>= 3.0.0). 146s python3-cryptography depends on libssl3 (>= 3.0.0). 146s openssh-server depends on libssl3 (>= 3.0.10). 146s openssh-client depends on libssl3 (>= 3.0.10). 146s mtd-utils depends on libssl3 (>= 3.0.0). 146s mokutil depends on libssl3 (>= 3.0.0). 146s linux-headers-6.8.0-11-generic depends on libssl3 (>= 3.0.0). 146s libsystemd-shared:arm64 depends on libssl3 (>= 3.0.0). 146s libssh-4:arm64 depends on libssl3 (>= 3.0.0). 146s libsasl2-modules:arm64 depends on libssl3 (>= 3.0.0). 146s libsasl2-2:arm64 depends on libssl3 (>= 3.0.0). 146s libpython3.12-minimal:arm64 depends on libssl3 (>= 3.0.0). 146s libnvme1 depends on libssl3 (>= 3.0.0). 146s libkrb5-3:arm64 depends on libssl3 (>= 3.0.0). 146s libkmod2:arm64 depends on libssl3 (>= 3.0.0). 146s libfido2-1:arm64 depends on libssl3 (>= 3.0.0). 146s libcurl4:arm64 depends on libssl3 (>= 3.0.0). 146s libcryptsetup12:arm64 depends on libssl3 (>= 3.0.0). 146s kmod depends on libssl3 (>= 3.0.0). 146s dhcpcd-base depends on libssl3 (>= 3.0.0). 146s bind9-libs:arm64 depends on libssl3 (>= 3.0.0). 146s 146s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74758 files and directories currently installed.) 146s Removing libssl3:arm64 (3.0.10-1ubuntu4) ... 146s Selecting previously unselected package libssl3t64:arm64. 146s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74747 files and directories currently installed.) 146s Preparing to unpack .../0-libssl3t64_3.0.13-0ubuntu1_arm64.deb ... 146s Unpacking libssl3t64:arm64 (3.0.13-0ubuntu1) ... 146s Preparing to unpack .../1-libglib2.0-data_2.79.3-3ubuntu5_all.deb ... 146s Unpacking libglib2.0-data (2.79.3-3ubuntu5) over (2.79.2-1~ubuntu1) ... 146s Preparing to unpack .../2-libtirpc-common_1.3.4+ds-1.1_all.deb ... 146s Unpacking libtirpc-common (1.3.4+ds-1.1) over (1.3.4+ds-1build1) ... 146s Preparing to unpack .../3-readline-common_8.2-3.1_all.deb ... 146s Unpacking readline-common (8.2-3.1) over (8.2-3) ... 146s Preparing to unpack .../4-ubuntu-minimal_1.536_arm64.deb ... 146s Unpacking ubuntu-minimal (1.536) over (1.535) ... 146s Selecting previously unselected package xdg-user-dirs. 146s Preparing to unpack .../5-xdg-user-dirs_0.18-1_arm64.deb ... 146s Unpacking xdg-user-dirs (0.18-1) ... 146s Preparing to unpack .../6-ubuntu-standard_1.536_arm64.deb ... 146s Unpacking ubuntu-standard (1.536) over (1.535) ... 146s Setting up ubuntu-minimal (1.536) ... 146s Setting up xdg-user-dirs (0.18-1) ... 146s Setting up libssl3t64:arm64 (3.0.13-0ubuntu1) ... 146s Setting up libtirpc-common (1.3.4+ds-1.1) ... 146s Setting up ubuntu-standard (1.536) ... 146s Setting up libglib2.0-0t64:arm64 (2.79.3-3ubuntu5) ... 146s No schema files found: doing nothing. 146s Setting up libglib2.0-data (2.79.3-3ubuntu5) ... 146s Setting up gir1.2-glib-2.0:arm64 (2.79.3-3ubuntu5) ... 146s Setting up openssl (3.0.13-0ubuntu1) ... 146s Setting up readline-common (8.2-3.1) ... 146s Processing triggers for man-db (2.12.0-3) ... 147s Processing triggers for install-info (7.1-3) ... 147s Processing triggers for libc-bin (2.39-0ubuntu2) ... 147s Reading package lists... 148s Building dependency tree... 148s Reading state information... 148s 0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded. 149s sh: Attempting to set up Debian/Ubuntu apt sources automatically 149s sh: Distribution appears to be Ubuntu 149s Reading package lists... 150s Building dependency tree... 150s Reading state information... 150s eatmydata is already the newest version (131-1). 150s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 150s Reading package lists... 150s Building dependency tree... 150s Reading state information... 151s dbus is already the newest version (1.14.10-4ubuntu1). 151s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 151s Reading package lists... 151s Building dependency tree... 151s Reading state information... 152s rng-tools-debian is already the newest version (2.4). 152s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 152s Reading package lists... 152s Building dependency tree... 152s Reading state information... 152s The following packages will be REMOVED: 152s cloud-init* python3-configobj* python3-debconf* 153s 0 upgraded, 0 newly installed, 3 to remove and 0 not upgraded. 153s After this operation, 3252 kB disk space will be freed. 153s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74774 files and directories currently installed.) 153s Removing cloud-init (24.1.1-0ubuntu1) ... 153s Removing python3-configobj (5.0.8-3) ... 153s Removing python3-debconf (1.5.86) ... 153s Processing triggers for man-db (2.12.0-3) ... 154s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74385 files and directories currently installed.) 154s Purging configuration files for cloud-init (24.1.1-0ubuntu1) ... 154s dpkg: warning: while removing cloud-init, directory '/etc/cloud/cloud.cfg.d' not empty so not removed 154s Processing triggers for rsyslog (8.2312.0-3ubuntu3) ... 154s invoke-rc.d: policy-rc.d denied execution of try-restart. 154s Reading package lists... 155s Building dependency tree... 155s Reading state information... 155s linux-generic is already the newest version (6.8.0-11.11+1). 155s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 155s Hit:1 http://ftpmaster.internal/ubuntu noble InRelease 156s Hit:2 http://ftpmaster.internal/ubuntu noble-updates InRelease 156s Hit:3 http://ftpmaster.internal/ubuntu noble-security InRelease 158s Reading package lists... 158s Reading package lists... 158s Building dependency tree... 158s Reading state information... 158s Calculating upgrade... 159s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 159s Reading package lists... 159s Building dependency tree... 159s Reading state information... 160s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 160s autopkgtest [20:25:49]: rebooting testbed after setup commands that affected boot 358s autopkgtest [20:29:07]: testbed running kernel: Linux 6.8.0-11-generic #11-Ubuntu SMP PREEMPT_DYNAMIC Wed Feb 14 02:53:31 UTC 2024 361s autopkgtest [20:29:10]: @@@@@@@@@@@@@@@@@@@@ apt-source r-cran-tensora 363s Get:1 http://ftpmaster.internal/ubuntu noble/universe r-cran-tensora 0.36.2.1-1 (dsc) [2084 B] 363s Get:2 http://ftpmaster.internal/ubuntu noble/universe r-cran-tensora 0.36.2.1-1 (tar) [47.3 kB] 363s Get:3 http://ftpmaster.internal/ubuntu noble/universe r-cran-tensora 0.36.2.1-1 (diff) [2432 B] 363s gpgv: Signature made Tue Jan 9 08:41:30 2024 UTC 363s gpgv: using RSA key F1F007320A035541F0A663CA578A0494D1C646D1 363s gpgv: issuer "tille@debian.org" 363s gpgv: Can't check signature: No public key 363s dpkg-source: warning: cannot verify inline signature for ./r-cran-tensora_0.36.2.1-1.dsc: no acceptable signature found 363s autopkgtest [20:29:12]: testing package r-cran-tensora version 0.36.2.1-1 363s autopkgtest [20:29:12]: build not needed 364s autopkgtest [20:29:13]: test run-unit-test: preparing testbed 365s Reading package lists... 366s Building dependency tree... 366s Reading state information... 366s Starting pkgProblemResolver with broken count: 0 366s Starting 2 pkgProblemResolver with broken count: 0 366s Done 367s The following additional packages will be installed: 367s fontconfig fontconfig-config fonts-dejavu-core fonts-dejavu-mono libblas3 367s libcairo2 libdatrie1 libdeflate0 libfontconfig1 libgfortran5 libgomp1 367s libgraphite2-3 libharfbuzz0b libice6 libjbig0 libjpeg-turbo8 libjpeg8 367s liblapack3 liblerc4 libpango-1.0-0 libpangocairo-1.0-0 libpangoft2-1.0-0 367s libpaper-utils libpaper1 libpixman-1-0 libsharpyuv0 libsm6 libtcl8.6 367s libthai-data libthai0 libtiff6 libtk8.6 libwebp7 libxcb-render0 libxcb-shm0 367s libxft2 libxrender1 libxss1 libxt6 r-base-core r-cran-tensora unzip 367s x11-common xdg-utils zip 367s Suggested packages: 367s tcl8.6 tk8.6 elpa-ess r-doc-info | r-doc-pdf r-mathlib r-base-html 367s Recommended packages: 367s r-recommended r-base-dev r-doc-html libfile-mimeinfo-perl libnet-dbus-perl 367s libx11-protocol-perl x11-utils x11-xserver-utils 367s The following NEW packages will be installed: 367s autopkgtest-satdep fontconfig fontconfig-config fonts-dejavu-core 367s fonts-dejavu-mono libblas3 libcairo2 libdatrie1 libdeflate0 libfontconfig1 367s libgfortran5 libgomp1 libgraphite2-3 libharfbuzz0b libice6 libjbig0 367s libjpeg-turbo8 libjpeg8 liblapack3 liblerc4 libpango-1.0-0 367s libpangocairo-1.0-0 libpangoft2-1.0-0 libpaper-utils libpaper1 libpixman-1-0 367s libsharpyuv0 libsm6 libtcl8.6 libthai-data libthai0 libtiff6 libtk8.6 367s libwebp7 libxcb-render0 libxcb-shm0 libxft2 libxrender1 libxss1 libxt6 367s r-base-core r-cran-tensora unzip x11-common xdg-utils zip 367s 0 upgraded, 46 newly installed, 0 to remove and 0 not upgraded. 367s Need to get 36.8 MB/36.8 MB of archives. 367s After this operation, 75.6 MB of additional disk space will be used. 367s Get:1 /tmp/autopkgtest.VN3CAc/1-autopkgtest-satdep.deb autopkgtest-satdep arm64 0 [708 B] 367s Get:2 http://ftpmaster.internal/ubuntu noble/main arm64 fonts-dejavu-mono all 2.37-8 [502 kB] 367s Get:3 http://ftpmaster.internal/ubuntu noble/main arm64 fonts-dejavu-core all 2.37-8 [835 kB] 367s Get:4 http://ftpmaster.internal/ubuntu noble/main arm64 fontconfig-config arm64 2.15.0-1ubuntu1 [37.0 kB] 367s Get:5 http://ftpmaster.internal/ubuntu noble/main arm64 libfontconfig1 arm64 2.15.0-1ubuntu1 [142 kB] 367s Get:6 http://ftpmaster.internal/ubuntu noble/main arm64 fontconfig arm64 2.15.0-1ubuntu1 [190 kB] 367s Get:7 http://ftpmaster.internal/ubuntu noble/main arm64 libblas3 arm64 3.12.0-3 [143 kB] 367s Get:8 http://ftpmaster.internal/ubuntu noble/main arm64 libpixman-1-0 arm64 0.42.2-1 [193 kB] 367s Get:9 http://ftpmaster.internal/ubuntu noble/main arm64 libxcb-render0 arm64 1.15-1 [16.1 kB] 367s Get:10 http://ftpmaster.internal/ubuntu noble/main arm64 libxcb-shm0 arm64 1.15-1 [5780 B] 367s Get:11 http://ftpmaster.internal/ubuntu noble/main arm64 libxrender1 arm64 1:0.9.10-1.1 [19.1 kB] 367s Get:12 http://ftpmaster.internal/ubuntu noble/main arm64 libcairo2 arm64 1.18.0-1 [550 kB] 367s Get:13 http://ftpmaster.internal/ubuntu noble/main arm64 libdatrie1 arm64 0.2.13-3 [21.7 kB] 367s Get:14 http://ftpmaster.internal/ubuntu noble/main arm64 libdeflate0 arm64 1.19-1 [43.4 kB] 367s Get:15 http://ftpmaster.internal/ubuntu noble/main arm64 libgfortran5 arm64 14-20240303-1ubuntu1 [444 kB] 367s Get:16 http://ftpmaster.internal/ubuntu noble/main arm64 libgomp1 arm64 14-20240303-1ubuntu1 [144 kB] 367s Get:17 http://ftpmaster.internal/ubuntu noble/main arm64 libgraphite2-3 arm64 1.3.14-2 [81.5 kB] 367s Get:18 http://ftpmaster.internal/ubuntu noble/main arm64 libharfbuzz0b arm64 8.3.0-2 [463 kB] 367s Get:19 http://ftpmaster.internal/ubuntu noble/main arm64 x11-common all 1:7.7+23ubuntu2 [23.4 kB] 367s Get:20 http://ftpmaster.internal/ubuntu noble/main arm64 libice6 arm64 2:1.0.10-1build2 [41.7 kB] 367s Get:21 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg-turbo8 arm64 2.1.5-2ubuntu1 [160 kB] 368s Get:22 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg8 arm64 8c-2ubuntu11 [2148 B] 368s Get:23 http://ftpmaster.internal/ubuntu noble/main arm64 liblapack3 arm64 3.12.0-3 [2241 kB] 368s Get:24 http://ftpmaster.internal/ubuntu noble/main arm64 liblerc4 arm64 4.0.0+ds-4ubuntu1 [153 kB] 368s Get:25 http://ftpmaster.internal/ubuntu noble/main arm64 libthai-data all 0.1.29-2 [158 kB] 368s Get:26 http://ftpmaster.internal/ubuntu noble/main arm64 libthai0 arm64 0.1.29-2 [18.1 kB] 368s Get:27 http://ftpmaster.internal/ubuntu noble/main arm64 libpango-1.0-0 arm64 1.51.0+ds-4 [226 kB] 368s Get:28 http://ftpmaster.internal/ubuntu noble/main arm64 libpangoft2-1.0-0 arm64 1.51.0+ds-4 [41.2 kB] 368s Get:29 http://ftpmaster.internal/ubuntu noble/main arm64 libpangocairo-1.0-0 arm64 1.51.0+ds-4 [27.6 kB] 368s Get:30 http://ftpmaster.internal/ubuntu noble/main arm64 libpaper1 arm64 1.1.29 [13.1 kB] 368s Get:31 http://ftpmaster.internal/ubuntu noble/main arm64 libpaper-utils arm64 1.1.29 [8480 B] 368s Get:32 http://ftpmaster.internal/ubuntu noble/main arm64 libsharpyuv0 arm64 1.3.2-0.4 [14.4 kB] 368s Get:33 http://ftpmaster.internal/ubuntu noble/main arm64 libsm6 arm64 2:1.2.3-1build2 [16.1 kB] 368s Get:34 http://ftpmaster.internal/ubuntu noble/main arm64 libtcl8.6 arm64 8.6.13+dfsg-2 [980 kB] 368s Get:35 http://ftpmaster.internal/ubuntu noble/main arm64 libjbig0 arm64 2.1-6.1ubuntu1 [28.9 kB] 368s Get:36 http://ftpmaster.internal/ubuntu noble/main arm64 libwebp7 arm64 1.3.2-0.4 [191 kB] 368s Get:37 http://ftpmaster.internal/ubuntu noble/main arm64 libtiff6 arm64 4.5.1+git230720-3ubuntu1 [226 kB] 368s Get:38 http://ftpmaster.internal/ubuntu noble/main arm64 libxft2 arm64 2.3.6-1 [43.3 kB] 368s Get:39 http://ftpmaster.internal/ubuntu noble/main arm64 libxss1 arm64 1:1.2.3-1build2 [8252 B] 368s Get:40 http://ftpmaster.internal/ubuntu noble/main arm64 libtk8.6 arm64 8.6.13-2 [760 kB] 368s Get:41 http://ftpmaster.internal/ubuntu noble/main arm64 libxt6 arm64 1:1.2.1-1.1 [167 kB] 368s Get:42 http://ftpmaster.internal/ubuntu noble/main arm64 zip arm64 3.0-13 [172 kB] 368s Get:43 http://ftpmaster.internal/ubuntu noble/main arm64 unzip arm64 6.0-28ubuntu3 [171 kB] 368s Get:44 http://ftpmaster.internal/ubuntu noble/main arm64 xdg-utils all 1.1.3-4.1ubuntu3 [62.0 kB] 368s Get:45 http://ftpmaster.internal/ubuntu noble/universe arm64 r-base-core arm64 4.3.2-1build1 [26.8 MB] 368s Get:46 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-tensora arm64 0.36.2.1-1 [222 kB] 369s Preconfiguring packages ... 369s Fetched 36.8 MB in 2s (21.0 MB/s) 369s Selecting previously unselected package fonts-dejavu-mono. 369s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 74330 files and directories currently installed.) 369s Preparing to unpack .../00-fonts-dejavu-mono_2.37-8_all.deb ... 369s Unpacking fonts-dejavu-mono (2.37-8) ... 369s Selecting previously unselected package fonts-dejavu-core. 369s Preparing to unpack .../01-fonts-dejavu-core_2.37-8_all.deb ... 369s Unpacking fonts-dejavu-core (2.37-8) ... 369s Selecting previously unselected package fontconfig-config. 369s Preparing to unpack .../02-fontconfig-config_2.15.0-1ubuntu1_arm64.deb ... 370s Unpacking fontconfig-config (2.15.0-1ubuntu1) ... 370s Selecting previously unselected package libfontconfig1:arm64. 370s Preparing to unpack .../03-libfontconfig1_2.15.0-1ubuntu1_arm64.deb ... 370s Unpacking libfontconfig1:arm64 (2.15.0-1ubuntu1) ... 370s Selecting previously unselected package fontconfig. 370s Preparing to unpack .../04-fontconfig_2.15.0-1ubuntu1_arm64.deb ... 370s Unpacking fontconfig (2.15.0-1ubuntu1) ... 370s Selecting previously unselected package libblas3:arm64. 370s Preparing to unpack .../05-libblas3_3.12.0-3_arm64.deb ... 370s Unpacking libblas3:arm64 (3.12.0-3) ... 370s Selecting previously unselected package libpixman-1-0:arm64. 370s Preparing to unpack .../06-libpixman-1-0_0.42.2-1_arm64.deb ... 370s Unpacking libpixman-1-0:arm64 (0.42.2-1) ... 370s Selecting previously unselected package libxcb-render0:arm64. 370s Preparing to unpack .../07-libxcb-render0_1.15-1_arm64.deb ... 370s Unpacking libxcb-render0:arm64 (1.15-1) ... 370s Selecting previously unselected package libxcb-shm0:arm64. 370s Preparing to unpack .../08-libxcb-shm0_1.15-1_arm64.deb ... 370s Unpacking libxcb-shm0:arm64 (1.15-1) ... 370s Selecting previously unselected package libxrender1:arm64. 370s Preparing to unpack .../09-libxrender1_1%3a0.9.10-1.1_arm64.deb ... 370s Unpacking libxrender1:arm64 (1:0.9.10-1.1) ... 370s Selecting previously unselected package libcairo2:arm64. 370s Preparing to unpack .../10-libcairo2_1.18.0-1_arm64.deb ... 370s Unpacking libcairo2:arm64 (1.18.0-1) ... 370s Selecting previously unselected package libdatrie1:arm64. 370s Preparing to unpack .../11-libdatrie1_0.2.13-3_arm64.deb ... 370s Unpacking libdatrie1:arm64 (0.2.13-3) ... 370s Selecting previously unselected package libdeflate0:arm64. 370s Preparing to unpack .../12-libdeflate0_1.19-1_arm64.deb ... 370s Unpacking libdeflate0:arm64 (1.19-1) ... 370s Selecting previously unselected package libgfortran5:arm64. 370s Preparing to unpack .../13-libgfortran5_14-20240303-1ubuntu1_arm64.deb ... 370s Unpacking libgfortran5:arm64 (14-20240303-1ubuntu1) ... 370s Selecting previously unselected package libgomp1:arm64. 370s Preparing to unpack .../14-libgomp1_14-20240303-1ubuntu1_arm64.deb ... 370s Unpacking libgomp1:arm64 (14-20240303-1ubuntu1) ... 370s Selecting previously unselected package libgraphite2-3:arm64. 370s Preparing to unpack .../15-libgraphite2-3_1.3.14-2_arm64.deb ... 370s Unpacking libgraphite2-3:arm64 (1.3.14-2) ... 370s Selecting previously unselected package libharfbuzz0b:arm64. 370s Preparing to unpack .../16-libharfbuzz0b_8.3.0-2_arm64.deb ... 370s Unpacking libharfbuzz0b:arm64 (8.3.0-2) ... 370s Selecting previously unselected package x11-common. 370s Preparing to unpack .../17-x11-common_1%3a7.7+23ubuntu2_all.deb ... 370s Unpacking x11-common (1:7.7+23ubuntu2) ... 370s Selecting previously unselected package libice6:arm64. 370s Preparing to unpack .../18-libice6_2%3a1.0.10-1build2_arm64.deb ... 370s Unpacking libice6:arm64 (2:1.0.10-1build2) ... 370s Selecting previously unselected package libjpeg-turbo8:arm64. 370s Preparing to unpack .../19-libjpeg-turbo8_2.1.5-2ubuntu1_arm64.deb ... 370s Unpacking libjpeg-turbo8:arm64 (2.1.5-2ubuntu1) ... 370s Selecting previously unselected package libjpeg8:arm64. 370s Preparing to unpack .../20-libjpeg8_8c-2ubuntu11_arm64.deb ... 370s Unpacking libjpeg8:arm64 (8c-2ubuntu11) ... 370s Selecting previously unselected package liblapack3:arm64. 370s Preparing to unpack .../21-liblapack3_3.12.0-3_arm64.deb ... 370s Unpacking liblapack3:arm64 (3.12.0-3) ... 370s Selecting previously unselected package liblerc4:arm64. 370s Preparing to unpack .../22-liblerc4_4.0.0+ds-4ubuntu1_arm64.deb ... 370s Unpacking liblerc4:arm64 (4.0.0+ds-4ubuntu1) ... 370s Selecting previously unselected package libthai-data. 370s Preparing to unpack .../23-libthai-data_0.1.29-2_all.deb ... 370s Unpacking libthai-data (0.1.29-2) ... 370s Selecting previously unselected package libthai0:arm64. 370s Preparing to unpack .../24-libthai0_0.1.29-2_arm64.deb ... 370s Unpacking libthai0:arm64 (0.1.29-2) ... 370s Selecting previously unselected package libpango-1.0-0:arm64. 370s Preparing to unpack .../25-libpango-1.0-0_1.51.0+ds-4_arm64.deb ... 370s Unpacking libpango-1.0-0:arm64 (1.51.0+ds-4) ... 370s Selecting previously unselected package libpangoft2-1.0-0:arm64. 370s Preparing to unpack .../26-libpangoft2-1.0-0_1.51.0+ds-4_arm64.deb ... 370s Unpacking libpangoft2-1.0-0:arm64 (1.51.0+ds-4) ... 370s Selecting previously unselected package libpangocairo-1.0-0:arm64. 370s Preparing to unpack .../27-libpangocairo-1.0-0_1.51.0+ds-4_arm64.deb ... 370s Unpacking libpangocairo-1.0-0:arm64 (1.51.0+ds-4) ... 370s Selecting previously unselected package libpaper1:arm64. 370s Preparing to unpack .../28-libpaper1_1.1.29_arm64.deb ... 370s Unpacking libpaper1:arm64 (1.1.29) ... 370s Selecting previously unselected package libpaper-utils. 370s Preparing to unpack .../29-libpaper-utils_1.1.29_arm64.deb ... 370s Unpacking libpaper-utils (1.1.29) ... 370s Selecting previously unselected package libsharpyuv0:arm64. 370s Preparing to unpack .../30-libsharpyuv0_1.3.2-0.4_arm64.deb ... 370s Unpacking libsharpyuv0:arm64 (1.3.2-0.4) ... 370s Selecting previously unselected package libsm6:arm64. 370s Preparing to unpack .../31-libsm6_2%3a1.2.3-1build2_arm64.deb ... 370s Unpacking libsm6:arm64 (2:1.2.3-1build2) ... 370s Selecting previously unselected package libtcl8.6:arm64. 370s Preparing to unpack .../32-libtcl8.6_8.6.13+dfsg-2_arm64.deb ... 370s Unpacking libtcl8.6:arm64 (8.6.13+dfsg-2) ... 371s Selecting previously unselected package libjbig0:arm64. 371s Preparing to unpack .../33-libjbig0_2.1-6.1ubuntu1_arm64.deb ... 371s Unpacking libjbig0:arm64 (2.1-6.1ubuntu1) ... 371s Selecting previously unselected package libwebp7:arm64. 371s Preparing to unpack .../34-libwebp7_1.3.2-0.4_arm64.deb ... 371s Unpacking libwebp7:arm64 (1.3.2-0.4) ... 371s Selecting previously unselected package libtiff6:arm64. 371s Preparing to unpack .../35-libtiff6_4.5.1+git230720-3ubuntu1_arm64.deb ... 371s Unpacking libtiff6:arm64 (4.5.1+git230720-3ubuntu1) ... 371s Selecting previously unselected package libxft2:arm64. 371s Preparing to unpack .../36-libxft2_2.3.6-1_arm64.deb ... 371s Unpacking libxft2:arm64 (2.3.6-1) ... 371s Selecting previously unselected package libxss1:arm64. 371s Preparing to unpack .../37-libxss1_1%3a1.2.3-1build2_arm64.deb ... 371s Unpacking libxss1:arm64 (1:1.2.3-1build2) ... 371s Selecting previously unselected package libtk8.6:arm64. 371s Preparing to unpack .../38-libtk8.6_8.6.13-2_arm64.deb ... 371s Unpacking libtk8.6:arm64 (8.6.13-2) ... 371s Selecting previously unselected package libxt6:arm64. 371s Preparing to unpack .../39-libxt6_1%3a1.2.1-1.1_arm64.deb ... 371s Unpacking libxt6:arm64 (1:1.2.1-1.1) ... 371s Selecting previously unselected package zip. 371s Preparing to unpack .../40-zip_3.0-13_arm64.deb ... 371s Unpacking zip (3.0-13) ... 371s Selecting previously unselected package unzip. 371s Preparing to unpack .../41-unzip_6.0-28ubuntu3_arm64.deb ... 371s Unpacking unzip (6.0-28ubuntu3) ... 371s Selecting previously unselected package xdg-utils. 371s Preparing to unpack .../42-xdg-utils_1.1.3-4.1ubuntu3_all.deb ... 371s Unpacking xdg-utils (1.1.3-4.1ubuntu3) ... 371s Selecting previously unselected package r-base-core. 371s Preparing to unpack .../43-r-base-core_4.3.2-1build1_arm64.deb ... 371s Unpacking r-base-core (4.3.2-1build1) ... 371s Selecting previously unselected package r-cran-tensora. 371s Preparing to unpack .../44-r-cran-tensora_0.36.2.1-1_arm64.deb ... 371s Unpacking r-cran-tensora (0.36.2.1-1) ... 371s Selecting previously unselected package autopkgtest-satdep. 371s Preparing to unpack .../45-1-autopkgtest-satdep.deb ... 371s Unpacking autopkgtest-satdep (0) ... 371s Setting up libgraphite2-3:arm64 (1.3.14-2) ... 371s Setting up libpixman-1-0:arm64 (0.42.2-1) ... 371s Setting up libsharpyuv0:arm64 (1.3.2-0.4) ... 371s Setting up libpaper1:arm64 (1.1.29) ... 371s 371s Creating config file /etc/papersize with new version 372s Setting up liblerc4:arm64 (4.0.0+ds-4ubuntu1) ... 372s Setting up libxrender1:arm64 (1:0.9.10-1.1) ... 372s Setting up libdatrie1:arm64 (0.2.13-3) ... 372s Setting up libxcb-render0:arm64 (1.15-1) ... 372s Setting up unzip (6.0-28ubuntu3) ... 372s Setting up x11-common (1:7.7+23ubuntu2) ... 372s Setting up libdeflate0:arm64 (1.19-1) ... 372s Setting up libxcb-shm0:arm64 (1.15-1) ... 372s Setting up libpaper-utils (1.1.29) ... 372s Setting up libgomp1:arm64 (14-20240303-1ubuntu1) ... 372s Setting up libjbig0:arm64 (2.1-6.1ubuntu1) ... 372s Setting up zip (3.0-13) ... 372s Setting up libblas3:arm64 (3.12.0-3) ... 372s update-alternatives: using /usr/lib/aarch64-linux-gnu/blas/libblas.so.3 to provide /usr/lib/aarch64-linux-gnu/libblas.so.3 (libblas.so.3-aarch64-linux-gnu) in auto mode 372s Setting up fonts-dejavu-mono (2.37-8) ... 372s Setting up libtcl8.6:arm64 (8.6.13+dfsg-2) ... 372s Setting up fonts-dejavu-core (2.37-8) ... 372s Setting up libjpeg-turbo8:arm64 (2.1.5-2ubuntu1) ... 372s Setting up libgfortran5:arm64 (14-20240303-1ubuntu1) ... 372s Setting up libwebp7:arm64 (1.3.2-0.4) ... 372s Setting up libharfbuzz0b:arm64 (8.3.0-2) ... 372s Setting up libthai-data (0.1.29-2) ... 372s Setting up libxss1:arm64 (1:1.2.3-1build2) ... 372s Setting up xdg-utils (1.1.3-4.1ubuntu3) ... 372s update-alternatives: using /usr/bin/xdg-open to provide /usr/bin/open (open) in auto mode 372s Setting up libjpeg8:arm64 (8c-2ubuntu11) ... 372s Setting up libice6:arm64 (2:1.0.10-1build2) ... 372s Setting up liblapack3:arm64 (3.12.0-3) ... 372s update-alternatives: using /usr/lib/aarch64-linux-gnu/lapack/liblapack.so.3 to provide /usr/lib/aarch64-linux-gnu/liblapack.so.3 (liblapack.so.3-aarch64-linux-gnu) in auto mode 372s Setting up fontconfig-config (2.15.0-1ubuntu1) ... 372s Setting up libthai0:arm64 (0.1.29-2) ... 372s Setting up libtiff6:arm64 (4.5.1+git230720-3ubuntu1) ... 372s Setting up libfontconfig1:arm64 (2.15.0-1ubuntu1) ... 372s Setting up libsm6:arm64 (2:1.2.3-1build2) ... 372s Setting up fontconfig (2.15.0-1ubuntu1) ... 374s Regenerating fonts cache... done. 374s Setting up libxft2:arm64 (2.3.6-1) ... 374s Setting up libtk8.6:arm64 (8.6.13-2) ... 374s Setting up libpango-1.0-0:arm64 (1.51.0+ds-4) ... 374s Setting up libcairo2:arm64 (1.18.0-1) ... 374s Setting up libxt6:arm64 (1:1.2.1-1.1) ... 374s Setting up libpangoft2-1.0-0:arm64 (1.51.0+ds-4) ... 374s Setting up libpangocairo-1.0-0:arm64 (1.51.0+ds-4) ... 374s Setting up r-base-core (4.3.2-1build1) ... 374s 374s Creating config file /etc/R/Renviron with new version 374s Setting up r-cran-tensora (0.36.2.1-1) ... 374s Setting up autopkgtest-satdep (0) ... 374s Processing triggers for man-db (2.12.0-3) ... 375s Processing triggers for install-info (7.1-3) ... 375s Processing triggers for libc-bin (2.39-0ubuntu2) ... 380s (Reading database ... 76354 files and directories currently installed.) 380s Removing autopkgtest-satdep (0) ... 380s autopkgtest [20:29:29]: test run-unit-test: [----------------------- 381s BEGIN TEST checker.R 381s 381s R version 4.3.2 (2023-10-31) -- "Eye Holes" 381s Copyright (C) 2023 The R Foundation for Statistical Computing 381s Platform: aarch64-unknown-linux-gnu (64-bit) 381s 381s R is free software and comes with ABSOLUTELY NO WARRANTY. 381s You are welcome to redistribute it under certain conditions. 381s Type 'license()' or 'licence()' for distribution details. 381s 381s R is a collaborative project with many contributors. 381s Type 'contributors()' for more information and 381s 'citation()' on how to cite R or R packages in publications. 381s 381s Type 'demo()' for some demos, 'help()' for on-line help, or 381s 'help.start()' for an HTML browser interface to help. 381s Type 'q()' to quit R. 381s 381s > require(tensorA) 381s Loading required package: tensorA 381s > if(FALSE) { 381s + # Commands for testing 381s + debugger() 381s + rm(list=objects()) 381s + options(error=dump.frames) 381s + detach("package:tensorA") 381s + dyn.unload("/home/boogaart/R/tensorA/tests/../../tensorA.Rcheck/tensorA/libs/tensorA.so") 381s + library(tensorA,lib.loc="../../tensorA.Rcheck") 381s + } 381s > 381s > set.seed(23) 381s > 381s > 381s > summary.tensor <- function(x,...) { 381s + n <- level.tensor(x) 381s + d <- dim(x) 381s + dm <- pmin(d,1) 381s + dm2<- pmin(d,2) 381s + print(dim(x)) 381s + if( !all(sapply(dimnames(x),is.null))) print(dimnames(x)) 381s + if( prod(dim(x)) < 10 ) 381s + print(x) 381s + else if( n == 1 ) 381s + print(x[1:min(length(x),10)]) 381s + else if( n == 2 ) 381s + print(x[1:dm[1],1:dm[2]]) 381s + else if( n == 3 ) 381s + print(x[1:dm[1],1:dm[2],1:dm2[3],drop=FALSE]) 381s + else if( n == 4 ) 381s + print(x[1:(dm2[1]),1:dm[1],1,1,drop=FALSE]) 381s + else if( n == 5 ) 381s + print(x[1:(dm2[1]),1:dm[1],1,1,1,drop=FALSE]) 381s + else if( n == 6 ) 381s + print(x[1:(dm2[1]),1:dm[1],1,1,1,1,drop=FALSE]) 381s + else 381s + print(x[1:min(length(x),10)]) 381s + } 381s > 381s > checker <- function(x,y) UseMethod("checker") 381s > 381s > checker.default <- function(x,y) { 381s + cat("Wrong type\n",deparse(match.call()),"\n---------------y=\n") 381s + print(y) 381s + cat("\n------------x=\n") 381s + print(x) 381s + stop("Unkown type") 381s + } 381s > 381s > 381s > checker.tensor <- function(x,y) { 381s + if( !cmp(x,y) ) { 381s + cat("Misfit\n",deparse(match.call()),"\n------------------y=\n") 381s + print(y) 381s + cat("\n-----------------------x=\n") 381s + print(x) 381s + # print(summary(x)) 381s + # print(summary(y)) 381s + stop("Missfit"); 381s + } else { 381s + x 381s + } 381s + } 381s > 381s > print.tensor <- function(x){ 381s + print.default(unclass(x)) 381s + print(dim(x)) 381s + } 381s > 381s > cmp.tensor <- function(x,y) { 381s + if(!is.null(names(y))) { 381s + mat <- match(names(y),names(x)) 381s + if( any(is.na(mat)) ) { 381s + print(names(y)) 381s + print(names(x)) 381s + return(FALSE) 381s + } 381s + else 381s + x <- reorder.tensor(x,mat) 381s + } 381s + return( length(x)==length(y) && !any(is.na(x)) && 381s + sum(abs(c(x)-c(y))^2)<1E-10 && 381s + length(dim(x))==length(dim(y)) && 381s + !any(is.na(dim(x))) && !any(is.na(dim(y))) && 381s + all(dim(x)==dim(y))) 381s + } 381s > 381s > cmp <- function(x,y) UseMethod("cmp") 381s > 381s > cmp.character <- function(x,y) { 381s + return( length(x)==length(y) && all(x==y) ) 381s + } 381s > 381s > 381s > cmp.numeric <- function(x,y){ 381s + if( length(x) != length(y) ) 381s + return(FALSE) 381s + if(!is.null(names(y))) { 381s + if( is.null(names(y)) || !all( names(x) %in% names(y) ) ) 381s + return(FALSE) 381s + if( ! identical(any( x[match(names(y),names(x))]!=y ),FALSE) ) 381s + return(FALSE) 381s + return(TRUE) 381s + } else { 381s + return(all(x==y)) 381s + } 381s + } 381s > 381s > cmp.default <- function(x,y) identical(x,y) 381s > 381s > checker.numeric <- function(x,y) { 381s + if( !cmp(x,y) ) { 381s + cat("Misfit\n",deparse(match.call()),"\n-----------------y=\n") 381s + print(y) 381s + cat("\n-------------------------x=\n") 381s + print(x) 381s + stop("Missfit"); 381s + } else print(x) 381s + } 381s > 381s > 381s > checker.character <- function(x,y) { 381s + if( !cmp(x,y) ) { 381s + cat("Misfit\n",deparse(match.call()),"\n-----------------y=\n") 381s + print(y) 381s + cat("\n----------------------------y=\n") 381s + print(x) 381s + stop("Missfit"); 381s + } else print(x) 381s + } 381s > 381s > checker.list <- function(x,y) { 381s + if( length(x) != length(y) || identical(!all(mapply(cmp,x,y)),TRUE) ) { 381s + cat("Misfit\n",deparse(match.call()),"\n---------------y=\n") 381s + print(y) 381s + cat("\n----------------------x=\n") 381s + print(x) 381s + stop("Missfit"); 381s + } else print(x) 381s + } 381s > 381s > nn <- function(...,nn=list(...)) { 381s + lapply(1:length(nn),function(i) paste(names(nn)[i],1:nn[[i]],sep="")) 381s + } 381s > 381s > 381s > 381s > # to.tensor 381s > I4 <- diag(4) 381s > names(dim(I4))<-c("Q","z") 381s > checker(to.tensor(I4,c(a=2,b=2)), 381s + to.tensor(c(diag(4)),c(a=2,b=2,z=4))) 381s 381s Attaching package: ‘tensorA’ 381s 381s The following object is masked from ‘package:base’: 381s 381s norm 381s 381s , , 1 381s 381s b 381s a [,1] [,2] 381s [1,] 1 0 381s [2,] 0 0 381s 381s , , 2 381s 381s b 381s a [,1] [,2] 381s [1,] 0 0 381s [2,] 1 0 381s 381s , , 3 381s 381s b 381s a [,1] [,2] 381s [1,] 0 1 381s [2,] 0 0 381s 381s , , 4 381s 381s b 381s a [,1] [,2] 381s [1,] 0 0 381s [2,] 0 1 381s 381s a b z 381s 2 2 4 381s > 381s > dimnames(I4) <- nn(Q=4,z=4) 381s > checker(to.tensor(I4,c(a=2,b=2),nn(a=2,b=2)), 381s + to.tensor(c(diag(4)),c(a=2,b=2,z=4),nn(a=2,b=2,z=4))) 381s , , z = z1 381s 381s b 381s a b1 b2 381s a1 1 0 381s a2 0 0 381s 381s , , z = z2 381s 381s b 381s a b1 b2 381s a1 0 0 381s a2 1 0 381s 381s , , z = z3 381s 381s b 381s a b1 b2 381s a1 0 1 381s a2 0 0 381s 381s , , z = z4 381s 381s b 381s a b1 b2 381s a1 0 0 381s a2 0 1 381s 381s a b z 381s 2 2 4 381s > 381s > 381s > # 381s > 381s > KT5 <- to.tensor(rnorm(30),c(a=3,b=2,c=5),nn(a=3,b=2,c=5)) 381s > dim(KT5[[c=2]]) 381s a b 381s 3 2 381s > dim(KT5[,,1:2]) 381s a b c 381s 3 2 2 381s > summary(KT5) 381s a b c 381s 3 2 5 381s $a 381s [1] "a1" "a2" "a3" 381s 381s $b 381s [1] "b1" "b2" 381s 381s $c 381s [1] "c1" "c2" "c3" "c4" "c5" 381s 381s , , 1 381s 381s b 381s a [,1] 381s [1,] 0.1932123 381s 381s , , 2 381s 381s b 381s a [,1] 381s [1,] -0.2780863 381s 381s a b c 381s 1 1 2 381s > 381s > KT5 <- to.tensor(rnorm(30),c(a=3,b=10,c=1),nn(a=3,b=10,c=1)) 381s > drop(KT5) 381s b 381s a b1 b2 b3 b4 b5 b6 381s a1 -0.55320524 -1.2499273 1.307647 0.232875 0.9459580 -1.62920594 381s a2 0.09818141 -0.2021117 -1.342935 1.042257 -0.9856255 0.09231624 381s a3 -1.14666586 0.1775003 0.861083 1.329098 -1.2158668 -0.02211742 381s b 381s a b7 b8 b9 b10 381s a1 0.5134779 -0.2384356 1.2208190 0.2772344 381s a2 -0.2295536 -1.9978126 -0.8509239 0.9707189 381s a3 1.2615159 0.7010760 -0.5636078 0.9526308 381s a b 381s 3 10 381s > 381s > checker(as.tensor(KT5),KT5) 381s , , c = c1 381s 381s b 381s a b1 b2 b3 b4 b5 b6 381s a1 -0.55320524 -1.2499273 1.307647 0.232875 0.9459580 -1.62920594 381s a2 0.09818141 -0.2021117 -1.342935 1.042257 -0.9856255 0.09231624 381s a3 -1.14666586 0.1775003 0.861083 1.329098 -1.2158668 -0.02211742 381s b 381s a b7 b8 b9 b10 381s a1 0.5134779 -0.2384356 1.2208190 0.2772344 381s a2 -0.2295536 -1.9978126 -0.8509239 0.9707189 381s a3 1.2615159 0.7010760 -0.5636078 0.9526308 381s 381s a b c 381s 3 10 1 381s > checker(as.tensor.default(KT5),KT5) 381s , , c = c1 381s 381s b 381s a b1 b2 b3 b4 b5 b6 381s a1 -0.55320524 -1.2499273 1.307647 0.232875 0.9459580 -1.62920594 381s a2 0.09818141 -0.2021117 -1.342935 1.042257 -0.9856255 0.09231624 381s a3 -1.14666586 0.1775003 0.861083 1.329098 -1.2158668 -0.02211742 381s b 381s a b7 b8 b9 b10 381s a1 0.5134779 -0.2384356 1.2208190 0.2772344 381s a2 -0.2295536 -1.9978126 -0.8509239 0.9707189 381s a3 1.2615159 0.7010760 -0.5636078 0.9526308 381s 381s a b c 381s 3 10 1 381s > checker(to.tensor(KT5),KT5) 381s , , c = c1 381s 381s b 381s a b1 b2 b3 b4 b5 b6 381s a1 -0.55320524 -1.2499273 1.307647 0.232875 0.9459580 -1.62920594 381s a2 0.09818141 -0.2021117 -1.342935 1.042257 -0.9856255 0.09231624 381s a3 -1.14666586 0.1775003 0.861083 1.329098 -1.2158668 -0.02211742 381s b 381s a b7 b8 b9 b10 381s a1 0.5134779 -0.2384356 1.2208190 0.2772344 381s a2 -0.2295536 -1.9978126 -0.8509239 0.9707189 381s a3 1.2615159 0.7010760 -0.5636078 0.9526308 381s 381s a b c 381s 3 10 1 381s > 381s > # 381s > I <- to.tensor(diag(3),c(a=3,b=3),what=1:2) 381s > checker(to.tensor(I),I) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 1 0 381s [3,] 0 0 1 381s a b 381s 3 3 381s > checker(as.tensor(I),I) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 1 0 381s [3,] 0 0 1 381s a b 381s 3 3 381s > checker(inv.tensor(I,"a","b"),I) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 1 0 381s [3,] 0 0 1 381s a b 381s 3 3 381s > 381s > R1 <- matrix(rnorm(9),nrow=3) 381s > R1i <- solve(R1) 381s > R2 <- to.tensor(R1,c(a=3,b=3),what=1:2) 381s > R2i <- to.tensor(R1i,c(b=3,a=3),what=1:2) 381s > 381s > checker(inv.tensor(R2,"a","b"),R2i) 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s a b 381s 3 3 381s > checker(inv.tensor(R2,"a","b",allowSingular=TRUE),R2i) 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s a b 381s 3 3 381s > 381s > checker(inv.tensor(rep(R2,4,1,"K"),"a","b",by="K"),rep(R2i,4,1,"K")) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s a b K 381s 3 3 4 381s > checker(inv.tensor(rep(R2,4,1,"K"),"a","b",by="K",allowSingular=TRUE),rep(R2i,4,3,"K")) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.1790702 -0.8283566 -1.1377162 381s [2,] -1.7599098 1.1013333 0.7651271 381s [3,] -2.9085503 0.8895587 1.2262476 381s 381s a b K 381s 3 3 4 381s > 381s > R3 <- to.tensor(rnorm(15),c(a=3,z=5)) 381s > 381s > checker(mul.tensor(R2i,"b",mul.tensor(R2,"a",R3)),R3) 381s z 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -1.2133785 -0.132575713 0.433409 -1.37265139 0.6287441 381s [2,] 0.7260075 1.031495770 1.287369 -0.47939998 1.9760633 381s [3,] -0.4299248 0.006971394 -2.418264 0.01101352 0.4615582 381s a z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a"),mul.tensor(R2,"a",R3[[z=1]])) 381s [1] 0.6378107 1.7559384 -0.1115847 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a"),mul.tensor(R2,"a",R3)) 381s z 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.6378107 0.04780378 0.7124511 0.5418899 -0.4232775 381s [2,] 1.7559384 1.87543054 5.0470798 -0.9446036 3.1326266 381s [3,] -0.1115847 -1.24142507 -3.9435252 1.9795415 -2.9000840 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a",allowSingular=TRUE),mul.tensor(R2,"a",R3[[z=1]])) 381s [1] 0.6378107 1.7559384 -0.1115847 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a",allowSingular=T),mul.tensor(R2,"a",R3)) 381s z 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.6378107 0.04780378 0.7124511 0.5418899 -0.4232775 381s [2,] 1.7559384 1.87543054 5.0470798 -0.9446036 3.1326266 381s [3,] -0.1115847 -1.24142507 -3.9435252 1.9795415 -2.9000840 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s [1,] 0.6378107 0.6378107 0.6378107 0.6378107 381s [2,] 1.7559384 1.7559384 1.7559384 1.7559384 381s [3,] -0.1115847 -0.1115847 -0.1115847 -0.1115847 381s b K 381s 3 4 381s > checker(solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s [1,] 0.6378107 0.6378107 0.6378107 0.6378107 381s [2,] 1.7559384 1.7559384 1.7559384 1.7559384 381s [3,] -0.1115847 -0.1115847 -0.1115847 -0.1115847 381s b K 381s 3 4 381s > checker(solve.tensor(R2i,rep(R3[[z=1]],4,1,"K"),"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s [1,] 0.6378107 0.6378107 0.6378107 0.6378107 381s [2,] 1.7559384 1.7559384 1.7559384 1.7559384 381s [3,] -0.1115847 -0.1115847 -0.1115847 -0.1115847 381s b K 381s 3 4 381s > 381s > checker(solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K",allowSingular=TRUE),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s [1,] 0.6378107 0.6378107 0.6378107 0.6378107 381s [2,] 1.7559384 1.7559384 1.7559384 1.7559384 381s [3,] -0.1115847 -0.1115847 -0.1115847 -0.1115847 381s b K 381s 3 4 381s > checker(solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K",allowSingular=TRUE),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s [1,] 0.6378107 0.6378107 0.6378107 0.6378107 381s [2,] 1.7559384 1.7559384 1.7559384 1.7559384 381s [3,] -0.1115847 -0.1115847 -0.1115847 -0.1115847 381s b K 381s 3 4 381s > checker(solve.tensor(R2i,rep(R3[[z=1]],4,1,"K"),"a",by="K",allowSingular=TRUE),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s [1,] 0.6378107 0.6378107 0.6378107 0.6378107 381s [2,] 1.7559384 1.7559384 1.7559384 1.7559384 381s [3,] -0.1115847 -0.1115847 -0.1115847 -0.1115847 381s b K 381s 3 4 381s > 381s > 381s > 381s > checker(solve.tensor(R2i,R3,"a"),mul.tensor(R2,"a",R3)) 381s z 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.6378107 0.04780378 0.7124511 0.5418899 -0.4232775 381s [2,] 1.7559384 1.87543054 5.0470798 -0.9446036 3.1326266 381s [3,] -0.1115847 -1.24142507 -3.9435252 1.9795415 -2.9000840 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a",allowSingular=TRUE),mul.tensor(R2,"a",R3[[z=1]])) 381s [1] 0.6378107 1.7559384 -0.1115847 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a",allowSingular=TRUE),mul.tensor(R2,"a",R3)) 381s z 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.6378107 0.04780378 0.7124511 0.5418899 -0.4232775 381s [2,] 1.7559384 1.87543054 5.0470798 -0.9446036 3.1326266 381s [3,] -0.1115847 -1.24142507 -3.9435252 1.9795415 -2.9000840 381s b z 381s 3 5 381s > 381s > 381s > 381s > summary(I) 381s a b 381s 3 3 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 1 0 381s [3,] 0 0 1 381s a b 381s 3 3 381s > 381s > 381s > A <- to.tensor(c(diag(3)),c(a=3,b=3)) 381s > 381s > A <- to.tensor(c(1,1,1,0,1,1,0,0,1),c(a=3,b=3)) 381s > checker(mul.tensor(A,"b",A,"a"),to.tensor(c(A%*%A),c(a=3,b=3))) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 2 1 0 381s [3,] 3 2 1 381s a b 381s 3 3 381s > 381s > A <- to.tensor(c(1,1,1,1,0,1,1,1,0,0,1,1),c(a=4,b=3)) 381s > checker(mul.tensor(A,"b",A[[a=~c]],"b"),to.tensor(c(A%*%t(A)),c(a=4,c=4))) 381s c 381s a [,1] [,2] [,3] [,4] 381s [1,] 1 1 1 1 381s [2,] 1 2 2 2 381s [3,] 1 2 3 3 381s [4,] 1 2 3 3 381s a c 381s 4 4 381s > 381s > A <- to.tensor(rnorm(15),c(a=5,b=3)) 381s > checker(mul.tensor(A,"b",A[[a=~c]],"b"),to.tensor(c(A%*%t(A)),dim=c(a=5,c=5))) 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.48487946 -1.171859 -1.0356860 -0.8487449 -0.04082473 381s [2,] -1.17185878 6.672876 2.5656107 1.8814479 -1.36931153 381s [3,] -1.03568604 2.565611 3.4759517 2.4724216 0.65587837 381s [4,] -0.84874495 1.881448 2.4724216 1.8405402 0.44716941 381s [5,] -0.04082473 -1.369312 0.6558784 0.4471694 0.84261320 381s a c 381s 5 5 381s > 381s > A <- to.tensor(rnorm(5*3),c(a=5,b=3)) 381s > B <- to.tensor(rnorm(3*17),c(a=3,b=17)) 381s > checker(mul.tensor(A,"b",B,"a"),to.tensor(c(A%*%B),c(a=5,b=17))) 381s b 381s a [,1] [,2] [,3] [,4] [,5] [,6] 381s [1,] 0.2835968 -0.6288554 -1.1024355 0.34856397 0.7732376 0.06690123 381s [2,] 0.2026823 -0.3879932 -0.6227903 0.04338919 0.6774254 0.10935856 381s [3,] 0.8389679 -0.9282417 -0.9003466 -1.76728639 3.7279537 1.04534942 381s [4,] -0.2028007 1.6904408 2.8639388 -1.57998143 -1.9972133 0.43989420 381s [5,] 1.0439324 -0.5872734 -1.1593335 -0.58953212 0.8631121 0.93065646 381s b 381s a [,7] [,8] [,9] [,10] [,11] [,12] 381s [1,] 1.1430151 -0.2139775 -1.9005751 0.04059520 -0.7037960 -0.01597474 381s [2,] 0.5909542 0.1549058 -1.0788930 0.18128784 -0.3796445 0.06428319 381s [3,] 0.3194522 3.2890280 -1.5114695 2.06223555 -0.4077643 1.16668904 381s [4,] -2.1780750 -0.1786617 5.8810175 -0.17532620 1.2696101 2.11348215 381s [5,] 2.2904873 -1.2036569 -0.6921025 -0.03172413 -1.5116327 2.86401892 381s b 381s a [,13] [,14] [,15] [,16] [,17] 381s [1,] 2.650703 -1.2018365 1.0259026 -0.1639387 -0.6384908 381s [2,] 1.236705 -0.5348833 0.1616677 -0.1887906 -0.3516245 381s [3,] -1.102975 0.7174578 -4.6073088 -1.2212888 -0.2583766 381s [4,] -6.130545 1.7723834 -3.2732726 1.7373403 2.9397765 381s [5,] 3.797352 -3.1134537 0.1772836 1.6308589 1.1046150 381s a b 381s 5 17 381s > 381s > A <- to.tensor(c(1,1,1,0,1,1,0,0,1),c(a=3,b=3)) 381s > 381s > # 381s > A <- to.tensor(c(1,1,1,0,1,1,0,0,1),c(a=3,b=3)) 381s > 381s > solve.tensor(mul.tensor(I,"b",I,"a"),I,"a","a") 381s b 381s b [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 1 0 381s [3,] 0 0 1 381s b b 381s 3 3 381s > checker(solve.tensor(mul.tensor(I,"b",I,"a"),I,"a","b"),I) 381s a 381s b [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 1 0 381s [3,] 0 0 1 381s b a 381s 3 3 381s > mul.tensor(A,"b",I,"a") 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 1 1 0 381s [3,] 1 1 1 381s a b 381s 3 3 381s > 381s > 381s > checker(solve.tensor(mul.tensor(A,"b",I[[a=~c]],"b"),A,"a","a",allowSingular=TRUE),I[[a=~c]]) 381s b 381s c [,1] [,2] [,3] 381s [1,] 1.000000e+00 -3.884318e-16 -1.948890e-16 381s [2,] -3.844293e-16 1.000000e+00 -2.018035e-16 381s [3,] 2.167890e-16 9.805941e-17 1.000000e+00 381s c b 381s 3 3 381s > 381s > B <- A[[b=~z]] 381s > checker(solve.tensor(B,mul.tensor(A,"a",B,"a"),"z","z",allowSingular=TRUE),A) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 -1.491882e-15 -6.826825e-16 381s [2,] 1 1.000000e+00 3.169299e-17 381s [3,] 1 1.000000e+00 1.000000e+00 381s a b 381s 3 3 381s > checker(solve.tensor(B,mul.tensor(A,"a",B,"a"),"z","z",allowSingular=TRUE), 381s + solve.tensor(B,mul.tensor(A,"a",B,"a"),"z","z")) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 -1.491882e-15 -6.826825e-16 381s [2,] 1 1.000000e+00 3.169299e-17 381s [3,] 1 1.000000e+00 1.000000e+00 381s a b 381s 3 3 381s > 381s > 381s > 381s > solve.tensor(mul.tensor(A,"b",A,"a"),A,"a","a") 381s b 381s b [,1] [,2] [,3] 381s [1,] 1.000000e+00 0 0 381s [2,] -1.000000e+00 1 0 381s [3,] -1.480297e-16 -1 1 381s b b 381s 3 3 381s > checker(solve.tensor(A[[b=~c]],mul.tensor(A,"b",A,"a"),"a","a"),structure(A,dim=c(c=3,b=3))) 381s b 381s c [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 1 1 0 381s [3,] 1 1 1 381s c b 381s 3 3 381s > 381s > A <- to.tensor(c(1,1,1,1,0,1,1,1,0,0,1,1),c(a=4,b=3)) 381s > A 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 1 1 0 381s [3,] 1 1 1 381s [4,] 1 1 1 381s a b 381s 4 3 381s > solve.tensor(A[[b=~c]],mul.tensor(A,"a",A[[b=~c]],"a"),"c",allowSingular=TRUE) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 1.096759e-15 9.011658e-16 381s [2,] 1 1.000000e+00 1.228375e-17 381s [3,] 1 1.000000e+00 1.000000e+00 381s [4,] 1 1.000000e+00 1.000000e+00 381s a b 381s 4 3 381s > 381s > 381s > A <- to.tensor(rnorm(100),c(a=4,b=5,c=5)) 381s > An <- to.tensor(rnorm(100),c(a=4,b=5,c=5),nn(a=4,b=5,c=5)) 381s > B <- to.tensor(rnorm(100),c(d=4,e=5,f=5)) 381s > An <- to.tensor(rnorm(100),c(a=4,b=5,c=5),nn(a=4,b=5,c=5)) 381s > 381s > mt <- mul.tensor(A,2,B,2) 381s > 381s > 381s > checker(einstein.tensor(A,b="e",B),mt) 381s , , 1, 1 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.1664657 -0.1735138 2.3682379 -2.6535748 0.6952208 381s [2,] 0.1878986 1.4201223 -0.3116057 -1.2314339 1.0757362 381s [3,] -2.0654260 1.2974278 -3.6173748 -1.8801222 1.0207638 381s [4,] 0.4222110 -0.8526971 1.1852001 -0.4587169 -3.2184737 381s 381s , , 2, 1 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.5453903 -1.2677778 -3.283028 3.41019974 1.4738566 381s [2,] -0.4228667 -1.1547859 -0.163464 1.35697325 -1.5296280 381s [3,] 2.4056515 -2.3296849 4.644448 0.74494857 -0.7015917Warning message: 381s In to.tensor.default(c(EE), d, dn) : 381s Tensor with duplicated names generated: b b 381s Warning message: 381s In to.tensor.default(c(EE), d, dn) : 381s Tensor with duplicated names generated: b b 381s 381s [4,] -0.1622752 -0.2054522 -2.067285 0.07094618 4.2873073 381s 381s , , 3, 1 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.42766435 0.2668229 1.2271464 -0.4923342 -1.65600199 381s [2,] 0.57245033 -2.3972655 -0.3071815 1.5180733 1.87808719 381s [3,] 0.09451645 0.4058412 1.9612444 0.9121079 0.05551148 381s [4,] 1.47091586 1.2086438 -0.3562725 -0.9890887 1.47934187 381s 381s , , 4, 1 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.18255527 -3.0856221 -0.3259953 -0.80431148 2.8727222 381s [2,] 0.27027986 0.9022521 -2.9553908 -1.69940438 -0.1486697 381s [3,] -1.49688857 0.3645903 0.2920817 -2.18856301 1.2837658 381s [4,] 0.08028232 -2.0728055 -1.5449607 -0.06859168 -0.4309841 381s 381s , , 1, 2 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.80194414 -1.6019015 -4.390016 2.582822 -0.1903908 381s [2,] 0.07491603 0.5878298 -3.023182 -2.441964 -3.3109145 381s [3,] 0.54768043 0.1791293 3.119206 1.886438 -0.7203625 381s [4,] -2.97704754 -0.4543580 -2.469483 2.867940 1.4728528 381s 381s , , 2, 2 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.8643788 3.54827654 3.080732 -2.65027492 -3.6787826 381s [2,] 0.2884080 0.01978188 1.518399 -0.08927177 1.7754215 381s [3,] -1.9732367 1.57114103 -4.102635 0.35939157 -0.2937039 381s [4,] 0.2801674 2.00183340 2.764711 -0.27869770 -3.1742487 381s 381s , , 3, 2 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -1.0857870 1.4848715 -5.3810152 4.4854287 -1.453426 381s [2,] -0.7347261 0.1342419 0.1160822 -0.4267855 -3.854403 381s [3,] 1.8750741 -2.1446809 3.1590033 2.4610896 -2.207166 381s [4,] -2.9813032 1.2605735 -1.1710965 2.3904060 3.092980 381s 381s , , 4, 2 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.6814001 0.7437529 0.1168068 1.2188632 -4.0934878 381s [2,] 0.8986125 -4.7282941 -0.1623813 2.8877948 1.7805501 381s [3,] 2.1545808 0.5596389 5.6793266 4.1263506 -0.8701873 381s [4,] 1.3336990 2.7558654 -1.3425689 -0.3964775 4.1603521 381s 381s , , 1, 3 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -1.1298375 3.7121590 0.3611709 -0.36881615 -0.2529230 381s [2,] -1.0023713 1.9343343 2.6942489 0.07536266 -0.3350522 381s [3,] -1.7758344 -2.0293572 -4.5982260 -2.48505484 -0.8026001 381s [4,] -0.2670123 0.9164454 2.7893490 -0.74991283 -1.8554237 381s 381s , , 2, 3 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.002837336 -2.55260672 -2.573010 1.4495271 -0.24307180 381s [2,] 0.760882805 -2.14358794 -4.307825 -0.6445793 -0.47135521 381s [3,] -0.248412577 0.09178334 5.492015 0.9810619 0.08362357 381s [4,] -0.318557031 0.04459940 -3.388131 0.7062858 3.47306415 381s 381s , , 3, 3 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.68699037 -0.7064901 -2.256882 0.8804852 0.9906013030 381s [2,] 0.06042483 -1.1112301 -3.505533 -0.3678321 0.0004223756 381s [3,] -2.72481282 -2.3358606 2.758863 -2.8373974 0.0188836499 381s [4,] 0.49528627 0.2678766 -1.995772 -0.9753823 3.0287661438 381s 381s , , 4, 3 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -2.1462027 1.1947097 -0.3519896 -2.056299 -2.2536148 381s [2,] 0.4653544 1.9211348 -3.3894111 -4.159688 -0.8994992 381s [3,] -4.5377897 1.8608204 -3.4156905 -1.004905 0.0114212 381s [4,] -2.3324408 0.4955766 0.4775765 1.902725 -3.6100607 381s 381s , , 1, 4 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 3.0007923 -2.7838243 3.4331984 -0.4828151 3.050809 381s [2,] 0.1365672 -2.0323261 3.0790273 4.1597130 2.919147 381s [3,] 4.1357732 0.1521197 2.1006591 0.5084960 1.392836 381s [4,] 3.7732825 -1.5347227 -0.1726469 -2.7657212 1.679192 381s 381s , , 2, 4 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 1.5865539 -0.4013158 2.0861046 -0.08309915 0.3403820 381s [2,] 0.2393429 -3.0420864 1.5448143 3.72384958 2.8501549 381s [3,] 1.7067734 -0.8804551 2.7405953 0.10713702 0.4017382 381s [4,] 3.2372827 0.6094085 -0.2456709 -2.66173712 2.8587858 381s 381s , , 3, 4 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 1.1764475 1.191738 2.595306 -0.5794752 4.1938603 381s [2,] -1.3157299 1.033681 4.951112 3.3807109 1.8351776 381s [3,] 0.5467456 -3.509342 -3.475947 -4.5163108 0.5493495 381s [4,] 3.1673997 -1.006108 2.593863 -3.8350295 -0.1394232 381s 381s , , 4, 4 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -1.699248 3.052134 -1.382195 0.5262189 -8.4136596 381s [2,] 1.297020 -2.970095 -2.455244 -1.2366065 -0.3989992 381s [3,] -0.549665 2.985687 3.044206 6.0612430 -1.8853647 381s [4,] -2.417202 4.199904 -0.695813 3.0512333 0.8168829 381s 381s , , 1, 5 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -1.9523992 1.7001105 -3.7568711 1.874232 -4.56323930 381s [2,] 0.3411858 0.1426824 -2.3987577 -2.872542 -3.08097225 381s [3,] -0.4574765 1.3578968 1.5336655 3.827166 -1.76109449 381s [4,] -3.9466844 1.9374514 -0.9600955 3.822500 0.08426608 381s 381s , , 2, 5 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.4884867 0.2715609 -3.76991562 3.0922066 2.7085028 381s [2,] -1.3027509 2.0748355 1.08167715 -0.3181959 -3.1210841 381s [3,] 0.8950942 -3.2827972 0.09681537 -1.5292215 -0.9519058 381s [4,] -1.5770076 -0.8929450 -0.26033938 0.5836015 1.4617001 381s 381s , , 3, 5 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.8172528 0.3459001 -0.426368 -0.4419827 -5.6346489 381s [2,] 1.6239619 -3.6899878 -4.293140 -0.8050815 1.1326296 381s [3,] -1.4484553 2.6387717 4.356360 3.6643178 -0.5062724 381s [4,] -0.5038483 2.7509440 -2.018184 1.3582959 1.8074412 381s 381s , , 4, 5 381s 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -1.4312235 -3.417183 -7.7603495 4.154755 5.4150506 381s [2,] -1.2891194 5.312822 -3.4375819 -5.215400 -7.0956976 381s [3,] -0.2138048 -2.249400 0.4036211 -2.051051 -0.4447401 381s [4,] -5.2062100 -3.719768 -2.7716127 3.879017 0.0698682 381s 381s a c d f 381s 4 5 4 5 381s > 381s > 381s > G <- to.tensor(rnorm(20*20*3),c(a=4,b=5,a1=4,b1=5,I=3)) 381s > mul.tensor(A,c("a","b"),G,c("a","b")) 381s , , 1, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.9160721 -1.723116 3.1344688 2.3590173 381s [2,] 1.5210764 1.926843 -0.2071013 1.5865098 381s [3,] 1.4196044 -6.785355 3.1785261 -0.8568046 381s [4,] -0.8708781 -2.585428 -6.2388113 -3.2546285 381s [5,] -5.2566360 -2.184446 -1.9477836 -1.8105832 381s 381s , , 2, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.01294063 0.481706 -1.282652 1.618568 381s [2,] -3.31353456 4.836402 -4.430307 -1.707034 381s [3,] -1.82680096 3.415630 -6.897968 5.301271 381s [4,] 0.03703797 1.215010 -1.978326 3.908937 381s [5,] 0.30849625 -6.146003 3.245114 -4.837900 381s 381s , , 3, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.700143 2.74125048 -4.365630 2.90847464 381s [2,] -3.320153 4.33641319 -2.280506 4.05000108 381s [3,] -7.206831 -2.55037470 -1.002285 4.17916989 381s [4,] -5.348353 4.19974883 2.569026 0.09905949 381s [5,] -3.691877 -0.01453547 -4.061927 -3.88339643 381s 381s , , 4, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7392852 -5.001167 -2.2350489 4.257032 381s [2,] 0.1181369 3.057290 -4.1693774 -4.584761 381s [3,] 3.4983241 4.535508 -8.5922870 3.228034 381s [4,] 3.4707759 4.995333 5.9143055 -1.567897 381s [5,] 1.7255907 -4.703328 -0.7070128 -1.266183 381s 381s , , 5, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.7507208 0.1441032 -1.475236 4.8025327 381s [2,] 0.4468442 2.1466639 -3.260027 -6.1556623 381s [3,] -5.9376256 7.4312306 -6.731992 -2.4167834 381s [4,] -0.9061706 6.7962766 -4.357772 0.1934279 381s [5,] 4.7216772 -1.4221077 -3.067015 6.4601642 381s 381s , , 1, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.7717774 -1.0494534 2.2896404 0.3092118 381s [2,] 3.8397016 -0.1127951 -0.8335418 -6.3967417 381s [3,] -0.8100704 -4.2972564 1.1073823 4.6080585 381s [4,] 3.4766291 1.3770775 1.6511925 2.6574728 381s [5,] -2.7626556 4.9611957 4.7837919 0.8523948 381s 381s , , 2, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 5.1069172 3.441578 1.36410161 -1.2914202 381s [2,] -0.5080645 1.760376 -4.87917619 -0.6830125 381s [3,] 7.7449907 7.015620 0.90922501 -4.2703954 381s [4,] -5.2977927 -9.397718 0.08209162 -1.6213990 381s [5,] -6.4533850 -1.356973 -7.99994560 -4.1932487 381s 381s , , 3, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -2.1180089 -1.56157657 -3.0444540 4.2419811 381s [2,] 2.9981322 -0.03294657 2.2035226 0.2996967 381s [3,] 1.5836696 -2.21068021 -7.7859515 2.6942964 381s [4,] -0.1582774 -0.87203400 0.7638035 -3.7604290 381s [5,] 1.3188926 -2.06083892 2.5351664 -2.7974677 381s 381s , , 4, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 2.4736368 2.066592 2.183554 3.7139112 381s [2,] -0.8914545 -5.822417 -4.559295 0.4679584 381s [3,] 0.4946849 -1.972233 -6.448038 -0.9158920 381s [4,] 1.2484854 -5.451237 2.068878 -5.9095896 381s [5,] 5.8790355 6.998398 2.950649 -2.9567472 381s 381s , , 5, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7962685 3.245443 -3.766613 1.349804 381s [2,] -4.4878560 8.978860 4.920742 -1.087291 381s [3,] -3.2783405 -3.926046 2.485509 -7.064981 381s [4,] 0.4119418 3.988261 -3.722817 1.768493 381s [5,] -1.4537835 6.484509 -5.459598 3.736263 381s 381s , , 1, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.635395 -0.06259169 -1.1735570 0.2423941 381s [2,] 1.423165 -7.43245512 -0.6383191 4.4453820 381s [3,] -1.665444 12.31114805 9.6365427 7.2993935 381s [4,] -1.463782 -2.17594642 1.9621656 0.6039105 381s [5,] 2.714725 6.71116834 -1.7466223 4.3896150 381s 381s , , 2, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.795694 -5.2264583 1.012156 -3.549915 381s [2,] -2.967193 1.8139114 6.061017 5.878039 381s [3,] -4.677186 -0.4598026 1.701504 -4.065478 381s [4,] -6.980607 5.1463264 -1.353597 -2.251123 381s [5,] 2.980398 -1.8570672 4.114319 -4.473137 381s 381s , , 3, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.984483 -5.1501280 -2.256806 -1.702531 381s [2,] 1.140526 -1.4480626 -4.329763 6.968992 381s [3,] -4.562724 -0.5055382 6.449451 3.054127 381s [4,] 7.246401 2.6268994 -2.994583 1.515928 381s [5,] 5.080812 -7.7338589 -5.677535 -2.415891 381s 381s , , 4, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3559434 2.606566 4.020425 -1.5594805 381s [2,] -2.7415992 -6.098343 -7.192729 5.3145753 381s [3,] -1.6320014 3.789132 -1.993286 9.8074484 381s [4,] -4.0828060 1.382317 -6.610842 0.2613842 381s [5,] -3.0323068 5.376626 -6.334314 -8.6589163 381s 381s , , 5, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.9203480 2.04598302 -0.6174551 2.0158551 381s [2,] 4.9986726 3.00100208 -4.8412744 -0.6807395 381s [3,] 7.4715170 -2.01476935 -11.4160423 -2.3368010 381s [4,] -0.5567231 0.04055137 -0.5709127 -5.3202880 381s [5,] -8.2461295 -1.79988534 -9.6717668 1.4865820 381s 381s c a1 b1 I 381s 5 4 5 3 381s > 381s > 381s > 381s > checker(einstein.tensor(A,G),einstein.tensor(G,A)) 381s , , 1, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.9160721 -1.723116 3.1344688 2.3590173 381s [2,] 1.5210764 1.926843 -0.2071013 1.5865098 381s [3,] 1.4196044 -6.785355 3.1785261 -0.8568046 381s [4,] -0.8708781 -2.585428 -6.2388113 -3.2546285 381s [5,] -5.2566360 -2.184446 -1.9477836 -1.8105832 381s 381s , , 2, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.01294063 0.481706 -1.282652 1.618568 381s [2,] -3.31353456 4.836402 -4.430307 -1.707034 381s [3,] -1.82680096 3.415630 -6.897968 5.301271 381s [4,] 0.03703797 1.215010 -1.978326 3.908937 381s [5,] 0.30849625 -6.146003 3.245114 -4.837900 381s 381s , , 3, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.700143 2.74125048 -4.365630 2.90847464 381s [2,] -3.320153 4.33641319 -2.280506 4.05000108 381s [3,] -7.206831 -2.55037470 -1.002285 4.17916989 381s [4,] -5.348353 4.19974883 2.569026 0.09905949 381s [5,] -3.691877 -0.01453547 -4.061927 -3.88339643 381s 381s , , 4, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7392852 -5.001167 -2.2350489 4.257032 381s [2,] 0.1181369 3.057290 -4.1693774 -4.584761 381s [3,] 3.4983241 4.535508 -8.5922870 3.228034 381s [4,] 3.4707759 4.995333 5.9143055 -1.567897 381s [5,] 1.7255907 -4.703328 -0.7070128 -1.266183 381s 381s , , 5, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.7507208 0.1441032 -1.475236 4.8025327 381s [2,] 0.4468442 2.1466639 -3.260027 -6.1556623 381s [3,] -5.9376256 7.4312306 -6.731992 -2.4167834 381s [4,] -0.9061706 6.7962766 -4.357772 0.1934279 381s [5,] 4.7216772 -1.4221077 -3.067015 6.4601642 381s 381s , , 1, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.7717774 -1.0494534 2.2896404 0.3092118 381s [2,] 3.8397016 -0.1127951 -0.8335418 -6.3967417 381s [3,] -0.8100704 -4.2972564 1.1073823 4.6080585 381s [4,] 3.4766291 1.3770775 1.6511925 2.6574728 381s [5,] -2.7626556 4.9611957 4.7837919 0.8523948 381s 381s , , 2, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 5.1069172 3.441578 1.36410161 -1.2914202 381s [2,] -0.5080645 1.760376 -4.87917619 -0.6830125 381s [3,] 7.7449907 7.015620 0.90922501 -4.2703954 381s [4,] -5.2977927 -9.397718 0.08209162 -1.6213990 381s [5,] -6.4533850 -1.356973 -7.99994560 -4.1932487 381s 381s , , 3, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -2.1180089 -1.56157657 -3.0444540 4.2419811 381s [2,] 2.9981322 -0.03294657 2.2035226 0.2996967 381s [3,] 1.5836696 -2.21068021 -7.7859515 2.6942964 381s [4,] -0.1582774 -0.87203400 0.7638035 -3.7604290 381s [5,] 1.3188926 -2.06083892 2.5351664 -2.7974677 381s 381s , , 4, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 2.4736368 2.066592 2.183554 3.7139112 381s [2,] -0.8914545 -5.822417 -4.559295 0.4679584 381s [3,] 0.4946849 -1.972233 -6.448038 -0.9158920 381s [4,] 1.2484854 -5.451237 2.068878 -5.9095896 381s [5,] 5.8790355 6.998398 2.950649 -2.9567472 381s 381s , , 5, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7962685 3.245443 -3.766613 1.349804 381s [2,] -4.4878560 8.978860 4.920742 -1.087291 381s [3,] -3.2783405 -3.926046 2.485509 -7.064981 381s [4,] 0.4119418 3.988261 -3.722817 1.768493 381s [5,] -1.4537835 6.484509 -5.459598 3.736263 381s 381s , , 1, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.635395 -0.06259169 -1.1735570 0.2423941 381s [2,] 1.423165 -7.43245512 -0.6383191 4.4453820 381s [3,] -1.665444 12.31114805 9.6365427 7.2993935 381s [4,] -1.463782 -2.17594642 1.9621656 0.6039105 381s [5,] 2.714725 6.71116834 -1.7466223 4.3896150 381s 381s , , 2, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.795694 -5.2264583 1.012156 -3.549915 381s [2,] -2.967193 1.8139114 6.061017 5.878039 381s [3,] -4.677186 -0.4598026 1.701504 -4.065478 381s [4,] -6.980607 5.1463264 -1.353597 -2.251123 381s [5,] 2.980398 -1.8570672 4.114319 -4.473137 381s 381s , , 3, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.984483 -5.1501280 -2.256806 -1.702531 381s [2,] 1.140526 -1.4480626 -4.329763 6.968992 381s [3,] -4.562724 -0.5055382 6.449451 3.054127 381s [4,] 7.246401 2.6268994 -2.994583 1.515928 381s [5,] 5.080812 -7.7338589 -5.677535 -2.415891 381s 381s , , 4, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3559434 2.606566 4.020425 -1.5594805 381s [2,] -2.7415992 -6.098343 -7.192729 5.3145753 381s [3,] -1.6320014 3.789132 -1.993286 9.8074484 381s [4,] -4.0828060 1.382317 -6.610842 0.2613842 381s [5,] -3.0323068 5.376626 -6.334314 -8.6589163 381s 381s , , 5, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.9203480 2.04598302 -0.6174551 2.0158551 381s [2,] 4.9986726 3.00100208 -4.8412744 -0.6807395 381s [3,] 7.4715170 -2.01476935 -11.4160423 -2.3368010 381s [4,] -0.5567231 0.04055137 -0.5709127 -5.3202880 381s [5,] -8.2461295 -1.79988534 -9.6717668 1.4865820 381s 381s c a1 b1 I 381s 5 4 5 3 381s > 381s > checker(einstein.tensor(A,G),einstein.tensor(G,A)) 381s , , 1, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.9160721 -1.723116 3.1344688 2.3590173 381s [2,] 1.5210764 1.926843 -0.2071013 1.5865098 381s [3,] 1.4196044 -6.785355 3.1785261 -0.8568046 381s [4,] -0.8708781 -2.585428 -6.2388113 -3.2546285 381s [5,] -5.2566360 -2.184446 -1.9477836 -1.8105832 381s 381s , , 2, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.01294063 0.481706 -1.282652 1.618568 381s [2,] -3.31353456 4.836402 -4.430307 -1.707034 381s [3,] -1.82680096 3.415630 -6.897968 5.301271 381s [4,] 0.03703797 1.215010 -1.978326 3.908937 381s [5,] 0.30849625 -6.146003 3.245114 -4.837900 381s 381s , , 3, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.700143 2.74125048 -4.365630 2.90847464 381s [2,] -3.320153 4.33641319 -2.280506 4.05000108 381s [3,] -7.206831 -2.55037470 -1.002285 4.17916989 381s [4,] -5.348353 4.19974883 2.569026 0.09905949 381s [5,] -3.691877 -0.01453547 -4.061927 -3.88339643 381s 381s , , 4, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7392852 -5.001167 -2.2350489 4.257032 381s [2,] 0.1181369 3.057290 -4.1693774 -4.584761 381s [3,] 3.4983241 4.535508 -8.5922870 3.228034 381s [4,] 3.4707759 4.995333 5.9143055 -1.567897 381s [5,] 1.7255907 -4.703328 -0.7070128 -1.266183 381s 381s , , 5, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.7507208 0.1441032 -1.475236 4.8025327 381s [2,] 0.4468442 2.1466639 -3.260027 -6.1556623 381s [3,] -5.9376256 7.4312306 -6.731992 -2.4167834 381s [4,] -0.9061706 6.7962766 -4.357772 0.1934279 381s [5,] 4.7216772 -1.4221077 -3.067015 6.4601642 381s 381s , , 1, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.7717774 -1.0494534 2.2896404 0.3092118 381s [2,] 3.8397016 -0.1127951 -0.8335418 -6.3967417 381s [3,] -0.8100704 -4.2972564 1.1073823 4.6080585 381s [4,] 3.4766291 1.3770775 1.6511925 2.6574728 381s [5,] -2.7626556 4.9611957 4.7837919 0.8523948 381s 381s , , 2, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 5.1069172 3.441578 1.36410161 -1.2914202 381s [2,] -0.5080645 1.760376 -4.87917619 -0.6830125 381s [3,] 7.7449907 7.015620 0.90922501 -4.2703954 381s [4,] -5.2977927 -9.397718 0.08209162 -1.6213990 381s [5,] -6.4533850 -1.356973 -7.99994560 -4.1932487 381s 381s , , 3, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -2.1180089 -1.56157657 -3.0444540 4.2419811 381s [2,] 2.9981322 -0.03294657 2.2035226 0.2996967 381s [3,] 1.5836696 -2.21068021 -7.7859515 2.6942964 381s [4,] -0.1582774 -0.87203400 0.7638035 -3.7604290 381s [5,] 1.3188926 -2.06083892 2.5351664 -2.7974677 381s 381s , , 4, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 2.4736368 2.066592 2.183554 3.7139112 381s [2,] -0.8914545 -5.822417 -4.559295 0.4679584 381s [3,] 0.4946849 -1.972233 -6.448038 -0.9158920 381s [4,] 1.2484854 -5.451237 2.068878 -5.9095896 381s [5,] 5.8790355 6.998398 2.950649 -2.9567472 381s 381s , , 5, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7962685 3.245443 -3.766613 1.349804 381s [2,] -4.4878560 8.978860 4.920742 -1.087291 381s [3,] -3.2783405 -3.926046 2.485509 -7.064981 381s [4,] 0.4119418 3.988261 -3.722817 1.768493 381s [5,] -1.4537835 6.484509 -5.459598 3.736263 381s 381s , , 1, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.635395 -0.06259169 -1.1735570 0.2423941 381s [2,] 1.423165 -7.43245512 -0.6383191 4.4453820 381s [3,] -1.665444 12.31114805 9.6365427 7.2993935 381s [4,] -1.463782 -2.17594642 1.9621656 0.6039105 381s [5,] 2.714725 6.71116834 -1.7466223 4.3896150 381s 381s , , 2, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.795694 -5.2264583 1.012156 -3.549915 381s [2,] -2.967193 1.8139114 6.061017 5.878039 381s [3,] -4.677186 -0.4598026 1.701504 -4.065478 381s [4,] -6.980607 5.1463264 -1.353597 -2.251123 381s [5,] 2.980398 -1.8570672 4.114319 -4.473137 381s 381s , , 3, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.984483 -5.1501280 -2.256806 -1.702531 381s [2,] 1.140526 -1.4480626 -4.329763 6.968992 381s [3,] -4.562724 -0.5055382 6.449451 3.054127 381s [4,] 7.246401 2.6268994 -2.994583 1.515928 381s [5,] 5.080812 -7.7338589 -5.677535 -2.415891 381s 381s , , 4, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3559434 2.606566 4.020425 -1.5594805 381s [2,] -2.7415992 -6.098343 -7.192729 5.3145753 381s [3,] -1.6320014 3.789132 -1.993286 9.8074484 381s [4,] -4.0828060 1.382317 -6.610842 0.2613842 381s [5,] -3.0323068 5.376626 -6.334314 -8.6589163 381s 381s , , 5, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.9203480 2.04598302 -0.6174551 2.0158551 381s [2,] 4.9986726 3.00100208 -4.8412744 -0.6807395 381s [3,] 7.4715170 -2.01476935 -11.4160423 -2.3368010 381s [4,] -0.5567231 0.04055137 -0.5709127 -5.3202880 381s [5,] -8.2461295 -1.79988534 -9.6717668 1.4865820 381s 381s c a1 b1 I 381s 5 4 5 3 381s > 381s > checker(einstein.tensor(einstein.tensor(A,G),inv.tensor(G,c("a","b"),by="I"),by=c("I")),rep(A,dim(G)["I"],1,"I")) 381s , , 1, 1 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.59416575 0.37849947 -0.6851564 -0.98508098 381s [2,] 0.52469868 0.04378833 1.3868142 0.61678028 381s [3,] -0.01769231 -0.94697786 -0.4022124 0.05612025 381s [4,] -0.52031683 -1.17733344 1.2292765 1.12002683 381s [5,] -1.89485633 -0.26303828 -0.2078783 -1.04187663 381s 381s , , 2, 1 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.4003801 0.3255066 -1.1684364 0.4212993 381s [2,] 0.7556916 -1.4186397 -0.2730597 1.2176170 381s [3,] -0.1562948 -1.1885058 1.2822683 -0.4260943 381s [4,] -0.0753744 0.2932872 -0.0288957 -0.3978164 381s [5,] -1.5422206 0.7527781 -0.2653699 1.2066058 381s 381s , , 3, 1 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3486553 0.34934077 1.0807408 0.06253499 381s [2,] -0.6696680 -1.29577102 0.4952249 0.35056369 381s [3,] -0.4371484 -0.58263237 2.3616330 -0.98172868 381s [4,] 0.6554814 0.49138467 1.6429060 0.32859100 381s [5,] -0.7979686 0.09586926 -0.1305040 1.38843020 381s 381s , , 4, 1 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.7560774 -0.4021343 -0.4444302 -0.9993098 381s [2,] 0.9606657 0.3254006 -1.4676450 0.5462929 381s [3,] -2.1371789 -0.3241383 0.5531834 -0.2679333 381s [4,] 1.4613930 -0.3980795 -0.3555964 0.5035616 381s [5,] -0.2500193 -1.3640832 -0.8105675 1.0824382 381s 381s , , 5, 1 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.2020531 0.2279937 0.2075888 -0.5953352 381s [2,] -2.2326815 0.2882842 0.5438345 -1.1919848 381s [3,] -1.0955978 -1.8981084 1.4605549 -1.5107880 381s [4,] 0.4008347 -1.0983184 0.1305792 0.7646588 381s [5,] 1.2946636 -0.8166615 0.4759993 0.3731633 381s 381s , , 1, 2 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.59416575 0.37849947 -0.6851564 -0.98508098 381s [2,] 0.52469868 0.04378833 1.3868142 0.61678028 381s [3,] -0.01769231 -0.94697786 -0.4022124 0.05612025 381s [4,] -0.52031683 -1.17733344 1.2292765 1.12002683 381s [5,] -1.89485633 -0.26303828 -0.2078783 -1.04187663 381s 381s , , 2, 2 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.4003801 0.3255066 -1.1684364 0.4212993 381s [2,] 0.7556916 -1.4186397 -0.2730597 1.2176170 381s [3,] -0.1562948 -1.1885058 1.2822683 -0.4260943 381s [4,] -0.0753744 0.2932872 -0.0288957 -0.3978164 381s [5,] -1.5422206 0.7527781 -0.2653699 1.2066058 381s 381s , , 3, 2 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3486553 0.34934077 1.0807408 0.06253499 381s [2,] -0.6696680 -1.29577102 0.4952249 0.35056369 381s [3,] -0.4371484 -0.58263237 2.3616330 -0.98172868 381s [4,] 0.6554814 0.49138467 1.6429060 0.32859100 381s [5,] -0.7979686 0.09586926 -0.1305040 1.38843020 381s 381s , , 4, 2 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.7560774 -0.4021343 -0.4444302 -0.9993098 381s [2,] 0.9606657 0.3254006 -1.4676450 0.5462929 381s [3,] -2.1371789 -0.3241383 0.5531834 -0.2679333 381s [4,] 1.4613930 -0.3980795 -0.3555964 0.5035616 381s [5,] -0.2500193 -1.3640832 -0.8105675 1.0824382 381s 381s , , 5, 2 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.2020531 0.2279937 0.2075888 -0.5953352 381s [2,] -2.2326815 0.2882842 0.5438345 -1.1919848 381s [3,] -1.0955978 -1.8981084 1.4605549 -1.5107880 381s [4,] 0.4008347 -1.0983184 0.1305792 0.7646588 381s [5,] 1.2946636 -0.8166615 0.4759993 0.3731633 381s 381s , , 1, 3 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.59416575 0.37849947 -0.6851564 -0.98508098 381s [2,] 0.52469868 0.04378833 1.3868142 0.61678028 381s [3,] -0.01769231 -0.94697786 -0.4022124 0.05612025 381s [4,] -0.52031683 -1.17733344 1.2292765 1.12002683 381s [5,] -1.89485633 -0.26303828 -0.2078783 -1.04187663 381s 381s , , 2, 3 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.4003801 0.3255066 -1.1684364 0.4212993 381s [2,] 0.7556916 -1.4186397 -0.2730597 1.2176170 381s [3,] -0.1562948 -1.1885058 1.2822683 -0.4260943 381s [4,] -0.0753744 0.2932872 -0.0288957 -0.3978164 381s [5,] -1.5422206 0.7527781 -0.2653699 1.2066058 381s 381s , , 3, 3 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3486553 0.34934077 1.0807408 0.06253499 381s [2,] -0.6696680 -1.29577102 0.4952249 0.35056369 381s [3,] -0.4371484 -0.58263237 2.3616330 -0.98172868 381s [4,] 0.6554814 0.49138467 1.6429060 0.32859100 381s [5,] -0.7979686 0.09586926 -0.1305040 1.38843020 381s 381s , , 4, 3 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] -0.7560774 -0.4021343 -0.4444302 -0.9993098 381s [2,] 0.9606657 0.3254006 -1.4676450 0.5462929 381s [3,] -2.1371789 -0.3241383 0.5531834 -0.2679333 381s [4,] 1.4613930 -0.3980795 -0.3555964 0.5035616 381s [5,] -0.2500193 -1.3640832 -0.8105675 1.0824382 381s 381s , , 5, 3 381s 381s a 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.2020531 0.2279937 0.2075888 -0.5953352 381s [2,] -2.2326815 0.2882842 0.5438345 -1.1919848 381s [3,] -1.0955978 -1.8981084 1.4605549 -1.5107880 381s [4,] 0.4008347 -1.0983184 0.1305792 0.7646588 381s [5,] 1.2946636 -0.8166615 0.4759993 0.3731633 381s 381s c a b I 381s 5 4 5 3 381s > 381s > einstein.tensor(A,G) 381s , , 1, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.9160721 -1.723116 3.1344688 2.3590173 381s [2,] 1.5210764 1.926843 -0.2071013 1.5865098 381s [3,] 1.4196044 -6.785355 3.1785261 -0.8568046 381s [4,] -0.8708781 -2.585428 -6.2388113 -3.2546285 381s [5,] -5.2566360 -2.184446 -1.9477836 -1.8105832 381s 381s , , 2, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.01294063 0.481706 -1.282652 1.618568 381s [2,] -3.31353456 4.836402 -4.430307 -1.707034 381s [3,] -1.82680096 3.415630 -6.897968 5.301271 381s [4,] 0.03703797 1.215010 -1.978326 3.908937 381s [5,] 0.30849625 -6.146003 3.245114 -4.837900 381s 381s , , 3, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.700143 2.74125048 -4.365630 2.90847464 381s [2,] -3.320153 4.33641319 -2.280506 4.05000108 381s [3,] -7.206831 -2.55037470 -1.002285 4.17916989 381s [4,] -5.348353 4.19974883 2.569026 0.09905949 381s [5,] -3.691877 -0.01453547 -4.061927 -3.88339643 381s 381s , , 4, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7392852 -5.001167 -2.2350489 4.257032 381s [2,] 0.1181369 3.057290 -4.1693774 -4.584761 381s [3,] 3.4983241 4.535508 -8.5922870 3.228034 381s [4,] 3.4707759 4.995333 5.9143055 -1.567897 381s [5,] 1.7255907 -4.703328 -0.7070128 -1.266183 381s 381s , , 5, 1 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.7507208 0.1441032 -1.475236 4.8025327 381s [2,] 0.4468442 2.1466639 -3.260027 -6.1556623 381s [3,] -5.9376256 7.4312306 -6.731992 -2.4167834 381s [4,] -0.9061706 6.7962766 -4.357772 0.1934279 381s [5,] 4.7216772 -1.4221077 -3.067015 6.4601642 381s 381s , , 1, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -4.7717774 -1.0494534 2.2896404 0.3092118 381s [2,] 3.8397016 -0.1127951 -0.8335418 -6.3967417 381s [3,] -0.8100704 -4.2972564 1.1073823 4.6080585 381s [4,] 3.4766291 1.3770775 1.6511925 2.6574728 381s [5,] -2.7626556 4.9611957 4.7837919 0.8523948 381s 381s , , 2, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 5.1069172 3.441578 1.36410161 -1.2914202 381s [2,] -0.5080645 1.760376 -4.87917619 -0.6830125 381s [3,] 7.7449907 7.015620 0.90922501 -4.2703954 381s [4,] -5.2977927 -9.397718 0.08209162 -1.6213990 381s [5,] -6.4533850 -1.356973 -7.99994560 -4.1932487 381s 381s , , 3, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -2.1180089 -1.56157657 -3.0444540 4.2419811 381s [2,] 2.9981322 -0.03294657 2.2035226 0.2996967 381s [3,] 1.5836696 -2.21068021 -7.7859515 2.6942964 381s [4,] -0.1582774 -0.87203400 0.7638035 -3.7604290 381s [5,] 1.3188926 -2.06083892 2.5351664 -2.7974677 381s 381s , , 4, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 2.4736368 2.066592 2.183554 3.7139112 381s [2,] -0.8914545 -5.822417 -4.559295 0.4679584 381s [3,] 0.4946849 -1.972233 -6.448038 -0.9158920 381s [4,] 1.2484854 -5.451237 2.068878 -5.9095896 381s [5,] 5.8790355 6.998398 2.950649 -2.9567472 381s 381s , , 5, 2 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 1.7962685 3.245443 -3.766613 1.349804 381s [2,] -4.4878560 8.978860 4.920742 -1.087291 381s [3,] -3.2783405 -3.926046 2.485509 -7.064981 381s [4,] 0.4119418 3.988261 -3.722817 1.768493 381s [5,] -1.4537835 6.484509 -5.459598 3.736263 381s 381s , , 1, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.635395 -0.06259169 -1.1735570 0.2423941 381s [2,] 1.423165 -7.43245512 -0.6383191 4.4453820 381s [3,] -1.665444 12.31114805 9.6365427 7.2993935 381s [4,] -1.463782 -2.17594642 1.9621656 0.6039105 381s [5,] 2.714725 6.71116834 -1.7466223 4.3896150 381s 381s , , 2, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -1.795694 -5.2264583 1.012156 -3.549915 381s [2,] -2.967193 1.8139114 6.061017 5.878039 381s [3,] -4.677186 -0.4598026 1.701504 -4.065478 381s [4,] -6.980607 5.1463264 -1.353597 -2.251123 381s [5,] 2.980398 -1.8570672 4.114319 -4.473137 381s 381s , , 3, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] -3.984483 -5.1501280 -2.256806 -1.702531 381s [2,] 1.140526 -1.4480626 -4.329763 6.968992 381s [3,] -4.562724 -0.5055382 6.449451 3.054127 381s [4,] 7.246401 2.6268994 -2.994583 1.515928 381s [5,] 5.080812 -7.7338589 -5.677535 -2.415891 381s 381s , , 4, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.3559434 2.606566 4.020425 -1.5594805 381s [2,] -2.7415992 -6.098343 -7.192729 5.3145753 381s [3,] -1.6320014 3.789132 -1.993286 9.8074484 381s [4,] -4.0828060 1.382317 -6.610842 0.2613842 381s [5,] -3.0323068 5.376626 -6.334314 -8.6589163 381s 381s , , 5, 3 381s 381s a1 381s c [,1] [,2] [,3] [,4] 381s [1,] 0.9203480 2.04598302 -0.6174551 2.0158551 381s [2,] 4.9986726 3.00100208 -4.8412744 -0.6807395 381s [3,] 7.4715170 -2.01476935 -11.4160423 -2.3368010 381s [4,] -0.5567231 0.04055137 -0.5709127 -5.3202880 381s [5,] -8.2461295 -1.79988534 -9.6717668 1.4865820 381s 381s c a1 b1 I 381s 5 4 5 3 381s > 381s > ## chol 381s > 381s > A <- to.tensor(rnorm(15),c(a=3,b=5)) 381s > AAt <- einstein.tensor(A,mark(A,i="a")) 381s > ch <- chol.tensor(AAt,"a","a'",name="lambda") 381s > #names(ch)[1]<-"lambda" 381s > checker(einstein.tensor(ch,mark(ch,i="a")),AAt) 381s a' 381s a [,1] [,2] [,3] 381s [1,] 6.984947 -2.9030232 1.4581482 381s [2,] -2.903023 6.8345200 -0.2415085 381s [3,] 1.458148 -0.2415085 2.2585281 381s a a' 381s 3 3 381s > 381s > A <- to.tensor(rnorm(30),c(a=3,b=5,c=2)) 381s > AAt <- einstein.tensor(A,mark(A,i="a"),by="c") 381s > ch <- chol.tensor(AAt,"a","a'",name="lambda") 381s > checker(einstein.tensor(ch,mark(ch,i="a"),by="c"),AAt) 381s , , 1 381s 381s a' 381s a [,1] [,2] [,3] 381s [1,] 0.4804315 -0.4854377 -0.7160533 381s [2,] -0.4854377 2.3300375 -1.5928575 381s [3,] -0.7160533 -1.5928575 5.2261142 381s 381s , , 2 381s 381s a' 381s a [,1] [,2] [,3] 381s [1,] 2.039175 -0.39424904 -1.77979967 381s [2,] -0.394249 1.07048922 0.06254919 381s [3,] -1.779800 0.06254919 7.61912388 381s 381s a a' c 381s 3 3 2 381s > 381s > ftable(A) 381s c c1 c2 381s a b 381s a1 b1 -0.09784599 1.34761937 381s b2 0.09225565 0.32222796 381s b3 -0.55385608 -0.05096052 381s b4 -0.19364675 0.32350045 381s b5 0.34364361 0.10962258 381s a2 b1 0.10041272 -0.22494352 381s b2 -0.94165174 0.13085593 381s b3 0.54406156 0.26990205 381s b4 1.01756980 -0.61980277 381s b5 0.31905404 0.73875826 381s a3 b1 0.09202849 -1.45734359 381s b2 1.44132363 1.41735358 381s b3 1.45227763 1.35317178 381s b4 -0.83674732 -0.19863919 381s b5 -0.57530405 -1.27116127 381s > 381s > # norm 381s > 381s > A <- to.tensor(c(1,1,1,1,0,1,1,1,0,0,1,1),c(a=4,b=3)) 381s > checker(norm.tensor(A),sqrt(9)) 381s [1] 3 381s > checker(norm.tensor(A,c(1,2)),sqrt(9)) 381s [1] 3 381s > checker(norm.tensor(A,"b"),to.tensor(sqrt(c(1,2,3,3)),c(a=4))) 381s [1] 1.000000 1.414214 1.732051 1.732051 381s a 381s 4 381s > checker(norm.tensor(A,"a"),to.tensor(sqrt(c(4,3,2)),c(b=3))) 381s [1] 2.000000 1.732051 1.414214 381s b 381s 3 381s > checker(norm.tensor(A,by="a"),to.tensor(sqrt(c(1,2,3,3)),c(a=4))) 381s [1] 1.000000 1.414214 1.732051 1.732051 381s a 381s 4 381s > checker(norm.tensor(A,by="b"),to.tensor(sqrt(c(4,3,2)),c(b=3))) 381s [1] 2.000000 1.732051 1.414214 381s b 381s 3 381s > 381s > # opnorm 381s > 381s > A <- to.tensor(c(1,0,0,0,1,0,0,1),c(a=2,b=2,s=2)) 381s > checker(opnorm(A,"a",by="s"),to.tensor(c(1,1),c(s=2))) 381s [1] 1 1 381s s 381s 2 381s > 381s > 381s > # margin 381s > 381s > 381s > A <- to.tensor(rnorm(30),c(a=3,b=2,c=5)) 381s > checker( margin.tensor(A,c("a","c")),einstein.tensor(A,one.tensor(c(a=3,c=5)))) 381s [1] 1.489604 -2.001261 381s b 381s 2 381s > checker( margin.tensor(A,by=c("a","c")),einstein.tensor(A,one.tensor(c(b=2)))) 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.5769965 -0.20187122 -0.3721776 -0.9407186 -0.3738240 381s [2,] 2.6281710 0.02626197 -0.2817764 0.5209827 0.1161373 381s [3,] -0.3472123 -2.10653371 0.9159899 1.5840502 -1.1021397 381s a c 381s 3 5 381s > checker(one.tensor(c(a=3,c=5)),to.tensor(rep(1,15),c(a=3,c=5))) 381s c 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] 1 1 1 1 1 381s [2,] 1 1 1 1 1 381s [3,] 1 1 1 1 1 381s a c 381s 3 5 381s > 381s > # diagmul 381s > 381s > A <- to.tensor(rnorm(30),c(a=3,b=2,c=5)) 381s > B <- to.tensor(rnorm(6),c(a=3,b=2)) 381s > 381s > checker(einstein.tensor(A,diag.tensor(B,mark="m")), 381s + diagmul.tensor(A,B,i=c("a","b"))[[a=~am,b=~bm]]) 381s , , 1 381s 381s am 381s c [,1] [,2] [,3] 381s [1,] -0.09234645 0.7680490 -0.146947930 381s [2,] -0.69025880 -1.4953515 0.128088503 381s [3,] 1.52252439 1.0115641 0.028617422 381s [4,] 1.88231190 0.6671632 0.006614462 381s [5,] 0.32903062 -1.6450917 -0.022248073 381s 381s , , 2 381s 381s am 381s c [,1] [,2] [,3] 381s [1,] 0.4613362 -0.03444576 0.05528349 381s [2,] -0.5728777 -0.52175024 0.02677008 381s [3,] -0.3521745 0.16717339 -0.18994383 381s [4,] -0.1400363 0.62922790 -0.72614126 381s [5,] -0.1624029 -0.41876036 0.29378116 381s 381s c am bm 381s 5 3 2 381s > 381s > # is.tensor 381s > if( !identical(c( 381s + is.tensor(FALSE), 381s + is.tensor(TRUE), 381s + is.tensor(matrix(1:3)), 381s + is.tensor(as.tensor(matrix(1:3))), 381s + is.tensor(A)),c(FALSE,FALSE,FALSE,TRUE,TRUE))) 381s + stop("Fehler") 381s > 381s > # 381s > 381s > A <- to.tensor(rnorm(30),c(a=3,b=2,c=5)) 381s > checker(reorder.tensor(reorder.tensor(reorder.tensor(A,c("c","b","a")),c(1,3,2)),c("a","b","c")),A) 381s , , 1 381s 381s b 381s a [,1] [,2] 381s [1,] 1.3608712 0.1388678 381s [2,] -0.2778444 1.0647286 381s [3,] -0.5903549 1.2437371 381s 381s , , 2 381s 381s b 381s a [,1] [,2] 381s [1,] 0.7501802 -0.23673761 381s [2,] 1.0943480 0.25025069 381s [3,] 0.4039253 0.03963538 381s 381s , , 3 381s 381s b 381s a [,1] [,2] 381s [1,] 0.03815099 -1.05704346 381s [2,] 1.75624450 -0.59121518 381s [3,] -2.27214495 -0.02258944 381s 381s , , 4 381s 381s b 381s a [,1] [,2] 381s [1,] -0.5508356 0.001771953 381s [2,] -1.9457278 -1.331896909 381s [3,] -0.6734224 0.163766168 381s 381s , , 5 381s 381s b 381s a [,1] [,2] 381s [1,] -0.81027860 -1.018249 381s [2,] 0.07552993 0.431965 381s [3,] 2.13937238 -1.398020 381s 381s a b c 381s 3 2 5 381s > 381s > 381s > 381s > 381s > mul.tensor(A,c(),B,c(),by=c("a","b")) 381s , , 1 381s 381s a 381s c [,1] [,2] [,3] 381s [1,] 1.18625583 -0.35781610 0.06050369 381s [2,] 0.65392346 1.40933301 -0.04139709 381s [3,] 0.03325578 2.26174256 0.23286527 381s [4,] -0.48015703 -2.50576470 0.06901703 381s [5,] -0.70631056 0.09726964 -0.21925781 381s 381s , , 2 381s 381s a 381s c [,1] [,2] [,3] 381s [1,] 0.0388051044 0.4709735 0.76548188 381s [2,] -0.0661537646 0.1106962 0.02439436 381s [3,] -0.2953793650 -0.2615189 -0.01390311 381s [4,] 0.0004951532 -0.5891531 0.10079303 381s [5,] -0.2845387527 0.1910760 -0.86043835 381s 381s c a b 381s 5 3 2 381s > #### complex 381s > 381s > A <- to.tensor( c(1+1i,1,0,2-13i) , c(a=2,b=2) ) 381s > B <- to.tensor( c(1+1i,1,0,2-13i) , c(a=2,b=2) ) 381s > A 381s b 381s a [,1] [,2] 381s [1,] 1+1i 0+ 0i 381s [2,] 1+0i 2-13i 381s a b 381s 2 2 381s > Am <- matrix(c(A),nrow=nrow(A)) 381s > Bm <- matrix(c(B),nrow=nrow(B)) 381s > checker(mul.tensor(A,"b",B,"a"),to.tensor(c(Am%*%Bm),c(nrow(A),ncol(B)))) 381s b 381s a [,1] [,2] 381s [1,] 0+ 2i 0+ 0i 381s [2,] 3-12i -165-52i 381s a b 381s 2 2 381s > 381s > 381s > R1 <- matrix(rnorm(9)+rnorm(9)*1i,nrow=3) 381s > R1i <- solve(R1) 381s > R2 <- to.tensor(R1,c(a=3,b=3),what=1:2) 381s > R2i <- to.tensor(R1i,c(b=3,a=3),what=1:2) 381s > 381s > checker(inv.tensor(R2,"a","b"),R2i) 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s a b 381s 3 3 381s > checker(inv.tensor(R2,"a","b",allowSingular=TRUE),R2i) 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s a b 381s 3 3 381s > 381s > checker(inv.tensor(rep(R2,4,1,"K"),"a","b",by="K"),rep(R2i,4,1,"K")) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s a b K 381s 3 3 4 381s > checker(inv.tensor(rep(R2,4,1,"K"),"a","b",by="K",allowSingular=TRUE),rep(R2i,4,3,"K")) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0.26891751+0.7628924i -0.7687779+0.8888999i 0.150048-1.282899i 381s [2,] -0.04531925-0.0322484i -0.2363306+1.5599185i -0.778443-0.658758i 381s [3,] 0.44526602-0.8088347i 1.5938597+0.4511647i -0.908303+1.221015i 381s 381s a b K 381s 3 3 4 381s > 381s > R3 <- to.tensor(rnorm(15),c(a=3,z=5)) 381s > 381s > checker(mul.tensor(R2i,"b",mul.tensor(R2,"a",R3)),R3) 381s z 381s a [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.2019466+0i -0.2347215+0i 1.7048268+0i 0.2304638+0i -0.5519107+0i 381s [2,] -1.0496095+0i -0.8950220+0i -1.8930449+0i -0.6858668+0i 1.0463292+0i 381s [3,] 0.4888999+0i -0.3455552+0i 0.2676867+0i -0.1873279+0i -0.1284069+0i 381s a z 381s 3 5 381s > 381s > 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a"),mul.tensor(R2,"a",R3[[z=1]])) 381s [1] 1.3713638-0.4742725i -0.2140516+0.0970410i 0.4118275-0.8361075i 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a"),mul.tensor(R2,"a",R3)) 381s z 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 0.3899320-0.6974421i 3.501221-1.056582i 381s [2,] -0.2140516+0.0970410i -0.2465436+0.7832036i 1.137403-0.661693i 381s [3,] 0.4118275-0.8361075i -0.5798237-0.2166972i 3.025978-0.164146i 381s z 381s b [,4] [,5] 381s [1,] 0.6935974-0.4980503i -1.6115079+0.5978944i 381s [2,] 0.1177914+0.2619836i -0.3381057+0.0907991i 381s [3,] 0.2284069-0.0365227i -1.0922744+0.2511951i 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a",allowSingular=TRUE),mul.tensor(R2,"a",R3[[z=1]])) 381s [1] 1.3713638-0.4742725i -0.2140516+0.0970410i 0.4118275-0.8361075i 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a",allowSingular=T),mul.tensor(R2,"a",R3)) 381s z 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 0.3899320-0.6974421i 3.501221-1.056582i 381s [2,] -0.2140516+0.0970410i -0.2465436+0.7832036i 1.137403-0.661693i 381s [3,] 0.4118275-0.8361075i -0.5798237-0.2166972i 3.025978-0.164146i 381s z 381s b [,4] [,5] 381s [1,] 0.6935974-0.4980503i -1.6115079+0.5978944i 381s [2,] 0.1177914+0.2619836i -0.3381057+0.0907991i 381s [3,] 0.2284069-0.0365227i -1.0922744+0.2511951i 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 1.3713638-0.4742725i 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i -0.2140516+0.0970410i -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 0.4118275-0.8361075i 0.4118275-0.8361075i 381s K 381s b [,4] 381s [1,] 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 381s b K 381s 3 4 381s > checker(solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 1.3713638-0.4742725i 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i -0.2140516+0.0970410i -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 0.4118275-0.8361075i 0.4118275-0.8361075i 381s K 381s b [,4] 381s [1,] 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 381s b K 381s 3 4 381s > checker(solve.tensor(R2i,rep(R3[[z=1]],4,1,"K"),"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 1.3713638-0.4742725i 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i -0.2140516+0.0970410i -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 0.4118275-0.8361075i 0.4118275-0.8361075i 381s K 381s b [,4] 381s [1,] 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 381s b K 381s 3 4 381s > 381s > checker(solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K",allowSingular=T),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 1.3713638-0.4742725i 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i -0.2140516+0.0970410i -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 0.4118275-0.8361075i 0.4118275-0.8361075i 381s K 381s b [,4] 381s [1,] 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 381s b K 381s 3 4 381s > checker(solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K",allowSingular=T),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 1.3713638-0.4742725i 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i -0.2140516+0.0970410i -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 0.4118275-0.8361075i 0.4118275-0.8361075i 381s K 381s b [,4] 381s [1,] 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 381s b K 381s 3 4 381s > checker(solve.tensor(R2i,rep(R3[[z=1]],4,1,"K"),"a",by="K",allowSingular=T),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] 381s [1,] 1.3713638-0.4742725i 1.3713638-0.4742725i 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i -0.2140516+0.0970410i -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 0.4118275-0.8361075i 0.4118275-0.8361075i 381s K 381s b [,4] 381s [1,] 1.3713638-0.4742725i 381s [2,] -0.2140516+0.0970410i 381s [3,] 0.4118275-0.8361075i 381s b K 381s 3 4 381s > 381s > # trace.tensor 381s > 381s > A <- to.tensor(rep(1,16),c(a=4,b=4)) 381s > checker(trace.tensor(A,"a","b"),4) 381s [1] 4 381s > 381s > A <- to.tensor(rep(1,16*3),c(a=4,c=3,b=4)) 381s > checker(trace.tensor(A,"a","b"),to.tensor(rep(4,3),c(c=3))) 381s [1] 4 4 4 381s c 381s 3 381s > 381s > A <- to.tensor(1:(2*2*3*3*5),c(a=2,b=3,c=2,d=3,e=5)) 381s > erg <- sapply(1:5,function(e) sum(diag(matrix(A[[e=e]],nrow=6)))) 381s > checker(trace.tensor(reorder(A,c(3,4,1,5,2)),c("a","b"),c("c","d")),to.tensor(c(erg),c(e=5))) 381s [1] 111 327 543 759 975 381s e 381s 5 381s > 381s > # delta.tensor 381s > 381s > checker(delta.tensor(c(a=2,b=3)),to.tensor(c(diag(6)),c(a=2,b=3,"a'"=2,"b'"=3))) 381s , , 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 0 0 381s 381s , , 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 1 0 0 381s 381s , , 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 1 0 381s [2,] 0 0 0 381s 381s , , 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 1 0 381s 381s , , 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 1 381s [2,] 0 0 0 381s 381s , , 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 1 381s 381s a b a' b' 381s 2 3 2 3 381s > # diag.tensor 381s > 381s > A <- to.tensor(1:6,c(a=2,b=3)) 381s > checker(diag.tensor(A),to.tensor(c(diag(c(A))),c(a=2,b=3,"a'"=2,"b'"=3))) 381s , , 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 0 0 381s [2,] 0 0 0 381s 381s , , 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 2 0 0 381s 381s , , 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 3 0 381s [2,] 0 0 0 381s 381s , , 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 4 0 381s 381s , , 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 5 381s [2,] 0 0 0 381s 381s , , 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 6 381s 381s a b a' b' 381s 2 3 2 3 381s > A <- to.tensor(1:6,c(a=2,b=3)) 381s > checker(diag.tensor(A,by="b"),to.tensor(c(1,0,0,2,3,0,0,4,5,0,0,6),c(a=2,"a'"=2,b=3))) 381s , , 1 381s 381s a' 381s a [,1] [,2] 381s [1,] 1 0 381s [2,] 0 2 381s 381s , , 2 381s 381s a' 381s a [,1] [,2] 381s [1,] 3 0 381s [2,] 0 4 381s 381s , , 3 381s 381s a' 381s a [,1] [,2] 381s [1,] 5 0 381s [2,] 0 6 381s 381s a a' b 381s 2 2 3 381s > 381s > # tripledelta.tensor 381s > checker(tripledelta.tensor(c(a=2)),to.tensor(c(1,0,0,0,0,0,0,1),c(a=2,"a'"=2,"a*"=2))) 381s , , 1 381s 381s a' 381s a [,1] [,2] 381s [1,] 1 0 381s [2,] 0 0 381s 381s , , 2 381s 381s a' 381s a [,1] [,2] 381s [1,] 0 0 381s [2,] 0 1 381s 381s a a' a* 381s 2 2 2 381s > 381s > checker(tripledelta.tensor(c(a=2,b=4)), 381s + einstein.tensor(tripledelta.tensor(c(a=2)),tripledelta.tensor(c(b=4)) ) 381s + ) 381s , , 1, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 1 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 1, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 1 0 0 0 381s 381s , , 1, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 2, 1 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 1 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 1, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 1 0 0 381s 381s , , 1, 3, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 2, 2 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 1 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 1, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 1 0 381s 381s , , 1, 4, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 2, 3 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 1 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 1, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 3, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 3, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 1, 4, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 0 381s 381s , , 2, 4, 2, 4 381s 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 0 0 0 0 381s [2,] 0 0 0 1 381s 381s a b a' b' a* b* 381s 2 4 2 4 2 4 381s > 381s > 381s > # one.tensor 381s > checker( one.tensor(c(a=3,b=4)), to.tensor(rep(1,12),c(a=3,b=4))) 381s b 381s a [,1] [,2] [,3] [,4] 381s [1,] 1 1 1 1 381s [2,] 1 1 1 1 381s [3,] 1 1 1 1 381s a b 381s 3 4 381s > 381s > 381s > checker(level.tensor(A),length(dim(A))) 381s [1] 2 381s > 381s > 381s > # svd.tensor 381s > 381s > A <- to.tensor(rnorm(120),c(a=2,b=2,c=5,d=3,e=2)) 381s > 381s > SVD <- svd.tensor(A,c("a","d"),c("b","c"),by="e") 381s > dim(SVD$v) 381s b c lambda e 381s 2 5 6 2 381s > # Kompositionseigenschaft 381s > checker(einstein.tensor(SVD$v,diag=SVD$d,SVD$u,by="e"),A) 381s , , 1, 1, 1 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.2112292 0.7759068 0.97572551 -0.1328569 -0.1943283 381s [2,] 0.5981027 -0.9267507 0.06261686 0.9219106 0.8307256 381s 381s , , 2, 1, 1 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 1.0684566 1.639471 -0.6603836 -0.7860032 -0.65244160 381s [2,] -0.5017716 1.019933 -0.2536954 -1.9145964 0.07667319 381s 381s , , 1, 2, 1 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.6888744 0.8835670 0.07474311 -1.012417 -2.2309244 381s [2,] -0.3056343 0.2124523 -1.67399869 1.310477 0.7927635 381s 381s , , 2, 2, 1 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.4605972 -0.8995181 -0.80537324 -0.8127535 -0.06055193 381s [2,] -0.6757943 0.4972475 0.09451003 0.9750504 -0.50655995 381s 381s , , 1, 3, 1 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.3400059 1.8128928 0.7341105 0.6316314 0.944529 381s [2,] 0.2744991 0.8242147 -0.1377282 -1.3227240 -1.086170 381s 381s , , 2, 3, 1 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 1.004712 0.6011503 0.9578005 1.2750765 0.1063853 381s [2,] 1.233143 -0.1252803 0.4062820 -0.0449864 -0.3107619 381s 381s , , 1, 1, 2 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.3765514 0.9475483 -0.3644304 -1.4059050 -1.163764 381s [2,] -0.5754314 -1.2223459 0.7700514 -0.2438532 -1.241059 381s 381s , , 2, 1, 2 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.1925301 -0.4369719 -2.0351162 1.683047 -0.06070507 381s [2,] 1.3538781 0.2187095 0.3870477 -2.399088 1.99051402 381s 381s , , 1, 2, 2 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.3442121 1.121962 -0.2164293 0.02356194 -1.367544 381s [2,] -0.6138355 -3.011622 -0.1302661 -1.71615896 -1.055192 381s 381s , , 2, 2, 2 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.4971773 -0.5085932 0.7124882 1.863717 0.3616040 381s [2,] -0.6028935 1.3156760 0.2127373 1.447884 0.3875377 381s 381s , , 1, 3, 2 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] -0.832771 -1.341818 0.6410505 -0.8590950 -1.4214650 381s [2,] -1.676125 -1.501852 0.4983737 0.8741259 -0.2354345 381s 381s , , 2, 3, 2 381s 381s c 381s b [,1] [,2] [,3] [,4] [,5] 381s [1,] 0.4488534 0.6525507 0.6579515 0.5440174 0.5178252 381s [2,] -0.8388363 0.4649224 0.7277738 0.1535633 -0.3644996 381s 381s b c a d e 381s 2 5 2 3 2 381s > # Orthogonalitaet: 381s > checker( SVD$v %e% SVD$v[[lambda=~"lambda'"]],2*delta.tensor(c(lambda=6))) 381s lambda' 381s lambda [,1] [,2] [,3] [,4] [,5] 381s [1,] 2.000000e+00 -8.068530e-17 1.849481e-16 -3.205782e-17 6.529982e-17 381s [2,] -8.068530e-17 2.000000e+00 1.556311e-16 -1.095372e-16 5.509961e-17 381s [3,] 1.849481e-16 1.556311e-16 2.000000e+00 1.003519e-16 3.732088e-16 381s [4,] -3.205782e-17 -1.095372e-16 1.003519e-16 2.000000e+00 -3.926857e-16 381s [5,] 6.529982e-17 5.509961e-17 3.732088e-16 -3.926857e-16 2.000000e+00 381s [6,] -1.465988e-16 -4.046449e-17 -1.065618e-16 2.088671e-16 -2.251822e-16 381s lambda' 381s lambda [,6] 381s [1,] -1.465988e-16 381s [2,] -4.046449e-17 381s [3,] -1.065618e-16 381s [4,] 2.088671e-16 381s [5,] -2.251822e-16 381s [6,] 2.000000e+00 381s lambda lambda' 381s 6 6 381s > checker( SVD$u %e% SVD$u[[lambda=~"lambda'"]],2*delta.tensor(c(lambda=6))) 381s lambda' 381s lambda [,1] [,2] [,3] [,4] [,5] 381s [1,] 2.000000e+00 -2.011960e-16 -1.707926e-16 -3.719510e-17 -2.661438e-16 381s [2,] -2.011960e-16 2.000000e+00 -4.103563e-16 9.607785e-17 -6.920406e-18 381s [3,] -1.707926e-16 -4.103563e-16 2.000000e+00 -3.744869e-16 1.859334e-16 381s [4,] -3.719510e-17 9.607785e-17 -3.744869e-16 2.000000e+00 1.102613e-18 381s [5,] -2.661438e-16 -6.920406e-18 1.859334e-16 1.102613e-18 2.000000e+00 381s [6,] 3.712727e-16 1.283856e-16 -5.368854e-17 -1.403044e-16 -3.691432e-16 381s lambda' 381s lambda [,6] 381s [1,] 3.712727e-16 381s [2,] 1.283856e-16 381s [3,] -5.368854e-17 381s [4,] -1.403044e-16 381s [5,] -3.691432e-16 381s [6,] 2.000000e+00 381s lambda lambda' 381s 6 6 381s > checker( SVD$u %e% mark(SVD$u,"'",c("a","d")),2*delta.tensor(c(a=2,d=3))) 381s , , 1, 1 381s 381s d 381s a [,1] [,2] [,3] 381s [1,] 2.000000e+00 -4.527707e-16 -2.410320e-16 381s [2,] 2.326819e-16 2.931997e-16 -2.419673e-16 381s 381s , , 2, 1 381s 381s d 381s a [,1] [,2] [,3] 381s [1,] 2.326819e-16 6.409928e-16 3.941615e-16 381s [2,] 2.000000e+00 -6.627845e-17 -4.447845e-16 381s 381s , , 1, 2 381s 381s d 381s a [,1] [,2] [,3] 381s [1,] -4.527707e-16 2.000000e+00 5.519342e-16 381s [2,] 6.409928e-16 -4.548529e-16 -1.401522e-16 381s 381s , , 2, 2 381s 381s d 381s a [,1] [,2] [,3] 381s [1,] 2.931997e-16 -4.548529e-16 6.149999e-16 381s [2,] -6.627845e-17 2.000000e+00 -7.896845e-17 381s 381s , , 1, 3 381s 381s d 381s a [,1] [,2] [,3] 381s [1,] -2.410320e-16 5.519342e-16 2.00000e+00 381s [2,] 3.941615e-16 6.149999e-16 -5.91041e-17 381s 381s , , 2, 3 381s 381s d 381s a [,1] [,2] [,3] 381s [1,] -2.419673e-16 -1.401522e-16 -5.91041e-17 381s [2,] -4.447845e-16 -7.896845e-17 2.00000e+00 381s 381s a d a' d' 381s 2 3 2 3 381s > 381s > 381s > # power.tensor 381s > A <- to.tensor(rnorm(120),c(a=2,b=2,c=5,d=3,e=2)) 381s > AAt <- A %e% mark(A,"'",c("a","b")) 381s > 381s > checker(power.tensor(AAt,c("a","b"),c("a'","b'"),-1),inv.tensor(AAt,c("a","b"))) 381s , , 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 0.029776814 -0.0057611829 381s [2,] -0.003357243 -0.0002404374 381s 381s , , 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] -0.003357243 -0.014490212 381s [2,] 0.036252940 0.003610196 381s 381s , , 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] -0.005761183 0.057998097 381s [2,] -0.014490212 -0.008216186 381s 381s , , 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] -0.0002404374 -0.008216186 381s [2,] 0.0036101963 0.037018942 381s 381s a b a' b' 381s 2 2 2 2 381s > checker(power.tensor(AAt,c("a","b"),c("a'","b'"),2), 381s + mul.tensor(AAt,c("a","b"),AAt,c("a'","b'"))) 381s , , 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 1283.5851 315.59043 381s [2,] 380.0011 63.26164 381s 381s , , 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 380.0011 444.64969 381s [2,] 1084.2964 -37.41947 381s 381s , , 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 315.5904 517.2407 381s [2,] 444.6497 174.4848 381s 381s , , 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 63.26164 174.4848 381s [2,] -37.41947 798.2598 381s 381s a b a' b' 381s 2 2 2 2 381s > 381s > checker(power.tensor(power.tensor(AAt,c("a","b"),c("a'","b'"),1/pi), 381s + c("a","b"),c("a'","b'"),pi),AAt) 381s , , 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 35.111935 4.882610 381s [2,] 5.122266 0.812186 381s 381s , , 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 5.122266 8.195341 381s [2,] 31.455015 -1.215398 381s 381s , , 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 4.882610 20.30414 381s [2,] 8.195341 3.73889 381s 381s , , 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 0.812186 3.73889 381s [2,] -1.215398 27.96683 381s 381s a b a' b' 381s 2 2 2 2 381s > 381s > 381s > AAt <- einstein.tensor(A , mark(A,"'",c("a","b")),by="e") 381s > 381s > checker(power.tensor(AAt,c("a","b"),c("a'","b'"),-1,by="e"), 381s + inv.tensor(AAt,c("a","b"),by="e")) 381s , , 1, 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 0.071705710 -0.03510685 381s [2,] 0.002243432 0.01581457 381s 381s , , 2, 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 0.002243432 -0.025451260 381s [2,] 0.118310356 -0.007846876 381s 381s , , 1, 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] -0.03510685 0.12372711 381s [2,] -0.02545126 -0.02939372 381s 381s , , 2, 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 0.015814566 -0.02939372 381s [2,] -0.007846876 0.07902494 381s 381s , , 1, 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 0.05905232 0.007024127 381s [2,] -0.01577288 -0.014094059 381s 381s , , 2, 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] -0.01577288 -0.03519319 381s [2,] 0.05916315 0.01658679 381s 381s , , 1, 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 0.007024127 0.12435313 381s [2,] -0.035193187 -0.01272061 381s 381s , , 2, 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] -0.01409406 -0.01272061 381s [2,] 0.01658679 0.08002825 381s 381s a b a' b' e 381s 2 2 2 2 2 381s > checker(power.tensor(AAt,c("a","b"),c("a'","b'"),2,by="e"), 381s + mul.tensor(AAt,c("a","b"),AAt,c("a'","b'"),by="e")) 381s , , 1, 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 292.14163 114.69087 381s [2,] 21.32936 -33.97464 381s 381s , , 2, 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 21.32936 55.54338 381s [2,] 91.36279 46.91888 381s 381s , , 1, 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 114.69087 148.6765 381s [2,] 55.54338 79.7332 381s 381s , , 2, 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] -33.97464 79.7332 381s [2,] 46.91888 223.0088 381s 381s , , 1, 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 376.1259 41.56311 381s [2,] 184.5156 64.78743 381s 381s , , 2, 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 184.5156 186.27286 381s [2,] 563.8173 -91.12751 381s 381s , , 1, 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 41.56311 127.739594 381s [2,] 186.27286 -5.607508 381s 381s , , 2, 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 64.78743 -5.607508 381s [2,] -91.12751 199.254576 381s 381s a b a' b' e 381s 2 2 2 2 2 381s > 381s > checker(power.tensor(power.tensor(AAt,c("a","b"),c("a'","b'"),1/pi,by="e"), 381s + c("a","b"),c("a'","b'"),pi,by="e"),AAt) 381s , , 1, 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 16.4323449 4.389979 381s [2,] 0.5264515 -1.603311 381s 381s , , 2, 1, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 0.5264515 2.418997 381s [2,] 9.0751998 1.695537 381s 381s , , 1, 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] 4.389979 10.611578 381s [2,] 2.418997 3.308699 381s 381s , , 2, 2, 1 381s 381s b 381s a [,1] [,2] 381s [1,] -1.603311 3.308699 381s [2,] 1.695537 14.374137 381s 381s , , 1, 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 18.679590 0.4926303 381s [2,] 4.595814 2.4154973 381s 381s , , 2, 1, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 4.595814 5.776345 381s [2,] 22.379815 -2.910934 381s 381s , , 1, 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 0.4926303 9.6925583 381s [2,] 5.7763447 0.4301909 381s 381s , , 2, 2, 2 381s 381s b 381s a [,1] [,2] 381s [1,] 2.415497 0.4301909 381s [2,] -2.910934 13.5926946 381s 381s a b a' b' e 381s 2 2 2 2 2 381s > 381s > 381s > # to.matrix.tensor # 381s > A <- reorder.tensor(to.tensor(1:30,c(a=2,b=3,c=5)),c("c","a","b")) 381s > 381s > checker(to.matrix.tensor(A,"a",c("b","c")),matrix(1:30,nrow=2)) 381s 381s [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] 381s [1,] 1 3 5 7 9 11 13 15 17 19 21 23 25 381s [2,] 2 4 6 8 10 12 14 16 18 20 22 24 26 381s 381s [,14] [,15] 381s [1,] 27 29 381s [2,] 28 30 381s > 381s > checker(to.matrix.tensor(A,c("a","b"),c("c")),matrix(1:30,nrow=6)) 381s 381s [,1] [,2] [,3] [,4] [,5] 381s [1,] 1 7 13 19 25 381s [2,] 2 8 14 20 26 381s [3,] 3 9 15 21 27 381s [4,] 4 10 16 22 28 381s [5,] 5 11 17 23 29 381s [6,] 6 12 18 24 30 381s > 381s > checker(to.matrix.tensor(A,c("a","b"),by=c("c")),structure(1:30,dim=c(6,1,5))) 381s , , 1 381s 381s 381s [,1] 381s [1,] 1 381s [2,] 2 381s [3,] 3 381s [4,] 4 381s [5,] 5 381s [6,] 6 381s 381s , , 2 381s 381s 381s [,1] 381s [1,] 7 381s [2,] 8 381s [3,] 9 381s [4,] 10 381s [5,] 11 381s [6,] 12 381s 381s , , 3 381s 381s 381s [,1] 381s [1,] 13 381s [2,] 14 381s [3,] 15 381s [4,] 16 381s [5,] 17 381s [6,] 18 381s 381s , , 4 381s 381s 381s [,1] 381s [1,] 19 381s [2,] 20 381s [3,] 21 381s [4,] 22 381s [5,] 23 381s [6,] 24 381s 381s , , 5 381s 381s 381s [,1] 381s [1,] 25 381s [2,] 26 381s [3,] 27 381s [4,] 28 381s [5,] 29 381s [6,] 30 381s 381s > checker(to.matrix.tensor(A,c("a"),by=c("c")),structure(1:30,dim=c(2,3,5))) 381s , , 1 381s 381s 381s [,1] [,2] [,3] 381s [1,] 1 3 5 381s [2,] 2 4 6 381s 381s , , 2 381s 381s 381s [,1] [,2] [,3] 381s [1,] 7 9 11 381s [2,] 8 10 12 381s 381s , , 3 381s 381s 381s [,1] [,2] [,3] 381s [1,] 13 15 17 381s [2,] 14 16 18 381s 381s , , 4 381s 381s 381s [,1] [,2] [,3] 381s [1,] 19 21 23 381s [2,] 20 22 24 381s 381s , , 5 381s 381s 381s [,1] [,2] [,3] 381s [1,] 25 27 29 381s [2,] 26 28 30 381s 381s > 381s > # untensor 381s > 381s > A <- reorder.tensor(to.tensor(1:30,c(a=2,b=3,c=5)),c("c","a","b")) 381s > 381s > checker(untensor(A,c("a","b"),pos=1),to.tensor(1:30,c(I1=6,c=5))) 381s c 381s I1 [,1] [,2] [,3] [,4] [,5] 381s [1,] 1 7 13 19 25 381s [2,] 2 8 14 20 26 381s [3,] 3 9 15 21 27 381s [4,] 4 10 16 22 28 381s [5,] 5 11 17 23 29 381s [6,] 6 12 18 24 30 381s I1 c 381s 6 5 381s > checker(untensor(A,c("a","b"),"new",pos=2),reorder(to.tensor(1:30,c(new=6,c=5)),2:1)) 381s new 381s c [,1] [,2] [,3] [,4] [,5] [,6] 381s [1,] 1 2 3 4 5 6 381s [2,] 7 8 9 10 11 12 381s [3,] 13 14 15 16 17 18 381s [4,] 19 20 21 22 23 24 381s [5,] 25 26 27 28 29 30 381s c new 381s 5 6 381s > checker(untensor(A,list(u=c("a","b"),v=c(c="c"))),to.tensor(1:30,c(u=6,v=5))) 381s u 381s v [,1] [,2] [,3] [,4] [,5] [,6] 381s [1,] 1 2 3 4 5 6 381s [2,] 7 8 9 10 11 12 381s [3,] 13 14 15 16 17 18 381s [4,] 19 20 21 22 23 24 381s [5,] 25 26 27 28 29 30 381s v u 381s 5 6 381s > 381s > 381s > # as.tensor 381s > 381s > checker(as.tensor(diag(5)),to.tensor(c(diag(5)),c(I1=5,I2=5))) 381s I2 381s I1 [,1] [,2] [,3] [,4] [,5] 381s [1,] 1 0 0 0 0 381s [2,] 0 1 0 0 0 381s [3,] 0 0 1 0 0 381s [4,] 0 0 0 1 0 381s [5,] 0 0 0 0 1 381s I1 I2 381s 5 5 381s > 381s > # Slice tensor 381s > 381s > A <- reorder.tensor(to.tensor(1:30,c(a=2,b=3,c=5)),c("c","a","b")) 381s > checker(slice.tensor(A,"c",1:2),to.tensor(1:12,c(a=2,b=3,c=2))) 381s , , 1 381s 381s a 381s c [,1] [,2] 381s [1,] 1 2 381s [2,] 7 8 381s 381s , , 2 381s 381s a 381s c [,1] [,2] 381s [1,] 3 4 381s [2,] 9 10 381s 381s , , 3 381s 381s a 381s c [,1] [,2] 381s [1,] 5 6 381s [2,] 11 12 381s 381s c a b 381s 2 2 3 381s > checker(slice.tensor(A,"c",1,drop=TRUE),to.tensor(1:6,c(a=2,b=3))) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 3 5 381s [2,] 2 4 6 381s a b 381s 2 3 381s > checker(slice.tensor(A,"c",1,drop=FALSE),to.tensor(1:6,c(a=2,b=3,c=1))) 381s , , 1 381s 381s a 381s c [,1] [,2] 381s [1,] 1 2 381s 381s , , 2 381s 381s a 381s c [,1] [,2] 381s [1,] 3 4 381s 381s , , 3 381s 381s a 381s c [,1] [,2] 381s [1,] 5 6 381s 381s c a b 381s 1 2 3 381s > 381s > # Indexing with [[]] 381s > 381s > A <- reorder.tensor(to.tensor(1:30,c(a=2,b=3,c=5)),c("c","a","b")) 381s > checker(A[[b=2]],slice.tensor(A,"b",2,drop=TRUE)) 381s a 381s c [,1] [,2] 381s [1,] 3 4 381s [2,] 9 10 381s [3,] 15 16 381s [4,] 21 22 381s [5,] 27 28 381s c a 381s 5 2 381s > checker(A[[b=2:3]],slice.tensor(A,"b",2:3)) 381s , , 1 381s 381s a 381s c [,1] [,2] 381s [1,] 3 4 381s [2,] 9 10 381s [3,] 15 16 381s [4,] 21 22 381s [5,] 27 28 381s 381s , , 2 381s 381s a 381s c [,1] [,2] 381s [1,] 5 6 381s [2,] 11 12 381s [3,] 17 18 381s [4,] 23 24 381s [5,] 29 30 381s 381s c a b 381s 5 2 2 381s > checker(A[[b=2:3,c=3:4]],slice.tensor(slice.tensor(A,"b",2:3),"c",3:4)) 381s , , 1 381s 381s a 381s c [,1] [,2] 381s [1,] 15 16 381s [2,] 21 22 381s 381s , , 2 381s 381s a 381s c [,1] [,2] 381s [1,] 17 18 381s [2,] 23 24 381s 381s c a b 381s 2 2 2 381s > checker(A[[b=~q]],to.tensor(1:30,c(a=2,q=3,c=5))) 381s , , 1 381s 381s a 381s c [,1] [,2] 381s [1,] 1 2 381s [2,] 7 8 381s [3,] 13 14 381s [4,] 19 20 381s [5,] 25 26 381s 381s , , 2 381s 381s a 381s c [,1] [,2] 381s [1,] 3 4 381s [2,] 9 10 381s [3,] 15 16 381s [4,] 21 22 381s [5,] 27 28 381s 381s , , 3 381s 381s a 381s c [,1] [,2] 381s [1,] 5 6 381s [2,] 11 12 381s [3,] 17 18 381s [4,] 23 24 381s [5,] 29 30 381s 381s c a q 381s 5 2 3 381s > 381s > #undrop.tensor 381s > 381s > checker(undrop.tensor(slice.tensor(A,"c",2,drop=TRUE),"c"), 381s + slice.tensor(A,"c",2,drop=FALSE)) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 7 9 11 381s [2,] 8 10 12 381s 381s a b c 381s 2 3 1 381s > 381s > # bind.tensor 381s > 381s > A <- to.tensor(1:6,c(a=2,b=3)) 381s > checker( bind.tensor(A,"a",A), to.tensor(c(1,2,1,2,3,4,3,4,5,6,5,6),c(a=4,b=3))) 381s a 381s b [,1] [,2] [,3] [,4] 381s [1,] 1 2 1 2 381s [2,] 3 4 3 4 381s [3,] 5 6 5 6 381s b a 381s 3 4 381s > checker( bind.tensor(A,"b",A), to.tensor(c(1:6,1:6),c(a=2,b=6))) 381s b 381s a [,1] [,2] [,3] [,4] [,5] [,6] 381s [1,] 1 3 5 1 3 5 381s [2,] 2 4 6 2 4 6 381s a b 381s 2 6 381s > 381s > 381s > 381s > 381s > # einstein.tensor 381s > A <- to.tensor(1:6,c(a=2,b=3)) 381s > checker( einstein.tensor(A,A), mul.tensor(A,c("a","b"),A)) 381s [1] 91 381s > checker( einstein.tensor(A,A,by="b"), mul.tensor(A,c("a"),A,by="b")) 381s [1] 5 25 61 381s b 381s 3 381s > checker( einstein.tensor(A,diag=A,by="b"), diagmul.tensor(A,c("a"),A,by="b")) 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 9 25 381s [2,] 4 16 36 381s a b 381s 2 3 381s > 381s > 381s > # adding 381s > A <- to.tensor(1:30,c(a=2,b=3,c=5)) 381s > 381s > checker(A + reorder(A,c("b","a","c")),2*A) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 2 6 10 381s [2,] 4 8 12 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 14 18 22 381s [2,] 16 20 24 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 50 54 58 381s [2,] 52 56 60 381s 381s a b c 381s 2 3 5 381s > checker(A - reorder(A,c("b","a","c")),to.tensor(rep(0,30),c(a=2,b=3,c=5))) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 0 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 0 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 0 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 0 381s 381s , , 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 0 0 0 381s [2,] 0 0 0 381s 381s a b c 381s 2 3 5 381s > 381s > B <- to.tensor(rnorm(6),c(b=3,a=2)) 381s > 381s > checker( A + B , rep.tensor(B,5,name="c") + A ) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] -0.8562447 3.055444 4.462506 381s [2,] 0.3844367 5.017177 6.275817 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 5.143755 9.055444 10.46251 381s [2,] 6.384437 11.017177 12.27582 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 11.14376 15.05544 16.46251 381s [2,] 12.38444 17.01718 18.27582 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 17.14376 21.05544 22.46251 381s [2,] 18.38444 23.01718 24.27582 381s 381s , , 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 23.14376 27.05544 28.46251 381s [2,] 24.38444 29.01718 30.27582 381s 381s a b c 381s 2 3 5 381s > checker( B + A , rep.tensor(B,5,name="c") + A ) 381s , , 1 381s 381s a 381s b [,1] [,2] 381s [1,] -0.8562447 0.3844367 381s [2,] 3.0554444 5.0171771 381s [3,] 4.4625059 6.2758165 381s 381s , , 2 381s 381s a 381s b [,1] [,2] 381s [1,] 5.143755 6.384437 381s [2,] 9.055444 11.017177 381s [3,] 10.462506 12.275817 381s 381s , , 3 381s 381s a 381s b [,1] [,2] 381s [1,] 11.14376 12.38444 381s [2,] 15.05544 17.01718 381s [3,] 16.46251 18.27582 381s 381s , , 4 381s 381s a 381s b [,1] [,2] 381s [1,] 17.14376 18.38444 381s [2,] 21.05544 23.01718 381s [3,] 22.46251 24.27582 381s 381s , , 5 381s 381s a 381s b [,1] [,2] 381s [1,] 23.14376 24.38444 381s [2,] 27.05544 29.01718 381s [3,] 28.46251 30.27582 381s 381s b a c 381s 3 2 5 381s > checker( A + (B - A), rep.tensor(B,5,name="c") ) 381s , , 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] -1.856245 0.0554444 -0.5374941 381s [2,] -1.615563 1.0171771 0.2758165 381s 381s , , 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] -1.856245 0.0554444 -0.5374941 381s [2,] -1.615563 1.0171771 0.2758165 381s 381s , , 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] -1.856245 0.0554444 -0.5374941 381s [2,] -1.615563 1.0171771 0.2758165 381s 381s , , 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] -1.856245 0.0554444 -0.5374941 381s [2,] -1.615563 1.0171771 0.2758165 381s 381s , , 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] -1.856245 0.0554444 -0.5374941 381s [2,] -1.615563 1.0171771 0.2758165 381s 381s a b c 381s 2 3 5 381s > checker( B + (A - B), A ) 381s , , 1 381s 381s a 381s b [,1] [,2] 381s [1,] 1 2 381s [2,] 3 4 381s [3,] 5 6 381s 381s , , 2 381s 381s a 381s b [,1] [,2] 381s [1,] 7 8 381s [2,] 9 10 381s [3,] 11 12 381s 381s , , 3 381s 381s a 381s b [,1] [,2] 381s [1,] 13 14 381s [2,] 15 16 381s [3,] 17 18 381s 381s , , 4 381s 381s a 381s b [,1] [,2] 381s [1,] 19 20 381s [2,] 21 22 381s [3,] 23 24 381s 381s , , 5 381s 381s a 381s b [,1] [,2] 381s [1,] 25 26 381s [2,] 27 28 381s [3,] 29 30 381s 381s b a c 381s 3 2 5 381s > 381s > C <- to.tensor(1:42,c(a=2,b=3,d=7)) 381s > 381s > checker( A+C , rep.tensor(A,7,name="d") + rep.tensor(C,5,name="c")) 381s , , 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 2 6 10 381s [2,] 4 8 12 381s 381s , , 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 8 12 16 381s [2,] 10 14 18 381s 381s , , 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 14 18 22 381s [2,] 16 20 24 381s 381s , , 4, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 20 24 28 381s [2,] 22 26 30 381s 381s , , 5, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 8 12 16 381s [2,] 10 14 18 381s 381s , , 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 14 18 22 381s [2,] 16 20 24 381s 381s , , 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 20 24 28 381s [2,] 22 26 30 381s 381s , , 4, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 5, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 32 36 40 381s [2,] 34 38 42 381s 381s , , 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 14 18 22 381s [2,] 16 20 24 381s 381s , , 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 20 24 28 381s [2,] 22 26 30 381s 381s , , 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 4, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 32 36 40 381s [2,] 34 38 42 381s 381s , , 5, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 20 24 28 381s [2,] 22 26 30 381s 381s , , 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 32 36 40 381s [2,] 34 38 42 381s 381s , , 4, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 5, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 44 48 52 381s [2,] 46 50 54 381s 381s , , 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 32 36 40 381s [2,] 34 38 42 381s 381s , , 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 4, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 44 48 52 381s [2,] 46 50 54 381s 381s , , 5, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 50 54 58 381s [2,] 52 56 60 381s 381s , , 1, 6 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 32 36 40 381s [2,] 34 38 42 381s 381s , , 2, 6 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 3, 6 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 44 48 52 381s [2,] 46 50 54 381s 381s , , 4, 6 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 50 54 58 381s [2,] 52 56 60 381s 381s , , 5, 6 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 56 60 64 381s [2,] 58 62 66 381s 381s , , 1, 7 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 2, 7 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 44 48 52 381s [2,] 46 50 54 381s 381s , , 3, 7 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 50 54 58 381s [2,] 52 56 60 381s 381s , , 4, 7 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 56 60 64 381s [2,] 58 62 66 381s 381s , , 5, 7 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 62 66 70 381s [2,] 64 68 72 381s 381s a b c d 381s 2 3 5 7 381s > 381s > # Einstein 381s > 381s > checker( C %e% A , einstein.tensor(C,A)) 381s c 381s d [,1] [,2] [,3] [,4] [,5] 381s [1,] 91 217 343 469 595 381s [2,] 217 559 901 1243 1585 381s [3,] 343 901 1459 2017 2575 381s [4,] 469 1243 2017 2791 3565 381s [5,] 595 1585 2575 3565 4555 381s [6,] 721 1927 3133 4339 5545 381s [7,] 847 2269 3691 5113 6535 381s d c 381s 7 5 381s > 381s > # Riemann + drag 381s > checker( C %r% mark(A), mul.tensor(C,c(),mark(A),c())) 381s , , 1, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 1 3 5 381s [2,] 2 4 6 381s 381s , , 2, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 7 9 11 381s [2,] 8 10 12 381s 381s , , 3, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 13 15 17 381s [2,] 14 16 18 381s 381s , , 4, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 19 21 23 381s [2,] 20 22 24 381s 381s , , 5, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 25 27 29 381s [2,] 26 28 30 381s 381s , , 6, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 31 33 35 381s [2,] 32 34 36 381s 381s , , 7, 1, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 37 39 41 381s [2,] 38 40 42 381s 381s , , 1, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 2 6 10 381s [2,] 4 8 12 381s 381s , , 2, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 14 18 22 381s [2,] 16 20 24 381s 381s , , 3, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 30 34 381s [2,] 28 32 36 381s 381s , , 4, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 38 42 46 381s [2,] 40 44 48 381s 381s , , 5, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 50 54 58 381s [2,] 52 56 60 381s 381s , , 6, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 62 66 70 381s [2,] 64 68 72 381s 381s , , 7, 2, 1, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 74 78 82 381s [2,] 76 80 84 381s 381s , , 1, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 3 9 15 381s [2,] 6 12 18 381s 381s , , 2, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 21 27 33 381s [2,] 24 30 36 381s 381s , , 3, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 39 45 51 381s [2,] 42 48 54 381s 381s , , 4, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 57 63 69 381s [2,] 60 66 72 381s 381s , , 5, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 75 81 87 381s [2,] 78 84 90 381s 381s , , 6, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 93 99 105 381s [2,] 96 102 108 381s 381s , , 7, 1, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 111 117 123 381s [2,] 114 120 126 381s 381s , , 1, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 4 12 20 381s [2,] 8 16 24 381s 381s , , 2, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 28 36 44 381s [2,] 32 40 48 381s 381s , , 3, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 52 60 68 381s [2,] 56 64 72 381s 381s , , 4, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 76 84 92 381s [2,] 80 88 96 381s 381s , , 5, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 100 108 116 381s [2,] 104 112 120 381s 381s , , 6, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 124 132 140 381s [2,] 128 136 144 381s 381s , , 7, 2, 2, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 148 156 164 381s [2,] 152 160 168 381s 381s , , 1, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 5 15 25 381s [2,] 10 20 30 381s 381s , , 2, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 35 45 55 381s [2,] 40 50 60 381s 381s , , 3, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 65 75 85 381s [2,] 70 80 90 381s 381s , , 4, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 95 105 115 381s [2,] 100 110 120 381s 381s , , 5, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 125 135 145 381s [2,] 130 140 150 381s 381s , , 6, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 155 165 175 381s [2,] 160 170 180 381s 381s , , 7, 1, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 185 195 205 381s [2,] 190 200 210 381s 381s , , 1, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 6 18 30 381s [2,] 12 24 36 381s 381s , , 2, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 42 54 66 381s [2,] 48 60 72 381s 381s , , 3, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 78 90 102 381s [2,] 84 96 108 381s 381s , , 4, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 114 126 138 381s [2,] 120 132 144 381s 381s , , 5, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 150 162 174 381s [2,] 156 168 180 381s 381s , , 6, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 186 198 210 381s [2,] 192 204 216 381s 381s , , 7, 2, 3, 1 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 222 234 246 381s [2,] 228 240 252 381s 381s , , 1, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 7 21 35 381s [2,] 14 28 42 381s 381s , , 2, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 49 63 77 381s [2,] 56 70 84 381s 381s , , 3, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 91 105 119 381s [2,] 98 112 126 381s 381s , , 4, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 133 147 161 381s [2,] 140 154 168 381s 381s , , 5, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 175 189 203 381s [2,] 182 196 210 381s 381s , , 6, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 217 231 245 381s [2,] 224 238 252 381s 381s , , 7, 1, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 259 273 287 381s [2,] 266 280 294 381s 381s , , 1, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 8 24 40 381s [2,] 16 32 48 381s 381s , , 2, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 56 72 88 381s [2,] 64 80 96 381s 381s , , 3, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 104 120 136 381s [2,] 112 128 144 381s 381s , , 4, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 152 168 184 381s [2,] 160 176 192 381s 381s , , 5, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 200 216 232 381s [2,] 208 224 240 381s 381s , , 6, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 248 264 280 381s [2,] 256 272 288 381s 381s , , 7, 2, 1, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 296 312 328 381s [2,] 304 320 336 381s 381s , , 1, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 9 27 45 381s [2,] 18 36 54 381s 381s , , 2, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 63 81 99 381s [2,] 72 90 108 381s 381s , , 3, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 117 135 153 381s [2,] 126 144 162 381s 381s , , 4, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 171 189 207 381s [2,] 180 198 216 381s 381s , , 5, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 225 243 261 381s [2,] 234 252 270 381s 381s , , 6, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 279 297 315 381s [2,] 288 306 324 381s 381s , , 7, 1, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 333 351 369 381s [2,] 342 360 378 381s 381s , , 1, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 10 30 50 381s [2,] 20 40 60 381s 381s , , 2, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 70 90 110 381s [2,] 80 100 120 381s 381s , , 3, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 130 150 170 381s [2,] 140 160 180 381s 381s , , 4, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 190 210 230 381s [2,] 200 220 240 381s 381s , , 5, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 250 270 290 381s [2,] 260 280 300 381s 381s , , 6, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 310 330 350 381s [2,] 320 340 360 381s 381s , , 7, 2, 2, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 370 390 410 381s [2,] 380 400 420 381s 381s , , 1, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 11 33 55 381s [2,] 22 44 66 381s 381s , , 2, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 77 99 121 381s [2,] 88 110 132 381s 381s , , 3, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 143 165 187 381s [2,] 154 176 198 381s 381s , , 4, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 209 231 253 381s [2,] 220 242 264 381s 381s , , 5, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 275 297 319 381s [2,] 286 308 330 381s 381s , , 6, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 341 363 385 381s [2,] 352 374 396 381s 381s , , 7, 1, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 407 429 451 381s [2,] 418 440 462 381s 381s , , 1, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 12 36 60 381s [2,] 24 48 72 381s 381s , , 2, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 84 108 132 381s [2,] 96 120 144 381s 381s , , 3, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 156 180 204 381s [2,] 168 192 216 381s 381s , , 4, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 228 252 276 381s [2,] 240 264 288 381s 381s , , 5, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 300 324 348 381s [2,] 312 336 360 381s 381s , , 6, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 372 396 420 381s [2,] 384 408 432 381s 381s , , 7, 2, 3, 2 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 444 468 492 381s [2,] 456 480 504 381s 381s , , 1, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 13 39 65 381s [2,] 26 52 78 381s 381s , , 2, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 91 117 143 381s [2,] 104 130 156 381s 381s , , 3, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 169 195 221 381s [2,] 182 208 234 381s 381s , , 4, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 247 273 299 381s [2,] 260 286 312 381s 381s , , 5, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 325 351 377 381s [2,] 338 364 390 381s 381s , , 6, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 403 429 455 381s [2,] 416 442 468 381s 381s , , 7, 1, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 481 507 533 381s [2,] 494 520 546 381s 381s , , 1, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 14 42 70 381s [2,] 28 56 84 381s 381s , , 2, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 98 126 154 381s [2,] 112 140 168 381s 381s , , 3, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 182 210 238 381s [2,] 196 224 252 381s 381s , , 4, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 266 294 322 381s [2,] 280 308 336 381s 381s , , 5, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 350 378 406 381s [2,] 364 392 420 381s 381s , , 6, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 434 462 490 381s [2,] 448 476 504 381s 381s , , 7, 2, 1, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 518 546 574 381s [2,] 532 560 588 381s 381s , , 1, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 15 45 75 381s [2,] 30 60 90 381s 381s , , 2, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 105 135 165 381s [2,] 120 150 180 381s 381s , , 3, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 195 225 255 381s [2,] 210 240 270 381s 381s , , 4, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 285 315 345 381s [2,] 300 330 360 381s 381s , , 5, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 375 405 435 381s [2,] 390 420 450 381s 381s , , 6, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 465 495 525 381s [2,] 480 510 540 381s 381s , , 7, 1, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 555 585 615 381s [2,] 570 600 630 381s 381s , , 1, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 16 48 80 381s [2,] 32 64 96 381s 381s , , 2, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 112 144 176 381s [2,] 128 160 192 381s 381s , , 3, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 208 240 272 381s [2,] 224 256 288 381s 381s , , 4, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 304 336 368 381s [2,] 320 352 384 381s 381s , , 5, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 400 432 464 381s [2,] 416 448 480 381s 381s , , 6, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 496 528 560 381s [2,] 512 544 576 381s 381s , , 7, 2, 2, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 592 624 656 381s [2,] 608 640 672 381s 381s , , 1, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 17 51 85 381s [2,] 34 68 102 381s 381s , , 2, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 119 153 187 381s [2,] 136 170 204 381s 381s , , 3, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 221 255 289 381s [2,] 238 272 306 381s 381s , , 4, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 323 357 391 381s [2,] 340 374 408 381s 381s , , 5, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 425 459 493 381s [2,] 442 476 510 381s 381s , , 6, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 527 561 595 381s [2,] 544 578 612 381s 381s , , 7, 1, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 629 663 697 381s [2,] 646 680 714 381s 381s , , 1, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 18 54 90 381s [2,] 36 72 108 381s 381s , , 2, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 126 162 198 381s [2,] 144 180 216 381s 381s , , 3, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 234 270 306 381s [2,] 252 288 324 381s 381s , , 4, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 342 378 414 381s [2,] 360 396 432 381s 381s , , 5, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 450 486 522 381s [2,] 468 504 540 381s 381s , , 6, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 558 594 630 381s [2,] 576 612 648 381s 381s , , 7, 2, 3, 3 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 666 702 738 381s [2,] 684 720 756 381s 381s , , 1, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 19 57 95 381s [2,] 38 76 114 381s 381s , , 2, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 133 171 209 381s [2,] 152 190 228 381s 381s , , 3, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 247 285 323 381s [2,] 266 304 342 381s 381s , , 4, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 361 399 437 381s [2,] 380 418 456 381s 381s , , 5, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 475 513 551 381s [2,] 494 532 570 381s 381s , , 6, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 589 627 665 381s [2,] 608 646 684 381s 381s , , 7, 1, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 703 741 779 381s [2,] 722 760 798 381s 381s , , 1, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 20 60 100 381s [2,] 40 80 120 381s 381s , , 2, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 140 180 220 381s [2,] 160 200 240 381s 381s , , 3, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 260 300 340 381s [2,] 280 320 360 381s 381s , , 4, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 380 420 460 381s [2,] 400 440 480 381s 381s , , 5, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 500 540 580 381s [2,] 520 560 600 381s 381s , , 6, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 620 660 700 381s [2,] 640 680 720 381s 381s , , 7, 2, 1, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 740 780 820 381s [2,] 760 800 840 381s 381s , , 1, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 21 63 105 381s [2,] 42 84 126 381s 381s , , 2, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 147 189 231 381s [2,] 168 210 252 381s 381s , , 3, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 273 315 357 381s [2,] 294 336 378 381s 381s , , 4, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 399 441 483 381s [2,] 420 462 504 381s 381s , , 5, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 525 567 609 381s [2,] 546 588 630 381s 381s , , 6, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 651 693 735 381s [2,] 672 714 756 381s 381s , , 7, 1, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 777 819 861 381s [2,] 798 840 882 381s 381s , , 1, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 22 66 110 381s [2,] 44 88 132 381s 381s , , 2, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 154 198 242 381s [2,] 176 220 264 381s 381s , , 3, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 286 330 374 381s [2,] 308 352 396 381s 381s , , 4, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 418 462 506 381s [2,] 440 484 528 381s 381s , , 5, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 550 594 638 381s [2,] 572 616 660 381s 381s , , 6, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 682 726 770 381s [2,] 704 748 792 381s 381s , , 7, 2, 2, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 814 858 902 381s [2,] 836 880 924 381s 381s , , 1, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 23 69 115 381s [2,] 46 92 138 381s 381s , , 2, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 161 207 253 381s [2,] 184 230 276 381s 381s , , 3, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 299 345 391 381s [2,] 322 368 414 381s 381s , , 4, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 437 483 529 381s [2,] 460 506 552 381s 381s , , 5, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 575 621 667 381s [2,] 598 644 690 381s 381s , , 6, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 713 759 805 381s [2,] 736 782 828 381s 381s , , 7, 1, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 851 897 943 381s [2,] 874 920 966 381s 381s , , 1, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 24 72 120 381s [2,] 48 96 144 381s 381s , , 2, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 168 216 264 381s [2,] 192 240 288 381s 381s , , 3, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 312 360 408 381s [2,] 336 384 432 381s 381s , , 4, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 456 504 552 381s [2,] 480 528 576 381s 381s , , 5, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 600 648 696 381s [2,] 624 672 720 381s 381s , , 6, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 744 792 840 381s [2,] 768 816 864 381s 381s , , 7, 2, 3, 4 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 888 936 984 381s [2,] 912 960 1008 381s 381s , , 1, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 25 75 125 381s [2,] 50 100 150 381s 381s , , 2, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 175 225 275 381s [2,] 200 250 300 381s 381s , , 3, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 325 375 425 381s [2,] 350 400 450 381s 381s , , 4, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 475 525 575 381s [2,] 500 550 600 381s 381s , , 5, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 625 675 725 381s [2,] 650 700 750 381s 381s , , 6, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 775 825 875 381s [2,] 800 850 900 381s 381s , , 7, 1, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 925 975 1025 381s [2,] 950 1000 1050 381s 381s , , 1, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 26 78 130 381s [2,] 52 104 156 381s 381s , , 2, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 182 234 286 381s [2,] 208 260 312 381s 381s , , 3, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 338 390 442 381s [2,] 364 416 468 381s 381s , , 4, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 494 546 598 381s [2,] 520 572 624 381s 381s , , 5, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 650 702 754 381s [2,] 676 728 780 381s 381s , , 6, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 806 858 910 381s [2,] 832 884 936 381s 381s , , 7, 2, 1, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 962 1014 1066 381s [2,] 988 1040 1092 381s 381s , , 1, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 27 81 135 381s [2,] 54 108 162 381s 381s , , 2, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 189 243 297 381s [2,] 216 270 324 381s 381s , , 3, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 351 405 459 381s [2,] 378 432 486 381s 381s , , 4, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 513 567 621 381s [2,] 540 594 648 381s 381s , , 5, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 675 729 783 381s [2,] 702 756 810 381s 381s , , 6, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 837 891 945 381s [2,] 864 918 972 381s 381s , , 7, 1, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 999 1053 1107 381s [2,] 1026 1080 1134 381s 381s , , 1, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 28 84 140 381s [2,] 56 112 168 381s 381s , , 2, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 196 252 308 381s [2,] 224 280 336 381s 381s , , 3, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 364 420 476 381s [2,] 392 448 504 381s 381s , , 4, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 532 588 644 381s [2,] 560 616 672 381s 381s , , 5, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 700 756 812 381s [2,] 728 784 840 381s 381s , , 6, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 868 924 980 381s [2,] 896 952 1008 381s 381s , , 7, 2, 2, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 1036 1092 1148 381s [2,] 1064 1120 1176 381s 381s , , 1, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 29 87 145 381s [2,] 58 116 174 381s 381s , , 2, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 203 261 319 381s [2,] 232 290 348 381s 381s , , 3, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 377 435 493 381s [2,] 406 464 522 381s 381s , , 4, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 551 609 667 381s [2,] 580 638 696 381s 381s , , 5, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 725 783 841 381s [2,] 754 812 870 381s 381s , , 6, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 899 957 1015 381s [2,] 928 986 1044 381s 381s , , 7, 1, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 1073 1131 1189 381s [2,] 1102 1160 1218 381s 381s , , 1, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 30 90 150 381s [2,] 60 120 180 381s 381s , , 2, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 210 270 330 381s [2,] 240 300 360 381s 381s , , 3, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 390 450 510 381s [2,] 420 480 540 381s 381s , , 4, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 570 630 690 381s [2,] 600 660 720 381s 381s , , 5, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 750 810 870 381s [2,] 780 840 900 381s 381s , , 6, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 930 990 1050 381s [2,] 960 1020 1080 381s 381s , , 7, 2, 3, 5 381s 381s b 381s a [,1] [,2] [,3] 381s [1,] 1110 1170 1230 381s [2,] 1140 1200 1260 381s 381s a b d a' b' c' 381s 2 3 7 2 3 5 381s > 381s > A <- to.tensor(1:16,c(a=2,b=2,c=2,d=2)) 381s > gij <- to.tensor(c(1,0.5,0.5,1),c(i=2,j=2)) 381s > 381s > ginv <- c(solve(matrix(c(1,0.5,0.5,1),2))) 381s > gij1 <- to.tensor(ginv,c("^a"=2,a=2)) 381s > gij2 <- to.tensor(ginv ,c("^b"=2,b=2)) 381s > is.covariate(gij) 381s [1] TRUE TRUE 381s > 381s > checker( drag.tensor(gij,gij,c("i")) , to.tensor(c(1,0,0,1),c("^i"=2,"j"=2))) 381s ^i 381s j [,1] [,2] 381s [1,] 1 0 381s [2,] 0 1 381s j ^i 381s 2 2 381s > checker( drag.tensor(gij,gij,c("j")) , to.tensor(c(1,0,0,1),c("i"=2,"^j"=2))) 381s ^j 381s i [,1] [,2] 381s [1,] 1 0 381s [2,] 0 1 381s i ^j 381s 2 2 381s > checker( drag.tensor(gij,gij,c("i","j")), to.tensor(ginv,c("^i"=2,"^j"=2))) 381s ^j 381s ^i [,1] [,2] 381s [1,] 1.3333333 -0.6666667 381s [2,] -0.6666667 1.3333333 381s ^i ^j 381s 2 2 381s > checker( drag.tensor(gij,gij,c("i","j"))[["^i"=~a,"^j"=~b]], riemann.tensor(gij[[i=~a,j=~b]],gij1,gij2)) 381s b 381s a [,1] [,2] 381s [1,] 1.3333333 -0.6666667 381s [2,] -0.6666667 1.3333333 381s a b 381s 2 2 381s > 381s > checker( drag.tensor(A,gij,c("a","b")), einstein.tensor(A,gij1,gij2) ) 381s , , 1, 1 381s 381s d 381s c [,1] [,2] 381s [1,] -0.8888889 2.666667 381s [2,] 0.8888889 4.444444 381s 381s , , 2, 1 381s 381s d 381s c [,1] [,2] 381s [1,] 0.4444444 4.000000 381s [2,] 2.2222222 5.777778 381s 381s , , 1, 2 381s 381s d 381s c [,1] [,2] 381s [1,] 1.777778 5.333333 381s [2,] 3.555556 7.111111 381s 381s , , 2, 2 381s 381s d 381s c [,1] [,2] 381s [1,] 3.111111 6.666667 381s [2,] 4.888889 8.444444 381s 381s c d ^a ^b 381s 2 2 2 2 381s > ########################################################################### 381s > ### Names 381s > 381s > 381s > 381s > 381s > 381s > 381s > ########################################################################## 381s > 381s > # 381s > I <- to.tensor(diag(3),c(a=3,b=3),nn(a=3,b=3),what=1:2) 381s > checker(to.tensor(I),I) 381s b 381s a b1 b2 b3 381s a1 1 0 0 381s a2 0 1 0 381s a3 0 0 1 381s a b 381s 3 3 381s > checker(as.tensor(I),I) 381s b 381s a b1 b2 b3 381s a1 1 0 0 381s a2 0 1 0 381s a3 0 0 1 381s a b 381s 3 3 381s > checker(inv.tensor(I,"a","b"),I) 381s b 381s a b1 b2 b3 381s a1 1 0 0 381s a2 0 1 0 381s a3 0 0 1 381s a b 381s 3 3 381s > 381s > R1 <- matrix(rnorm(9),nrow=3) 381s > R1i <- solve(R1) 381s > R2 <- to.tensor(R1,c(a=3,b=3),nn(a=3,b=3),what=1:2) 381s > R2i <- to.tensor(R1i,c(b=3,a=3),nn(b=3,a=3),what=1:2) 381s > 381s > checker(inv.tensor(R2,"a","b"),R2i) 381s b 381s a b1 b2 b3 381s a1 1.3545115 -1.536721 1.581124 381s a2 0.6374175 9.477398 -6.440188 381s a3 -1.8180201 -45.234574 29.223512 381s a b 381s 3 3 381s > checker(inv.tensor(R2,"a","b",allowSingular=TRUE),R2i) 381s b 381s a b1 b2 b3 381s a1 1.3545115 -1.536721 1.581124 381s a2 0.6374175 9.477398 -6.440188 381s a3 -1.8180201 -45.234574 29.223512 381s a b 381s 3 3 381s > 381s > 381s > R3 <- to.tensor(rnorm(15),c(a=3,z=5),nn(a=3,z=5)) 381s > 381s > checker(mul.tensor(R2i,"b",mul.tensor(R2,"a",R3)),R3) 381s z 381s a z1 z2 z3 z4 z5 381s a1 -0.8953954 1.134311 -2.1651420 0.7238549 -0.01731484 381s a2 -0.3222050 -0.826831 1.5151313 -1.3050957 -0.59587376 381s a3 0.3591246 -1.437899 -0.4997368 -0.2023622 -1.64688035 381s a z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a"),mul.tensor(R2,"a",R3[[z=1]])) 381s b 381s b1 b2 b3 381s -0.7217544 0.1469166 0.1947976 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a"),mul.tensor(R2,"a",R3)) 381s z 381s b z1 z2 z3 z4 z5 381s b1 -0.7217544 -0.479997 0.2465513 -0.9341408 -0.9015859 381s b2 0.1469166 2.096782 -2.7411728 2.2971945 1.5172076 381s b3 0.1947976 3.166509 -4.2447767 3.4907497 2.2360166 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a",allowSingular=TRUE),mul.tensor(R2,"a",R3[[z=1]])) 381s b 381s b1 b2 b3 381s -0.7217544 0.1469166 0.1947976 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a",allowSingular=TRUE),mul.tensor(R2,"a",R3)) 381s z 381s b z1 z2 z3 z4 z5 381s b1 -0.7217544 -0.479997 0.2465513 -0.9341408 -0.9015859 381s b2 0.1469166 2.096782 -2.7411728 2.2971945 1.5172076 381s b3 0.1947976 3.166509 -4.2447767 3.4907497 2.2360166 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s b1 -0.7217544 -0.7217544 -0.7217544 -0.7217544 381s b2 0.1469166 0.1469166 0.1469166 0.1469166 381s b3 0.1947976 0.1947976 0.1947976 0.1947976 381s b K 381s 3 4 381s > checker(solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s b1 -0.7217544 -0.7217544 -0.7217544 -0.7217544 381s b2 0.1469166 0.1469166 0.1469166 0.1469166 381s b3 0.1947976 0.1947976 0.1947976 0.1947976 381s b K 381s 3 4 381s > checker(solve.tensor(R2i,rep(R3[[z=1]],4,1,"K"),"a",by="K"),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s b1 -0.7217544 -0.7217544 -0.7217544 -0.7217544 381s b2 0.1469166 0.1469166 0.1469166 0.1469166 381s b3 0.1947976 0.1947976 0.1947976 0.1947976 381s b K 381s 3 4 381s > 381s > checker(solve.tensor(rep(R2i,4,1,"K"),R3[[z=1]],"a",by="K",allowSingular=TRUE),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s b1 -0.7217544 -0.7217544 -0.7217544 -0.7217544 381s b2 0.1469166 0.1469166 0.1469166 0.1469166 381s b3 0.1947976 0.1947976 0.1947976 0.1947976 381s b K 381s 3 4 381s > checker(solve.tensor(rep(R2i,4,1,"K"),rep(R3[[z=1]],4,1,"K"),"a",by="K",allowSingular=TRUE),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s b1 -0.7217544 -0.7217544 -0.7217544 -0.7217544 381s b2 0.1469166 0.1469166 0.1469166 0.1469166 381s b3 0.1947976 0.1947976 0.1947976 0.1947976 381s b K 381s 3 4 381s > checker(solve.tensor(R2i,rep(R3[[z=1]],4,1,"K"),"a",by="K",allowSingular=TRUE),rep(mul.tensor(R2,"a",R3[[z=1]]),4,1,"K")) 381s K 381s b [,1] [,2] [,3] [,4] 381s b1 -0.7217544 -0.7217544 -0.7217544 -0.7217544 381s b2 0.1469166 0.1469166 0.1469166 0.1469166 381s b3 0.1947976 0.1947976 0.1947976 0.1947976 381s b K 381s 3 4 381s > 381s > 381s > 381s > checker(solve.tensor(R2i,R3,"a"),mul.tensor(R2,"a",R3)) 381s z 381s b z1 z2 z3 z4 z5 381s b1 -0.7217544 -0.479997 0.2465513 -0.9341408 -0.9015859 381s b2 0.1469166 2.096782 -2.7411728 2.2971945 1.5172076 381s b3 0.1947976 3.166509 -4.2447767 3.4907497 2.2360166 381s b z 381s 3 5 381s > 381s > checker(solve.tensor(R2i,R3[[z=1]],"a",allowSingular=TRUE),mul.tensor(R2,"a",R3[[z=1]])) 381s b 381s b1 b2 b3 381s -0.7217544 0.1469166 0.1947976 381s b 381s 3 381s > checker(solve.tensor(R2i,R3,"a",allowSingular=TRUE),mul.tensor(R2,"a",R3)) 381s z 381s b z1 z2 z3 z4 z5 381s b1 -0.7217544 -0.479997 0.2465513 -0.9341408 -0.9015859 381s b2 0.1469166 2.096782 -2.7411728 2.2971945 1.5172076 381s b3 0.1947976 3.166509 -4.2447767 3.4907497 2.2360166 381s b z 381s 3 5 381s > 381s > 381s > 381s > summary(I) 381s a b 381s 3 3 381s $a 381s [1] "a1" "a2" "a3" 381s 381s $b 381s [1] "b1" "b2" "b3" 381s 381s b 381s a b1 b2 b3 381s a1 1 0 0 381s a2 0 1 0 381s a3 0 0 1 381s a b 381s 3 3 381s > 381s > 381s > A <- to.tensor(c(diag(3)),c(a=3,b=3),nn(a=3,b=3)) 381s > 381s > A <- to.tensor(c(1,1,1,0,1,1,0,0,1),c(a=3,b=3),nn(a=3,b=3)) 381s > checker(mul.tensor(A,"b",A,"a"),to.tensor(c(A%*%A),c(a=3,b=3),nn(a=3,b=3))) 381s b 381s a b1 b2 b3 381s a1 1 0 0 381s a2 2 1 0 381s a3 3 2 1 381s a b 381s 3 3 381s > 381s > A <- to.tensor(c(1,1,1,1,0,1,1,1,0,0,1,1),c(a=4,b=3),nn(a=4,b=3)) 381s > checker(mul.tensor(A,"b",A[[a=~c]],"b"), 381s + to.tensor(c(A%*%t(A)),dim=c(a=4,c=4),nn(a=4,a=4))) 381s c 381s a a1 a2 a3 a4 381s a1 1 1 1 1 381s a2 1 2 2 2 381s a3 1 2 3 3 381s a4 1 2 3 3 381s a c 381s 4 4 381s > 381s > A <- to.tensor(rnorm(15),c(a=5,b=3),nn(a=5,b=3)) 381s > checker(mul.tensor(A,"b",A[[a=~c]],"b"), 381s + to.tensor(c(A%*%t(A)),dim=c(a=5,c=5),nn(a=5,a=5))) 381s c 381s a a1 a2 a3 a4 a5 381s a1 2.0411789 0.9713976 0.5001267 1.5129363 -0.2202321 381s a2 0.9713976 1.4931326 0.9861560 0.1418050 -0.3591459 381s a3 0.5001267 0.9861560 3.6559484 -2.6034072 0.5042811 381s a4 1.5129363 0.1418050 -2.6034072 3.6277751 -0.6551148 381s a5 -0.2202321 -0.3591459 0.5042811 -0.6551148 0.2710343 381s a c 381s 5 5 381s > 381s > # 381s > A <- to.tensor(c(1,1,1,0,1,1,0,0,1),c(a=3,b=3)) 381s > 381s > solve.tensor(mul.tensor(I,"b",I,"a"),I,"a","a") 381s b 381s b b1 b2 b3 381s b1 1 0 0 381s b2 0 1 0 381s b3 0 0 1 381s b b 381s 3 3 381s > checker(solve.tensor(mul.tensor(I,"b",I,"a"),I,"a","b"),I) 381s Warning message: 381s In to.tensor.default(c(EE), d, dn) : 381s Tensor with duplicated names generated: b b 381s a 381s b a1 a2 a3 381s b1 1 0 0 381s b2 0 1 0 381s b3 0 0 1 381s b a 381s 3 3 381s > mul.tensor(A,"b",I,"a") 381s b 381s a b1 b2 b3 381s [1,] 1 0 0 381s [2,] 1 1 0 381s [3,] 1 1 1 381s a b 381s 3 3 381s > 381s > # + - * / 381s > A <- to.tensor(1:4,c(i=4)) 381s > B <- to.tensor(1:4,c(j=4)) 381s > 381s > checker((A+B-A-B),0*(A %e% B)) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 0 0 0 0 382s [2,] 0 0 0 0 382s [3,] 0 0 0 0 382s [4,] 0 0 0 0 382s i j 382s 4 4 382s > checker((A-B-A+B),0*(A %e% B)) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 0 0 0 0 382s [2,] 0 0 0 0 382s [3,] 0 0 0 0 382s [4,] 0 0 0 0 382s i j 382s 4 4 382s > checker((A+B-B-A),0*(A %e% B)) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 0 0 0 0 382s [2,] 0 0 0 0 382s [3,] 0 0 0 0 382s [4,] 0 0 0 0 382s i j 382s 4 4 382s > checker((A-B+B-A),0*(A %e% B)) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 0 0 0 0 382s [2,] 0 0 0 0 382s [3,] 0 0 0 0 382s [4,] 0 0 0 0 382s i j 382s 4 4 382s > checker((A-A+B-B),0*(A %e% B)) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 0 0 0 0 382s [2,] 0 0 0 0 382s [3,] 0 0 0 0 382s [4,] 0 0 0 0 382s i j 382s 4 4 382s > checker((A*B/A/B),one.tensor(c(dim(A),dim(B)))) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 1 1 1 1 382s [2,] 1 1 1 1 382s [3,] 1 1 1 1 382s [4,] 1 1 1 1 382s i j 382s 4 4 382s > checker((A/B/A*B),one.tensor(c(dim(A),dim(B)))) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 1 1 1 1 382s [2,] 1 1 1 1 382s [3,] 1 1 1 1 382s [4,] 1 1 1 1 382s i j 382s 4 4 382s > checker((A*B/B/A),one.tensor(c(dim(A),dim(B)))) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 1 1 1 1 382s [2,] 1 1 1 1 382s [3,] 1 1 1 1 382s [4,] 1 1 1 1 382s i j 382s 4 4 382s > checker((A/B*B/A),one.tensor(c(dim(A),dim(B)))) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 1 1 1 1 382s [2,] 1 1 1 1 382s [3,] 1 1 1 1 382s [4,] 1 1 1 1 382s i j 382s 4 4 382s > checker((A/A*B/B),one.tensor(c(dim(A),dim(B)))) 382s j 382s i [,1] [,2] [,3] [,4] 382s [1,] 1 1 1 1 382s [2,] 1 1 1 1 382s [3,] 1 1 1 1 382s [4,] 1 1 1 1 382s i j 382s 4 4 382s > 382s > # $,|,^ 382s > 382s > A <- to.tensor(1:6,c(a=1,b=2,c=3)) 382s > checker( names(A$ijk) , c("i","j","k") ) 382s [1] "i" "j" "k" 382s > checker( names(A$i.j.k) , c("i","j","k") ) 382s [1] "i" "j" "k" 382s > checker( A$ijk^c("a","b","c") , A ) 382s , , 1 382s 382s b 382s a [,1] [,2] 382s [1,] 1 2 382s 382s , , 2 382s 382s b 382s a [,1] [,2] 382s [1,] 3 4 382s 382s , , 3 382s 382s b 382s a [,1] [,2] 382s [1,] 5 6 382s 382s a b c 382s 1 2 3 382s > checker( A$ijk^"a.b.c" , A ) 382s , , 1 382s 382s b 382s a [,1] [,2] 382s [1,] 1 2 382s 382s , , 2 382s 382s b 382s a [,1] [,2] 382s [1,] 3 4 382s 382s , , 3 382s 382s b 382s a [,1] [,2] 382s [1,] 5 6 382s 382s a b c 382s 1 2 3 382s > checker( A$ijk^"$abc" , A ) 382s , , 1 382s 382s b 382s a [,1] [,2] 382s [1,] 1 2 382s 382s , , 2 382s 382s b 382s a [,1] [,2] 382s [1,] 3 4 382s 382s , , 3 382s 382s b 382s a [,1] [,2] 382s [1,] 5 6 382s 382s a b c 382s 1 2 3 382s > checker( names(A|"$bca"), c("b","c","a")) 382s [1] "b" "c" "a" 382s > checker( names(A|"b.c.a"), c("b","c","a")) 382s [1] "b" "c" "a" 382s > checker( names(A|"$b.c.a"), c("b","c","a")) 382s [1] "b" "c" "a" 382s > checker( names(A|c("$b","c.a")), c("b","c","a")) 382s [1] "b" "c" "a" 382s > checker( names(A|c("$b","c","a")), c("b","c","a")) 382s [1] "b" "c" "a" 382s > checker( names(A|c("$","b","c","a")), c("b","c","a")) 382s [1] "b" "c" "a" 382s > checker( names(A|c("b.c.a")), c("b","c","a")) 382s [1] "b" "c" "a" 382s > 382s > 382s > # slice.tensor<- 382s > #A <- to.tensor(1:24,c(a=2,b=3,c=4)) 382s > #B <- to.tensor(25:48,c(a=2,b=3,c=4)) 382s > #slice.tensor(A,"c",1:2)<- slice.tensor(B,"c",1:2) 382s > #checker(slice.tensor(A,"c",1:2),slice.tensor(B,"c",1:2)) 382s > #slice.tensor(A,"b",2)<- slice.tensor(B,"b",2) 382s > #checker(slice.tensor(A,"b",2),slice.tensor(B,"b",2)) 382s > 382s BEGIN TEST examples.R 382s 382s R version 4.3.2 (2023-10-31) -- "Eye Holes" 382s Copyright (C) 2023 The R Foundation for Statistical Computing 382s Platform: aarch64-unknown-linux-gnu (64-bit) 382s 382s R is free software and comes with ABSOLUTELY NO WARRANTY. 382s You are welcome to redistribute it under certain conditions. 382s Type 'license()' or 'licence()' for distribution details. 382s 382s R is a collaborative project with many contributors. 382s Type 'contributors()' for more information and 382s 'citation()' on how to cite R or R packages in publications. 382s 382s Type 'demo()' for some demos, 'help()' for on-line help, or 382s 'help.start()' for an HTML browser interface to help. 382s Type 'q()' to quit R. 382s 382s > require(tensorA) 382s Loading required package: tensorA 382s 382s Attaching package: ‘tensorA’ 382s 382s The following object is masked from ‘package:base’: 382s 382s norm 382s 382s > 382s > if(FALSE) { 382s + # Commands for testing 382s + debugger() 382s + options(error=dump.frames) 382s + detach("package:tensorA") 382s + library(tensorA,lib.loc="../../tensorA.Rcheck") 382s + } 382s > 382s > #Aidx(3,4) # c(1,2,3,1,2,3,1,2,3,1,2,3) 382s > #Bidx(3,4) # c(1,1,1,2,2,2,3,3,3,4,4,4) 382s > 382s > # gsi.eps 382s > #gsi.eps # 1E-10 382s > # gs.setarg 382s > #tmp <- function(a=2,b=3) {a*b} 382s > #if( gsi.setarg(tmp,b=5)()!=10 ) 382s > # stop("Fehler gs.setarg") 382s > 382s > # to.tensor 382s > to.tensor(c(1,2,3)) 382s [1] 1 2 3 382s attr(,"class") 382s [1] "tensor" 382s > dim(to.tensor(c(1,2,3))) 382s I 382s 3 382s > 382s > set.seed(23) 382s > 382s > A <- to.tensor(1:20,c(U=2,V=2,W=5)) 382s > A 382s , , 1 382s 382s V 382s U [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2 382s 382s V 382s U [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3 382s 382s V 382s U [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4 382s 382s V 382s U [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5 382s 382s V 382s U [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > dim(A) 382s U V W 382s 2 2 5 382s > names(A) 382s [1] "U" "V" "W" 382s > dimnames(A) 382s $U 382s NULL 382s 382s $V 382s NULL 382s 382s $W 382s NULL 382s 382s > 382s > ftable(to.tensor(A)) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(c(A),dim(A))) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(c(A),dim(A),dimnames(A))) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(A,dim(A),what=1:3)) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(A,dim(A)[1:2],dimnames(A)[1:2],1:2)) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(A,dim(A)[1],dimnames(A)[1],1,addIndex=TRUE)) 382s W W1 W2 W3 W4 W5 382s U @.I1 V 382s U1 @.I11 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 @.I11 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > 382s > 382s > Anamed <- A 382s > #dimnames(Anamed)[["U"]]<- gsi.stdnames(2,"u") 382s > #dimnames(Anamed)[["V"]]<- gsi.stdnames(2,"v") 382s > #dimnames(Anamed)[["U"]]<- gsi.stdnames(dim(A)["w"],"w") 382s > ftable(Anamed) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(Anamed)) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(c(Anamed),dim(Anamed))) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(c(Anamed),dim(Anamed),dimnames(Anamed))) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(Anamed,dim(Anamed),what=1:3)) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(Anamed,dim(Anamed)[1:2],dimnames(Anamed)[1:2],1:2)) 382s W W1 W2 W3 W4 W5 382s U V 382s U1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(Anamed,dim(Anamed)[1],dimnames(Anamed)[1],1,addIndex=TRUE)) 382s W W1 W2 W3 W4 W5 382s U @.I1 V 382s U1 @.I11 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 @.I11 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > ftable(to.tensor(Anamed,dim(Anamed)[1],dimnames(Anamed)[1],1,addIndex="I")) 382s W W1 W2 W3 W4 W5 382s U I V 382s U1 I1 V1 1 5 9 13 17 382s V2 3 7 11 15 19 382s U2 I1 V1 2 6 10 14 18 382s V2 4 8 12 16 20 382s > 382s > 382s > B <- to.tensor(1:30,list(U=c("a","b","c"),V=c("B1","B2"),W=1:5)) 382s > B 382s , , W = 1 382s 382s V 382s U B1 B2 382s a 1 4 382s b 2 5 382s c 3 6 382s 382s , , W = 2 382s 382s V 382s U B1 B2 382s a 7 10 382s b 8 11 382s c 9 12 382s 382s , , W = 3 382s 382s V 382s U B1 B2 382s a 13 16 382s b 14 17 382s c 15 18 382s 382s , , W = 4 382s 382s V 382s U B1 B2 382s a 19 22 382s b 20 23 382s c 21 24 382s 382s , , W = 5 382s 382s V 382s U B1 B2 382s a 25 28 382s b 26 29 382s c 27 30 382s 382s attr(,"class") 382s [1] "tensor" 382s > dim(B) 382s U V W 382s 3 2 5 382s > names(B) 382s [1] "U" "V" "W" 382s > dimnames(B) 382s $U 382s [1] "a" "b" "c" 382s 382s $V 382s [1] "B1" "B2" 382s 382s $W 382s [1] "1" "2" "3" "4" "5" 382s 382s > 382s > B2 <- to.tensor(B,c(x=1,y=3,z=1)) 382s > ftable(B2) 382s W 1 2 3 4 5 382s x y z V 382s x1 y1 z1 B1 1 7 13 19 25 382s B2 4 10 16 22 28 382s y2 z1 B1 2 8 14 20 26 382s B2 5 11 17 23 29 382s y3 z1 B1 3 9 15 21 27 382s B2 6 12 18 24 30 382s > 382s > 382s > C <- to.tensor(1:20,c(A=4,B=5)) 382s > C 382s B 382s A [,1] [,2] [,3] [,4] [,5] 382s [1,] 1 5 9 13 17 382s [2,] 2 6 10 14 18 382s [3,] 3 7 11 15 19 382s [4,] 4 8 12 16 20 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > C <- to.tensor(C,c(A1=2,A2=2)) 382s > C 382s , , 1 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > D <- C 382s > C <- to.tensor(C,c(A1=1,A2=4),what=c("A2","A1")) 382s > C 382s , , 1 382s 382s A2 382s A1 [,1] [,2] [,3] [,4] 382s [1,] 1 3 2 4 382s 382s , , 2 382s 382s A2 382s A1 [,1] [,2] [,3] [,4] 382s [1,] 5 7 6 8 382s 382s , , 3 382s 382s A2 382s A1 [,1] [,2] [,3] [,4] 382s [1,] 9 11 10 12 382s 382s , , 4 382s 382s A2 382s A1 [,1] [,2] [,3] [,4] 382s [1,] 13 15 14 16 382s 382s , , 5 382s 382s A2 382s A1 [,1] [,2] [,3] [,4] 382s [1,] 17 19 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > C <- to.tensor(C,c(A1=2),what=c("A2","A1"),addIndex="Q") 382s > C 382s , , 1 382s 382s Q 382s A1 [,1] [,2] 382s [1,] 1 2 382s [2,] 3 4 382s 382s , , 2 382s 382s Q 382s A1 [,1] [,2] 382s [1,] 5 6 382s [2,] 7 8 382s 382s , , 3 382s 382s Q 382s A1 [,1] [,2] 382s [1,] 9 10 382s [2,] 11 12 382s 382s , , 4 382s 382s Q 382s A1 [,1] [,2] 382s [1,] 13 14 382s [2,] 15 16 382s 382s , , 5 382s 382s Q 382s A1 [,1] [,2] 382s [1,] 17 18 382s [2,] 19 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > Cnamed <- to.tensor(1:20,c(A=4,B=5)) 382s > dimnames(Cnamed)[["B"]]<-LETTERS[1:5] 382s > dimnames(Cnamed)[["A"]]<-letters[1:4] 382s > Cnamed 382s B 382s A A B C D E 382s a 1 5 9 13 17 382s b 2 6 10 14 18 382s c 3 7 11 15 19 382s d 4 8 12 16 20 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > Cnamed <- to.tensor(Cnamed,c(A1=2,A2=2)) 382s > dimnames(Cnamed) 382s $A1 382s NULL 382s 382s $A2 382s NULL 382s 382s $B 382s [1] "A" "B" "C" "D" "E" 382s 382s > Dnamed <- Cnamed 382s > Cnamed <- to.tensor(Cnamed,c(A1=1,A2=4),what=c("A2","A1")) 382s > ftable(Cnamed) 382s B A B C D E 382s A1 A2 382s A11 A21 1 5 9 13 17 382s A22 3 7 11 15 19 382s A23 2 6 10 14 18 382s A24 4 8 12 16 20 382s > 382s > Cnamed <- to.tensor(Cnamed,c(A1=2),what=c("A2","A1"),addIndex="Q") 382s > ftable(Cnamed) 382s B A B C D E 382s A1 Q 382s A11 Q1 1 5 9 13 17 382s Q2 2 6 10 14 18 382s A12 Q1 3 7 11 15 19 382s Q2 4 8 12 16 20 382s > 382s > 382s > 382s > # names 382s > names( C ) 382s [1] "A1" "Q" "B" 382s > names( C ) <- c("A1","A2","A3") 382s > C 382s , , 1 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 1 2 382s [2,] 3 4 382s 382s , , 2 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 5 6 382s [2,] 7 8 382s 382s , , 3 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 9 10 382s [2,] 11 12 382s 382s , , 4 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 13 14 382s [2,] 15 16 382s 382s , , 5 382s 382s A2 382s A1 [,1] [,2] 382s [1,] 17 18 382s [2,] 19 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > names(C) 382s [1] "A1" "A2" "A3" 382s > 382s > names( Cnamed ) 382s [1] "A1" "Q" "B" 382s > names( Cnamed ) <- c("A1","A2","A3") 382s > ftable(Cnamed) 382s A3 A B C D E 382s A1 A2 382s A11 A21 1 5 9 13 17 382s A22 2 6 10 14 18 382s A12 A21 3 7 11 15 19 382s A22 4 8 12 16 20 382s > names(Cnamed) 382s [1] "A1" "A2" "A3" 382s > 382s > 382s > # norm 382s > norm.tensor(C) - sqrt(sum((1:20)^2)) 382s [1] 0 382s > norm.tensor(Cnamed) - sqrt(sum((1:20)^2)) 382s [1] 0 382s > 382s > # margin.tensor 382s > margin.tensor(C,"A1") 382s A3 382s A2 [,1] [,2] [,3] [,4] [,5] 382s [1,] 4 12 20 28 36 382s [2,] 6 14 22 30 38 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > margin.tensor(Cnamed,"A1") 382s A3 382s A2 A B C D E 382s [1,] 4 12 20 28 36 382s [2,] 6 14 22 30 38 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > 382s > # diagmul.tensor 382s > norm.tensor( diagmul.tensor(C,D=C)-C^2 ) # 0 382s [1] 0 382s > norm.tensor( diagmul.tensor(Cnamed,D=Cnamed)-Cnamed^2 ) # 0 382s [1] 0 382s > 382s > Cr <- rep.tensor(C,10,1,name="K") 382s > #norm(diagmul.tensor(Cr,names(C),C,names(C),by="K") - diagmul.tensor(Cr,names(C),D=Cr,names(C),by="K")) # 0 382s > 382s > # pos.tensor 382s > pos.tensor(dim(C)) 382s A1 A2 A3 382s [1,] 1 1 1 382s [2,] 2 1 1 382s [3,] 1 2 1 382s [4,] 2 2 1 382s [5,] 1 1 2 382s [6,] 2 1 2 382s [7,] 1 2 2 382s [8,] 2 2 2 382s [9,] 1 1 3 382s [10,] 2 1 3 382s [11,] 1 2 3 382s [12,] 2 2 3 382s [13,] 1 1 4 382s [14,] 2 1 4 382s [15,] 1 2 4 382s [16,] 2 2 4 382s [17,] 1 1 5 382s [18,] 2 1 5 382s [19,] 1 2 5 382s [20,] 2 2 5 382s > 382s > # reorder.tensor 382s > reorder.tensor(C,c(2)) 382s , , 1 382s 382s A1 382s A2 [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2 382s 382s A1 382s A2 [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3 382s 382s A1 382s A2 [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4 382s 382s A1 382s A2 [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5 382s 382s A1 382s A2 [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > reorder.tensor(C,c("A3","A2")) 382s , , 1 382s 382s A2 382s A3 [,1] [,2] 382s [1,] 1 2 382s [2,] 5 6 382s [3,] 9 10 382s [4,] 13 14 382s [5,] 17 18 382s 382s , , 2 382s 382s A2 382s A3 [,1] [,2] 382s [1,] 3 4 382s [2,] 7 8 382s [3,] 11 12 382s [4,] 15 16 382s [5,] 19 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > ftable(reorder.tensor(Cnamed,c(2))) 382s A3 A B C D E 382s A2 A1 382s A21 A11 1 5 9 13 17 382s A12 3 7 11 15 19 382s A22 A11 2 6 10 14 18 382s A12 4 8 12 16 20 382s > ftable(reorder.tensor(Cnamed,c("A3","A2"))) 382s A1 A11 A12 382s A3 A2 382s A A21 1 3 382s A22 2 4 382s B A21 5 7 382s A22 6 8 382s C A21 9 11 382s A22 10 12 382s D A21 13 15 382s A22 14 16 382s E A21 17 19 382s A22 18 20 382s > 382s > # mul.tensor 382s > AA <- mul.tensor(A,1,mark(A),1) 382s > AA 382s , , 1, 1 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 5 17 29 41 53 382s [2,] 11 23 35 47 59 382s 382s , , 2, 1 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 11 39 67 95 123 382s [2,] 25 53 81 109 137 382s 382s , , 1, 2 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 17 61 105 149 193 382s [2,] 39 83 127 171 215 382s 382s , , 2, 2 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 23 83 143 203 263 382s [2,] 53 113 173 233 293 382s 382s , , 1, 3 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 29 105 181 257 333 382s [2,] 67 143 219 295 371 382s 382s , , 2, 3 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 35 127 219 311 403 382s [2,] 81 173 265 357 449 382s 382s , , 1, 4 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 41 149 257 365 473 382s [2,] 95 203 311 419 527 382s 382s , , 2, 4 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 47 171 295 419 543 382s [2,] 109 233 357 481 605 382s 382s , , 1, 5 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 53 193 333 473 613 382s [2,] 123 263 403 543 683 382s 382s , , 2, 5 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 59 215 371 527 683 382s [2,] 137 293 449 605 761 382s 382s attr(,"class") 382s [1] "tensor" 382s > dim(AA) 382s V W V' W' 382s 2 5 2 5 382s > 382s > AA <- mul.tensor(Anamed,1,mark(Anamed),1) 382s > ftable(AA) 382s W' W'1 W'2 W'3 W'4 W'5 382s V W V' 382s V1 W1 V'1 5 17 29 41 53 382s V'2 11 23 35 47 59 382s W2 V'1 17 61 105 149 193 382s V'2 39 83 127 171 215 382s W3 V'1 29 105 181 257 333 382s V'2 67 143 219 295 371 382s W4 V'1 41 149 257 365 473 382s V'2 95 203 311 419 527 382s W5 V'1 53 193 333 473 613 382s V'2 123 263 403 543 683 382s V2 W1 V'1 11 39 67 95 123 382s V'2 25 53 81 109 137 382s W2 V'1 23 83 143 203 263 382s V'2 53 113 173 233 293 382s W3 V'1 35 127 219 311 403 382s V'2 81 173 265 357 449 382s W4 V'1 47 171 295 419 543 382s V'2 109 233 357 481 605 382s W5 V'1 59 215 371 527 683 382s V'2 137 293 449 605 761 382s > dim(AA) 382s V W V' W' 382s 2 5 2 5 382s > 382s > A <- to.tensor(as.complex(1:20),c(U=2,V=2,W=5)) 382s > AA <- mul.tensor(A,1,mark(A),1) 382s > 382s > 382s > # 382s > 382s > 382s > # rep.tensor 382s > rep(A,3,name="Q",pos=4) 382s , , 1, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s , , 1, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s , , 1, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > rep(Anamed,3,name="Q",pos=4) 382s , , 1, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5, 1 382s 382s V 382s U [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s , , 1, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5, 2 382s 382s V 382s U [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s , , 1, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5, 3 382s 382s V 382s U [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > ftable(rep(Anamed,3,name="Q",pos=4)) 382s Q Q1 Q2 Q3 382s U V W 382s U1 V1 W1 1 1 1 382s W2 5 5 5 382s W3 9 9 9 382s W4 13 13 13 382s W5 17 17 17 382s V2 W1 3 3 3 382s W2 7 7 7 382s W3 11 11 11 382s W4 15 15 15 382s W5 19 19 19 382s U2 V1 W1 2 2 2 382s W2 6 6 6 382s W3 10 10 10 382s W4 14 14 14 382s W5 18 18 18 382s V2 W1 4 4 4 382s W2 8 8 8 382s W3 12 12 12 382s W4 16 16 16 382s W5 20 20 20 382s > 382s > # trace.tensor 382s > 382s > trace.tensor(D,"A1","A2") 382s [1] 5 13 21 29 37 382s attr(,"class") 382s [1] "tensor" 382s > dim(trace.tensor(D,"A1","A2")) 382s B 382s 5 382s > 382s > trace.tensor(Dnamed,"A1","A2") 382s B 382s A B C D E 382s 5 13 21 29 37 382s attr(,"class") 382s [1] "tensor" 382s > dim(trace.tensor(Dnamed,"A1","A2")) 382s B 382s 5 382s > 382s > 382s > #delta.tensor 382s > 382s > delta.tensor(c(a=2)) 382s a' 382s a [,1] [,2] 382s [1,] 1 0 382s [2,] 0 1 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > delta.tensor(c(a=2,b=3)) 382s , , 1, 1 382s 382s b 382s a [,1] [,2] [,3] 382s [1,] 1 0 0 382s [2,] 0 0 0 382s 382s , , 2, 1 382s 382s b 382s a [,1] [,2] [,3] 382s [1,] 0 0 0 382s [2,] 1 0 0 382s 382s , , 1, 2 382s 382s b 382s a [,1] [,2] [,3] 382s [1,] 0 1 0 382s [2,] 0 0 0 382s 382s , , 2, 2 382s 382s b 382s a [,1] [,2] [,3] 382s [1,] 0 0 0 382s [2,] 0 1 0 382s 382s , , 1, 3 382s 382s b 382s a [,1] [,2] [,3] 382s [1,] 0 0 1 382s [2,] 0 0 0 382s 382s , , 2, 3 382s 382s b 382s a [,1] [,2] [,3] 382s [1,] 0 0 0 382s [2,] 0 0 1 382s 382s attr(,"class") 382s [1] "tensor" 382s > dim(delta.tensor(c(a=2,b=4),".")) 382s a b a. b. 382s 2 4 2 4 382s > 382s > ftable(delta.tensor(c(a=2,b=2))) 382s b' b'1 b'2 382s a b a' 382s a1 b1 a'1 1 0 382s a'2 0 0 382s b2 a'1 0 1 382s a'2 0 0 382s a2 b1 a'1 0 0 382s a'2 1 0 382s b2 a'1 0 0 382s a'2 0 1 382s > ftable(delta.tensor(c(a=2,b=3))) 382s b' b'1 b'2 b'3 382s a b a' 382s a1 b1 a'1 1 0 0 382s a'2 0 0 0 382s b2 a'1 0 1 0 382s a'2 0 0 0 382s b3 a'1 0 0 1 382s a'2 0 0 0 382s a2 b1 a'1 0 0 0 382s a'2 1 0 0 382s b2 a'1 0 0 0 382s a'2 0 1 0 382s b3 a'1 0 0 0 382s a'2 0 0 1 382s > 382s > # tripledelta.tensor 382s > 382s > tripledelta.tensor(c(a=2)) 382s , , 1 382s 382s a' 382s a [,1] [,2] 382s [1,] 1 0 382s [2,] 0 0 382s 382s , , 2 382s 382s a' 382s a [,1] [,2] 382s [1,] 0 0 382s [2,] 0 1 382s 382s attr(,"class") 382s [1] "tensor" 382s > ftable(tripledelta.tensor(c(a=2))) 382s a* a*1 a*2 382s a a' 382s a1 a'1 1 0 382s a'2 0 0 382s a2 a'1 0 0 382s a'2 0 1 382s > dim(tripledelta.tensor(c(a=2),"1","2")) 382s a a1 a2 382s 2 2 2 382s > 382s > 382s > # mark.tensor 382s > A 382s , , 1 382s 382s V 382s U [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2 382s 382s V 382s U [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3 382s 382s V 382s U [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4 382s 382s V 382s U [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5 382s 382s V 382s U [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > mark(A,"*") 382s , , 1 382s 382s V* 382s U* [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2 382s 382s V* 382s U* [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3 382s 382s V* 382s U* [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4 382s 382s V* 382s U* [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5 382s 382s V* 382s U* [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > names(mark(A,"*")) 382s [1] "U*" "V*" "W*" 382s > mark(A,"*","U") 382s , , 1 382s 382s V 382s U* [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2 382s 382s V 382s U* [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3 382s 382s V 382s U* [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4 382s 382s V 382s U* [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5 382s 382s V 382s U* [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > names(mark(A,"*","U")) 382s [1] "U*" "V" "W" 382s > names(mark(A,"*",2:3)) 382s [1] "U" "V*" "W*" 382s > 382s > Anamed 382s , , 1 382s 382s V 382s U [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2 382s 382s V 382s U [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3 382s 382s V 382s U [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4 382s 382s V 382s U [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5 382s 382s V 382s U [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > mark(Anamed,"*") 382s , , 1 382s 382s V* 382s U* [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2 382s 382s V* 382s U* [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3 382s 382s V* 382s U* [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4 382s 382s V* 382s U* [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5 382s 382s V* 382s U* [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > names(mark(Anamed,"*")) 382s [1] "U*" "V*" "W*" 382s > mark(Anamed,"*","U") 382s , , 1 382s 382s V 382s U* [,1] [,2] 382s [1,] 1 3 382s [2,] 2 4 382s 382s , , 2 382s 382s V 382s U* [,1] [,2] 382s [1,] 5 7 382s [2,] 6 8 382s 382s , , 3 382s 382s V 382s U* [,1] [,2] 382s [1,] 9 11 382s [2,] 10 12 382s 382s , , 4 382s 382s V 382s U* [,1] [,2] 382s [1,] 13 15 382s [2,] 14 16 382s 382s , , 5 382s 382s V 382s U* [,1] [,2] 382s [1,] 17 19 382s [2,] 18 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > names(mark(Anamed,"*","U")) 382s [1] "U*" "V" "W" 382s > names(mark(Anamed,"*",2:3)) 382s [1] "U" "V*" "W*" 382s > 382s > 382s > # mark.numeric 382s > mark(dim(A),"*") 382s U* V* W* 382s 2 2 5 382s > mark(dim(A),"*","U") 382s U* V W 382s 2 2 5 382s > mark(dim(A),"*",2:3) 382s U V* W* 382s 2 2 5 382s > 382s > # mark.character 382s > mark(names(A),"*") 382s [1] "U*" "V*" "W*" 382s > mark(names(A),"*","U") 382s [1] "U*" "V" "W" 382s > mark(names(A),"*",2:3) 382s [1] "U" "V*" "W*" 382s > 382s > 382s > # inv.tensor 382s > E <- to.tensor(rnorm(16),c(a=2,b=2,A=2,B=2)) 382s > Ei <- inv.tensor(E,c("A","B")) 382s > E 382s , , 1, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 0.1932123 0.9132671 382s [2,] -0.4346821 1.7933881 382s 382s , , 2, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 0.9966051 -0.2780863 382s [2,] 1.1074905 1.0192055 382s 382s , , 1, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 0.04543718 0.2182885 382s [2,] 1.57577959 -1.0465353 382s 382s , , 2, 2 382s 382s b 382s a [,1] [,2] 382s [1,] -0.2886886 -1.2163764 382s [2,] 0.4815503 0.3081369 382s 382s attr(,"class") 382s [1] "tensor" 382s > dim(Ei) 382s A B a b 382s 2 2 2 2 382s > names(Ei) 382s [1] "A" "B" "a" "b" 382s > dim(mul.tensor(E,c("A","B"),mark(Ei,c("a","b")))) 382s a b aa bb 382s 2 2 2 2 382s > dim(delta.tensor(c(a=2,b=2))) 382s a b a' b' 382s 2 2 2 2 382s > norm.tensor(mul.tensor(E,c("A","B"),mark(Ei,c("a","b")))-delta.tensor(c(a=2,b=2))) 382s [1] 4.898979 382s > 382s > AA <- to.tensor(rnorm(20),c(a=2,b=2,C=5)) 382s > inv.tensor(AA,"a",by="C") 382s , , 1 382s 382s b 382s a [,1] [,2] 382s [1,] -1.3794181 -0.4713009 382s [2,] -0.6385888 0.5542682 382s 382s , , 2 382s 382s b 382s a [,1] [,2] 382s [1,] 2.209246 -1.072506 382s [2,] 1.493926 -1.582930 382s 382s , , 3 382s 382s b 382s a [,1] [,2] 382s [1,] -1.8823294 -0.001603462 382s [2,] -0.7762784 0.803929715 382s 382s , , 4 382s 382s b 382s a [,1] [,2] 382s [1,] 3.593699 -6.098887 382s [2,] 20.248775 -24.179080 382s 382s , , 5 382s 382s b 382s a [,1] [,2] 382s [1,] -0.3891199 -2.740116 382s [2,] -0.4430734 2.513745 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > 382s > 382s > E <- to.tensor(rnorm(16),c(a=2,b=2,A=2,B=2),list(c("a","b"),NULL,c("A1","A2"),c("B1","B2"))) 382s > Ei <- inv.tensor(E,c("A","B")) 382s > E 382s , , A = A1, B = B1 382s 382s b 382s a [,1] [,2] 382s a 1.307647 0.861083 382s b -1.342935 0.232875 382s 382s , , A = A2, B = B1 382s 382s b 382s a [,1] [,2] 382s a 1.042257 0.9459580 382s b 1.329098 -0.9856255 382s 382s , , A = A1, B = B2 382s 382s b 382s a [,1] [,2] 382s a -1.215867 0.09231624 382s b -1.629206 -0.02211742 382s 382s , , A = A2, B = B2 382s 382s b 382s a [,1] [,2] 382s a 0.5134779 1.2615159 382s b -0.2295536 -0.2384356 382s 382s attr(,"class") 382s [1] "tensor" 382s > dim(Ei) 382s A B a b 382s 2 2 2 2 382s > names(Ei) 382s [1] "A" "B" "a" "b" 382s > norm.tensor(mul.tensor(E,c("A","B"),mark(Ei,c("a","b")))-delta.tensor(c(a=2,b=2))) 382s [1] 4.898979 382s > ftable(round(mul.tensor(E,c("A","B"),mark(Ei,c("a","b")))),3) 382s bb bb1 bb2 382s a b aa 382s a b1 a 1 0 382s b 0 0 382s b2 a 0 1 382s b 0 0 382s b b1 a 0 0 382s b 1 0 382s b2 a 0 0 382s b 0 1 382s > 382s > # solve.tensor 382s > 382s > X1 <- to.tensor( 382s + c( 0 , 10 , 20 ,30 , 2,2,2,2, 45,21,34,5, 67,0,0,0 ), 382s + c(a=2,b=2,"a'"=2,"b'"=2) ) 382s > b1 <- to.tensor(c( 0,10,20,30),c(a=2,b=2)) 382s > solve.tensor(X1,b1,c("a","b")) 382s b' 382s a' [,1] [,2] 382s [1,] 1.000000e+00 3.965082e-17 382s [2,] -1.586033e-16 -2.189672e-17 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > norm.tensor(solve.tensor(X1,b1,c("a","b")) - to.tensor(c( 1,0,0,0 ),c(a=2,b=2))) #0 382s [1] 2.44949 382s > 382s > dimnames(X1)[["a"]]<- 1:2 382s > dimnames(X1)[["b"]]<- 1:2 382s > dimnames(X1)[["a'"]]<- 1:2 382s > dimnames(b1)[["a"]] <-c("M","K") 382s > 382s > solve.tensor(X1,b1,c("a","b")) 382s b' 382s a' [,1] [,2] 382s 1 1.000000e+00 3.965082e-17 382s 2 -1.586033e-16 -2.189672e-17 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > norm.tensor(solve.tensor(X1,b1,c("a","b")) - to.tensor(c( 1,0,0,0 ),c(a=2,b=2))) #0 382s [1] 2.44949 382s > 382s > 382s > # chol.tensor 382s > Xs <- einstein.tensor(X1,a="a*",b="b*",X1) 382s > dim(Xs) 382s a* b* a b 382s 2 2 2 2 382s > norm.tensor( Xs - mul.tensor(X1,c("a'","b'"),mark(X1,"*",c("a","b")),c("a'","b'"))) #0 382s [1] 0 382s > RXs <- chol.tensor(Xs,c("a","b"),c("a*","b*")) 382s > norm.tensor(mul.tensor(RXs,1,mark(RXs),1) - Xs ) # 0 382s [1] 14289.66 382s > 382s > dimnames(X1)[["a"]]<-c("q1","q2") 382s > dimnames(X1)[["a'"]]<-c("p1","p2") 382s > 382s > Xs <- einstein.tensor(X1,a="a*",b="b*",X1) 382s > dimnames(Xs) 382s $`a*` 382s [1] "q1" "q2" 382s 382s $`b*` 382s [1] "1" "2" 382s 382s $a 382s [1] "q1" "q2" 382s 382s $b 382s [1] "1" "2" 382s 382s > dimnames(Xs)["a*"]<-list(NULL) 382s > dim(Xs) 382s a* b* a b 382s 2 2 2 2 382s > norm.tensor( Xs - mul.tensor(X1,c("a'","b'"),mark(X1,"*",c("a","b")),c("a'","b'"))) #0 382s [1] 0 382s > RXs <- chol.tensor(Xs,c("a","b"),c("a*","b*")) 382s > norm.tensor(mul.tensor(RXs,1,mark(RXs),1) - Xs ) # 0 382s [1] 14289.66 382s > 382s > 382s > # level.tensor 382s > dim(X1) 382s a b a' b' 382s 2 2 2 2 382s > level.tensor(X1) # 4 382s [1] 4 382s > 382s > # svd.tensor 382s > SXs <- svd.tensor(X1,c("a","b")) 382s > SXs 382s $u 382s , , 1 382s 382s b 382s a 1 2 382s q1 -0.9351202 -0.29458399 382s q2 -0.1789514 -0.08213968 382s 382s , , 2 382s 382s b 382s a 1 2 382s q1 -0.3285545 0.6614184 382s q2 0.3690916 0.5642243 382s 382s , , 3 382s 382s b 382s a 1 2 382s q1 0.1326733 -0.4386166 382s q2 -0.3468797 0.8183445 382s 382s , , 4 382s 382s b 382s a 1 2 382s q1 -6.244866e-05 -0.5323171 382s q2 8.434585e-01 0.0722237 382s 382s attr(,"class") 382s [1] "tensor" 382s 382s $d 382s [1] 84.8702965 44.3906688 19.4399279 0.7684437 382s attr(,"class") 382s [1] "tensor" 382s 382s $v 382s , , 1 382s 382s b' 382s a' [,1] [,2] 382s p1 -0.11953986 -0.6629521 382s p2 -0.03513114 -0.7382212 382s 382s , , 2 382s 382s b' 382s a' [,1] [,2] 382s p1 0.76245782 0.4116928 382s p2 0.05704712 -0.4958959 382s 382s , , 3 382s 382s b' 382s a' [,1] [,2] 382s p1 0.63319205 -0.6242522 382s p2 0.01702903 0.4572604 382s 382s , , 4 382s 382s b' 382s a' [,1] [,2] 382s p1 -0.05861846 -0.03623242 382s p2 0.99760786 -0.00544485 382s 382s attr(,"class") 382s [1] "tensor" 382s 382s > DXs <- to.tensor(c(diag(SXs$d)),c(lambda=length(SXs$d),"lambda'"=length(SXs$d))) 382s > SXs2<-mul.tensor(mul.tensor(SXs$u,"lambda",DXs,"lambda'"),"lambda",SXs$v) # 382s > SXs2 382s , , a' = p1, 1 382s 382s b 382s a 1 2 382s q1 -7.425659e-16 20 382s q2 1.000000e+01 30 382s 382s , , a' = p2, 1 382s 382s b 382s a 1 2 382s q1 2 2 382s q2 2 2 382s 382s , , a' = p1, 2 382s 382s b 382s a 1 2 382s q1 45 34 382s q2 21 5 382s 382s , , a' = p2, 2 382s 382s b 382s a 1 2 382s q1 6.700000e+01 -2.097169e-14 382s q2 -9.164946e-15 -5.895202e-15 382s 382s attr(,"class") 382s [1] "tensor" 382s > norm.tensor(SXs2-X1) #0 382s [1] 8.64547e-14 382s > 382s > # power.tensor 382s > Xs 382s , , a = q1, b = 1 382s 382s b* 382s a* 1 2 382s [1,] 6518 1534 382s [2,] 949 229 382s 382s , , a = q2, b = 1 382s 382s b* 382s a* 1 2 382s [1,] 949 918 382s [2,] 545 409 382s 382s , , a = q1, b = 2 382s 382s b* 382s a* 1 2 382s [1,] 1534 1560 382s [2,] 918 774 382s 382s , , a = q2, b = 2 382s 382s b* 382s a* 1 2 382s [1,] 229 774 382s [2,] 409 929 382s 382s attr(,"class") 382s [1] "tensor" 382s > rXs <- power.tensor(Xs,c(1,2),c(3,4),p=0.5) 382s > Xs2 <- mul.tensor(rXs,c("a","b"),rXs,c("a*","b*")) 382s > Xs2 382s , , a = q1, b = 1 382s 382s b* 382s a* 1 2 382s [1,] 6518 1534 382s [2,] 949 229 382s 382s , , a = q2, b = 1 382s 382s b* 382s a* 1 2 382s [1,] 949 918 382s [2,] 545 409 382s 382s , , a = q1, b = 2 382s 382s b* 382s a* 1 2 382s [1,] 1534 1560 382s [2,] 918 774 382s 382s , , a = q2, b = 2 382s 382s b* 382s a* 1 2 382s [1,] 229 774 382s [2,] 409 929 382s 382s attr(,"class") 382s [1] "tensor" 382s > norm.tensor((Xs-Xs2)) # 0 382s [1] 2.732035e-12 382s > 382s > # to.matrix.tensor 382s > to.matrix.tensor(X1,j=c("a'","b'")) 382s 382s [,1] [,2] [,3] [,4] 382s [1,] 0 2 45 67 382s [2,] 10 2 21 0 382s [3,] 20 2 34 0 382s [4,] 30 2 5 0 382s > to.matrix.tensor(X1,i=c("a","b") ) 382s 382s [,1] [,2] [,3] [,4] 382s [1,] 0 2 45 67 382s [2,] 10 2 21 0 382s [3,] 20 2 34 0 382s [4,] 30 2 5 0 382s > 382s > # gsi.stdnames 382s > #gsi.stdnames(7,avoid=gsi.stdnames(5)) 382s > #gsi.stdnames(3,"B") 382s > #gsi.stdnames(3,"B",avoid=gsi.stdnames(5)) 382s > 382s > 382s > # gsi.namedlist 382s > #gsi.namedlist(c("Holla","Hoppla"),1,3) 382s > # gsi.lefts/gsi.rights 382s > #gsi.lefts(X1) 382s > #gsi.rights(X1) 382s > 382s > # untensor 382s > tmp <- untensor(X1,c("a","b"),"A",1) 382s > X1 <- to.tensor( 382s + c( 0 , 10 , 20 ,30 , 2,2,2,2, 45,21,34,5, 67,0,0,0 ), 382s + c(a=2,b=2,"a'"=2,"b'"=2) ) 382s > tmp <- untensor(X1,c("a","b"),"A",1) 382s > tmp 382s , , 1 382s 382s a' 382s A [,1] [,2] 382s [1,] 0 2 382s [2,] 10 2 382s [3,] 20 2 382s [4,] 30 2 382s 382s , , 2 382s 382s a' 382s A [,1] [,2] 382s [1,] 45 67 382s [2,] 21 0 382s [3,] 34 0 382s [4,] 5 0 382s 382s attr(,"class") 382s [1] "tensor" 382s > untensor(tmp,c("a'","b'"),"B",2) 382s B 382s A [,1] [,2] [,3] [,4] 382s [1,] 0 2 45 67 382s [2,] 10 2 21 0 382s [3,] 20 2 34 0 382s [4,] 30 2 5 0 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > 382s > # gsi.untensornames 382s > untensor(A,c(1,2)) 382s W 382s I1 [,1] [,2] [,3] [,4] [,5] 382s [1,] 1+0i 5+0i 9+0i 13+0i 17+0i 382s [2,] 2+0i 6+0i 10+0i 14+0i 18+0i 382s [3,] 3+0i 7+0i 11+0i 15+0i 19+0i 382s [4,] 4+0i 8+0i 12+0i 16+0i 20+0i 382s attr(,"class") 382s [1] "tensor" 382s > untensor(Anamed,c(1,2)) 382s W 382s I1 [,1] [,2] [,3] [,4] [,5] 382s [1,] 1 5 9 13 17 382s [2,] 2 6 10 14 18 382s [3,] 3 7 11 15 19 382s [4,] 4 8 12 16 20 382s attr(,"class") 382s [1] "tensor" 382s > 382s > # as.tensor 382s > as.tensor(X1) 382s , , 1, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 0 20 382s [2,] 10 30 382s 382s , , 2, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 2 2 382s [2,] 2 2 382s 382s , , 1, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 45 34 382s [2,] 21 5 382s 382s , , 2, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 67 0 382s [2,] 0 0 382s 382s attr(,"class") 382s [1] "tensor" 382s > as.tensor(c(1,2,3)) 382s [1] 1 2 3 382s attr(,"class") 382s [1] "tensor" 382s > dim(as.tensor(c(1,2,3))) 382s I 382s 3 382s > 382s > # renorm.matrix / renorm.tensor 382s > #renorm.rows(X1[,,1,1]) 382s > #renorm.tensor(X1[,,1,1]) 382s > #norm.tensor(renorm.tensor(X1,c(1,2)),c(1,2)) # 1 1 1 1 382s > 382s > # slice.tensor 382s > slice.tensor(B,"U","a") 382s , , W = 1 382s 382s V 382s U B1 B2 382s a 1 4 382s 382s , , W = 2 382s 382s V 382s U B1 B2 382s a 7 10 382s 382s , , W = 3 382s 382s V 382s U B1 B2 382s a 13 16 382s 382s , , W = 4 382s 382s V 382s U B1 B2 382s a 19 22 382s 382s , , W = 5 382s 382s V 382s U B1 B2 382s a 25 28 382s 382s attr(,"class") 382s [1] "tensor" 382s > slice.tensor(B,"U","a",drop=TRUE) 382s W 382s V 1 2 3 4 5 382s B1 1 7 13 19 25 382s B2 4 10 16 22 28 382s attr(,"class") 382s [1] "tensor" 382s > slice.tensor(B,"U",c("a","c")) 382s , , W = 1 382s 382s V 382s U B1 B2 382s a 1 4 382s c 3 6 382s 382s , , W = 2 382s 382s V 382s U B1 B2 382s a 7 10 382s c 9 12 382s 382s , , W = 3 382s 382s V 382s U B1 B2 382s a 13 16 382s c 15 18 382s 382s , , W = 4 382s 382s V 382s U B1 B2 382s a 19 22 382s c 21 24 382s 382s , , W = 5 382s 382s V 382s U B1 B2 382s a 25 28 382s c 27 30 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > # [[]].tensor 382s > B[[U="a"]] 382s W 382s V 1 2 3 4 5 382s B1 1 7 13 19 25 382s B2 4 10 16 22 28 382s attr(,"class") 382s [1] "tensor" 382s > B[[U="a",drop=FALSE]] 382s , , W = 1 382s 382s V 382s U B1 B2 382s a 1 4 382s 382s , , W = 2 382s 382s V 382s U B1 B2 382s a 7 10 382s 382s , , W = 3 382s 382s V 382s U B1 B2 382s a 13 16 382s 382s , , W = 4 382s 382s V 382s U B1 B2 382s a 19 22 382s 382s , , W = 5 382s 382s V 382s U B1 B2 382s a 25 28 382s 382s attr(,"class") 382s [1] "tensor" 382s > old <- B[[U=c("a","c")]] 382s > B[1:2,,] 382s , , 1 382s 382s V 382s U [,1] [,2] 382s [1,] 1 4 382s [2,] 2 5 382s 382s , , 2 382s 382s V 382s U [,1] [,2] 382s [1,] 7 10 382s [2,] 8 11 382s 382s , , 3 382s 382s V 382s U [,1] [,2] 382s [1,] 13 16 382s [2,] 14 17 382s 382s , , 4 382s 382s V 382s U [,1] [,2] 382s [1,] 19 22 382s [2,] 20 23 382s 382s , , 5 382s 382s V 382s U [,1] [,2] 382s [1,] 25 28 382s [2,] 26 29 382s 382s attr(,"class") 382s [1] "tensor" 382s > B[[1]] 382s [1] 1 382s > B[[U=c("a","c")]]<-7 382s > B 382s , , W = 1 382s 382s V 382s U B1 B2 382s a 7 7 382s b 2 5 382s c 7 7 382s 382s , , W = 2 382s 382s V 382s U B1 B2 382s a 7 7 382s b 8 11 382s c 7 7 382s 382s , , W = 3 382s 382s V 382s U B1 B2 382s a 7 7 382s b 14 17 382s c 7 7 382s 382s , , W = 4 382s 382s V 382s U B1 B2 382s a 7 7 382s b 20 23 382s c 7 7 382s 382s , , W = 5 382s 382s V 382s U B1 B2 382s a 7 7 382s b 26 29 382s c 7 7 382s 382s attr(,"class") 382s [1] "tensor" 382s > B[[U=c("a","c")]]<- old 382s > 382s > # undrop.tensor 382s > undrop.tensor(A,name="Q",2) 382s , , 1, 1 382s 382s U 382s V [,1] [,2] 382s [1,] 1+0i 2+0i 382s [2,] 3+0i 4+0i 382s 382s , , 2, 1 382s 382s U 382s V [,1] [,2] 382s [1,] 5+0i 6+0i 382s [2,] 7+0i 8+0i 382s 382s , , 3, 1 382s 382s U 382s V [,1] [,2] 382s [1,] 9+0i 10+0i 382s [2,] 11+0i 12+0i 382s 382s , , 4, 1 382s 382s U 382s V [,1] [,2] 382s [1,] 13+0i 14+0i 382s [2,] 15+0i 16+0i 382s 382s , , 5, 1 382s 382s U 382s V [,1] [,2] 382s [1,] 17+0i 18+0i 382s [2,] 19+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > # combineCF.tensor 382s > # combineCF.tensor(Xs,c("a","b"),Xs,c("a","b")) 382s > 382s > # bind.tensor 382s > bind.tensor(A,1,einstein.tensor(A,V="q","U"="V",q="U"),2) 382s , , 1 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1+0i 5+0i 9+0i 13+0i 17+0i 382s [2,] 3+0i 7+0i 11+0i 15+0i 19+0i 382s 382s , , 2 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 2+0i 6+0i 10+0i 14+0i 18+0i 382s [2,] 4+0i 8+0i 12+0i 16+0i 20+0i 382s 382s , , 3 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1+0i 5+0i 9+0i 13+0i 17+0i 382s [2,] 2+0i 6+0i 10+0i 14+0i 18+0i 382s 382s , , 4 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 3+0i 7+0i 11+0i 15+0i 19+0i 382s [2,] 4+0i 8+0i 12+0i 16+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > bind.tensor(A,1,A,1) 382s , , 1 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1+0i 5+0i 9+0i 13+0i 17+0i 382s [2,] 3+0i 7+0i 11+0i 15+0i 19+0i 382s 382s , , 2 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 2+0i 6+0i 10+0i 14+0i 18+0i 382s [2,] 4+0i 8+0i 12+0i 16+0i 20+0i 382s 382s , , 3 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1+0i 5+0i 9+0i 13+0i 17+0i 382s [2,] 3+0i 7+0i 11+0i 15+0i 19+0i 382s 382s , , 4 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 2+0i 6+0i 10+0i 14+0i 18+0i 382s [2,] 4+0i 8+0i 12+0i 16+0i 20+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > bind.tensor(Anamed,1,einstein.tensor(Anamed,V="q","U"="V",q="U"),2) 382s , , 1 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1 5 9 13 17 382s [2,] 3 7 11 15 19 382s 382s , , 2 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 2 6 10 14 18 382s [2,] 4 8 12 16 20 382s 382s , , 3 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1 5 9 13 17 382s [2,] 2 6 10 14 18 382s 382s , , 4 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 3 7 11 15 19 382s [2,] 4 8 12 16 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > bind.tensor(Anamed,1,Anamed,1) 382s , , 1 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1 5 9 13 17 382s [2,] 3 7 11 15 19 382s 382s , , 2 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 2 6 10 14 18 382s [2,] 4 8 12 16 20 382s 382s , , 3 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 1 5 9 13 17 382s [2,] 3 7 11 15 19 382s 382s , , 4 382s 382s W 382s V [,1] [,2] [,3] [,4] [,5] 382s [1,] 2 6 10 14 18 382s [2,] 4 8 12 16 20 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > # toPos.tensor 382s > #toPos.tensor(A,c("A","U","I")) # error 382s > toPos.tensor(A,rev(names(A))) 382s [1] 3 2 1 382s > 382s > # einstein.tensor 382s > einstein.tensor(A,U="U'",B) 382s U 382s U' a b c 382s [1,] 1945+0i 2045+0i 2145+0i 382s [2,] 2090+0i 2200+0i 2310+0i 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > einstein.tensor(A,U="U'",mark(B,"k")) 382s , , 1, Uk = a, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 1+0i 3+0i 382s [2,] 2+0i 4+0i 382s 382s , , 2, Uk = a, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 5+0i 7+0i 382s [2,] 6+0i 8+0i 382s 382s , , 3, Uk = a, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 9+0i 11+0i 382s [2,] 10+0i 12+0i 382s 382s , , 4, Uk = a, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 13+0i 15+0i 382s [2,] 14+0i 16+0i 382s 382s , , 5, Uk = a, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 17+0i 19+0i 382s [2,] 18+0i 20+0i 382s 382s , , 1, Uk = b, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 2+0i 6+0i 382s [2,] 4+0i 8+0i 382s 382s , , 2, Uk = b, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 10+0i 14+0i 382s [2,] 12+0i 16+0i 382s 382s , , 3, Uk = b, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 18+0i 22+0i 382s [2,] 20+0i 24+0i 382s 382s , , 4, Uk = b, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 26+0i 30+0i 382s [2,] 28+0i 32+0i 382s 382s , , 5, Uk = b, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 34+0i 38+0i 382s [2,] 36+0i 40+0i 382s 382s , , 1, Uk = c, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 3+0i 9+0i 382s [2,] 6+0i 12+0i 382s 382s , , 2, Uk = c, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 15+0i 21+0i 382s [2,] 18+0i 24+0i 382s 382s , , 3, Uk = c, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 27+0i 33+0i 382s [2,] 30+0i 36+0i 382s 382s , , 4, Uk = c, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 39+0i 45+0i 382s [2,] 42+0i 48+0i 382s 382s , , 5, Uk = c, Vk = B1, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 51+0i 57+0i 382s [2,] 54+0i 60+0i 382s 382s , , 1, Uk = a, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 4+0i 12+0i 382s [2,] 8+0i 16+0i 382s 382s , , 2, Uk = a, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 20+0i 28+0i 382s [2,] 24+0i 32+0i 382s 382s , , 3, Uk = a, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 36+0i 44+0i 382s [2,] 40+0i 48+0i 382s 382s , , 4, Uk = a, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 52+0i 60+0i 382s [2,] 56+0i 64+0i 382s 382s , , 5, Uk = a, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 68+0i 76+0i 382s [2,] 72+0i 80+0i 382s 382s , , 1, Uk = b, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 5+0i 15+0i 382s [2,] 10+0i 20+0i 382s 382s , , 2, Uk = b, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 25+0i 35+0i 382s [2,] 30+0i 40+0i 382s 382s , , 3, Uk = b, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 45+0i 55+0i 382s [2,] 50+0i 60+0i 382s 382s , , 4, Uk = b, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 65+0i 75+0i 382s [2,] 70+0i 80+0i 382s 382s , , 5, Uk = b, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 85+0i 95+0i 382s [2,] 90+0i 100+0i 382s 382s , , 1, Uk = c, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 6+0i 18+0i 382s [2,] 12+0i 24+0i 382s 382s , , 2, Uk = c, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 30+0i 42+0i 382s [2,] 36+0i 48+0i 382s 382s , , 3, Uk = c, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 54+0i 66+0i 382s [2,] 60+0i 72+0i 382s 382s , , 4, Uk = c, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 78+0i 90+0i 382s [2,] 84+0i 96+0i 382s 382s , , 5, Uk = c, Vk = B2, Wk = 1 382s 382s V 382s U' [,1] [,2] 382s [1,] 102+0i 114+0i 382s [2,] 108+0i 120+0i 382s 382s , , 1, Uk = a, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 7+0i 21+0i 382s [2,] 14+0i 28+0i 382s 382s , , 2, Uk = a, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 35+0i 49+0i 382s [2,] 42+0i 56+0i 382s 382s , , 3, Uk = a, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 63+0i 77+0i 382s [2,] 70+0i 84+0i 382s 382s , , 4, Uk = a, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 91+0i 105+0i 382s [2,] 98+0i 112+0i 382s 382s , , 5, Uk = a, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 119+0i 133+0i 382s [2,] 126+0i 140+0i 382s 382s , , 1, Uk = b, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 8+0i 24+0i 382s [2,] 16+0i 32+0i 382s 382s , , 2, Uk = b, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 40+0i 56+0i 382s [2,] 48+0i 64+0i 382s 382s , , 3, Uk = b, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 72+0i 88+0i 382s [2,] 80+0i 96+0i 382s 382s , , 4, Uk = b, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 104+0i 120+0i 382s [2,] 112+0i 128+0i 382s 382s , , 5, Uk = b, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 136+0i 152+0i 382s [2,] 144+0i 160+0i 382s 382s , , 1, Uk = c, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 9+0i 27+0i 382s [2,] 18+0i 36+0i 382s 382s , , 2, Uk = c, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 45+0i 63+0i 382s [2,] 54+0i 72+0i 382s 382s , , 3, Uk = c, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 81+0i 99+0i 382s [2,] 90+0i 108+0i 382s 382s , , 4, Uk = c, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 117+0i 135+0i 382s [2,] 126+0i 144+0i 382s 382s , , 5, Uk = c, Vk = B1, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 153+0i 171+0i 382s [2,] 162+0i 180+0i 382s 382s , , 1, Uk = a, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 10+0i 30+0i 382s [2,] 20+0i 40+0i 382s 382s , , 2, Uk = a, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 50+0i 70+0i 382s [2,] 60+0i 80+0i 382s 382s , , 3, Uk = a, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 90+0i 110+0i 382s [2,] 100+0i 120+0i 382s 382s , , 4, Uk = a, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 130+0i 150+0i 382s [2,] 140+0i 160+0i 382s 382s , , 5, Uk = a, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 170+0i 190+0i 382s [2,] 180+0i 200+0i 382s 382s , , 1, Uk = b, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 11+0i 33+0i 382s [2,] 22+0i 44+0i 382s 382s , , 2, Uk = b, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 55+0i 77+0i 382s [2,] 66+0i 88+0i 382s 382s , , 3, Uk = b, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 99+0i 121+0i 382s [2,] 110+0i 132+0i 382s 382s , , 4, Uk = b, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 143+0i 165+0i 382s [2,] 154+0i 176+0i 382s 382s , , 5, Uk = b, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 187+0i 209+0i 382s [2,] 198+0i 220+0i 382s 382s , , 1, Uk = c, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 12+0i 36+0i 382s [2,] 24+0i 48+0i 382s 382s , , 2, Uk = c, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 60+0i 84+0i 382s [2,] 72+0i 96+0i 382s 382s , , 3, Uk = c, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 108+0i 132+0i 382s [2,] 120+0i 144+0i 382s 382s , , 4, Uk = c, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 156+0i 180+0i 382s [2,] 168+0i 192+0i 382s 382s , , 5, Uk = c, Vk = B2, Wk = 2 382s 382s V 382s U' [,1] [,2] 382s [1,] 204+0i 228+0i 382s [2,] 216+0i 240+0i 382s 382s , , 1, Uk = a, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 13+0i 39+0i 382s [2,] 26+0i 52+0i 382s 382s , , 2, Uk = a, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 65+0i 91+0i 382s [2,] 78+0i 104+0i 382s 382s , , 3, Uk = a, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 117+0i 143+0i 382s [2,] 130+0i 156+0i 382s 382s , , 4, Uk = a, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 169+0i 195+0i 382s [2,] 182+0i 208+0i 382s 382s , , 5, Uk = a, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 221+0i 247+0i 382s [2,] 234+0i 260+0i 382s 382s , , 1, Uk = b, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 14+0i 42+0i 382s [2,] 28+0i 56+0i 382s 382s , , 2, Uk = b, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 70+0i 98+0i 382s [2,] 84+0i 112+0i 382s 382s , , 3, Uk = b, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 126+0i 154+0i 382s [2,] 140+0i 168+0i 382s 382s , , 4, Uk = b, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 182+0i 210+0i 382s [2,] 196+0i 224+0i 382s 382s , , 5, Uk = b, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 238+0i 266+0i 382s [2,] 252+0i 280+0i 382s 382s , , 1, Uk = c, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 15+0i 45+0i 382s [2,] 30+0i 60+0i 382s 382s , , 2, Uk = c, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 75+0i 105+0i 382s [2,] 90+0i 120+0i 382s 382s , , 3, Uk = c, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 135+0i 165+0i 382s [2,] 150+0i 180+0i 382s 382s , , 4, Uk = c, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 195+0i 225+0i 382s [2,] 210+0i 240+0i 382s 382s , , 5, Uk = c, Vk = B1, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 255+0i 285+0i 382s [2,] 270+0i 300+0i 382s 382s , , 1, Uk = a, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 16+0i 48+0i 382s [2,] 32+0i 64+0i 382s 382s , , 2, Uk = a, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 80+0i 112+0i 382s [2,] 96+0i 128+0i 382s 382s , , 3, Uk = a, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 144+0i 176+0i 382s [2,] 160+0i 192+0i 382s 382s , , 4, Uk = a, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 208+0i 240+0i 382s [2,] 224+0i 256+0i 382s 382s , , 5, Uk = a, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 272+0i 304+0i 382s [2,] 288+0i 320+0i 382s 382s , , 1, Uk = b, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 17+0i 51+0i 382s [2,] 34+0i 68+0i 382s 382s , , 2, Uk = b, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 85+0i 119+0i 382s [2,] 102+0i 136+0i 382s 382s , , 3, Uk = b, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 153+0i 187+0i 382s [2,] 170+0i 204+0i 382s 382s , , 4, Uk = b, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 221+0i 255+0i 382s [2,] 238+0i 272+0i 382s 382s , , 5, Uk = b, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 289+0i 323+0i 382s [2,] 306+0i 340+0i 382s 382s , , 1, Uk = c, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 18+0i 54+0i 382s [2,] 36+0i 72+0i 382s 382s , , 2, Uk = c, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 90+0i 126+0i 382s [2,] 108+0i 144+0i 382s 382s , , 3, Uk = c, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 162+0i 198+0i 382s [2,] 180+0i 216+0i 382s 382s , , 4, Uk = c, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 234+0i 270+0i 382s [2,] 252+0i 288+0i 382s 382s , , 5, Uk = c, Vk = B2, Wk = 3 382s 382s V 382s U' [,1] [,2] 382s [1,] 306+0i 342+0i 382s [2,] 324+0i 360+0i 382s 382s , , 1, Uk = a, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 19+0i 57+0i 382s [2,] 38+0i 76+0i 382s 382s , , 2, Uk = a, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 95+0i 133+0i 382s [2,] 114+0i 152+0i 382s 382s , , 3, Uk = a, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 171+0i 209+0i 382s [2,] 190+0i 228+0i 382s 382s , , 4, Uk = a, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 247+0i 285+0i 382s [2,] 266+0i 304+0i 382s 382s , , 5, Uk = a, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 323+0i 361+0i 382s [2,] 342+0i 380+0i 382s 382s , , 1, Uk = b, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 20+0i 60+0i 382s [2,] 40+0i 80+0i 382s 382s , , 2, Uk = b, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 100+0i 140+0i 382s [2,] 120+0i 160+0i 382s 382s , , 3, Uk = b, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 180+0i 220+0i 382s [2,] 200+0i 240+0i 382s 382s , , 4, Uk = b, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 260+0i 300+0i 382s [2,] 280+0i 320+0i 382s 382s , , 5, Uk = b, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 340+0i 380+0i 382s [2,] 360+0i 400+0i 382s 382s , , 1, Uk = c, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 21+0i 63+0i 382s [2,] 42+0i 84+0i 382s 382s , , 2, Uk = c, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 105+0i 147+0i 382s [2,] 126+0i 168+0i 382s 382s , , 3, Uk = c, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 189+0i 231+0i 382s [2,] 210+0i 252+0i 382s 382s , , 4, Uk = c, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 273+0i 315+0i 382s [2,] 294+0i 336+0i 382s 382s , , 5, Uk = c, Vk = B1, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 357+0i 399+0i 382s [2,] 378+0i 420+0i 382s 382s , , 1, Uk = a, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 22+0i 66+0i 382s [2,] 44+0i 88+0i 382s 382s , , 2, Uk = a, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 110+0i 154+0i 382s [2,] 132+0i 176+0i 382s 382s , , 3, Uk = a, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 198+0i 242+0i 382s [2,] 220+0i 264+0i 382s 382s , , 4, Uk = a, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 286+0i 330+0i 382s [2,] 308+0i 352+0i 382s 382s , , 5, Uk = a, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 374+0i 418+0i 382s [2,] 396+0i 440+0i 382s 382s , , 1, Uk = b, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 23+0i 69+0i 382s [2,] 46+0i 92+0i 382s 382s , , 2, Uk = b, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 115+0i 161+0i 382s [2,] 138+0i 184+0i 382s 382s , , 3, Uk = b, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 207+0i 253+0i 382s [2,] 230+0i 276+0i 382s 382s , , 4, Uk = b, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 299+0i 345+0i 382s [2,] 322+0i 368+0i 382s 382s , , 5, Uk = b, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 391+0i 437+0i 382s [2,] 414+0i 460+0i 382s 382s , , 1, Uk = c, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 24+0i 72+0i 382s [2,] 48+0i 96+0i 382s 382s , , 2, Uk = c, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 120+0i 168+0i 382s [2,] 144+0i 192+0i 382s 382s , , 3, Uk = c, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 216+0i 264+0i 382s [2,] 240+0i 288+0i 382s 382s , , 4, Uk = c, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 312+0i 360+0i 382s [2,] 336+0i 384+0i 382s 382s , , 5, Uk = c, Vk = B2, Wk = 4 382s 382s V 382s U' [,1] [,2] 382s [1,] 408+0i 456+0i 382s [2,] 432+0i 480+0i 382s 382s , , 1, Uk = a, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 25+0i 75+0i 382s [2,] 50+0i 100+0i 382s 382s , , 2, Uk = a, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 125+0i 175+0i 382s [2,] 150+0i 200+0i 382s 382s , , 3, Uk = a, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 225+0i 275+0i 382s [2,] 250+0i 300+0i 382s 382s , , 4, Uk = a, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 325+0i 375+0i 382s [2,] 350+0i 400+0i 382s 382s , , 5, Uk = a, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 425+0i 475+0i 382s [2,] 450+0i 500+0i 382s 382s , , 1, Uk = b, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 26+0i 78+0i 382s [2,] 52+0i 104+0i 382s 382s , , 2, Uk = b, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 130+0i 182+0i 382s [2,] 156+0i 208+0i 382s 382s , , 3, Uk = b, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 234+0i 286+0i 382s [2,] 260+0i 312+0i 382s 382s , , 4, Uk = b, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 338+0i 390+0i 382s [2,] 364+0i 416+0i 382s 382s , , 5, Uk = b, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 442+0i 494+0i 382s [2,] 468+0i 520+0i 382s 382s , , 1, Uk = c, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 27+0i 81+0i 382s [2,] 54+0i 108+0i 382s 382s , , 2, Uk = c, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 135+0i 189+0i 382s [2,] 162+0i 216+0i 382s 382s , , 3, Uk = c, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 243+0i 297+0i 382s [2,] 270+0i 324+0i 382s 382s , , 4, Uk = c, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 351+0i 405+0i 382s [2,] 378+0i 432+0i 382s 382s , , 5, Uk = c, Vk = B1, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 459+0i 513+0i 382s [2,] 486+0i 540+0i 382s 382s , , 1, Uk = a, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 28+0i 84+0i 382s [2,] 56+0i 112+0i 382s 382s , , 2, Uk = a, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 140+0i 196+0i 382s [2,] 168+0i 224+0i 382s 382s , , 3, Uk = a, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 252+0i 308+0i 382s [2,] 280+0i 336+0i 382s 382s , , 4, Uk = a, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 364+0i 420+0i 382s [2,] 392+0i 448+0i 382s 382s , , 5, Uk = a, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 476+0i 532+0i 382s [2,] 504+0i 560+0i 382s 382s , , 1, Uk = b, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 29+0i 87+0i 382s [2,] 58+0i 116+0i 382s 382s , , 2, Uk = b, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 145+0i 203+0i 382s [2,] 174+0i 232+0i 382s 382s , , 3, Uk = b, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 261+0i 319+0i 382s [2,] 290+0i 348+0i 382s 382s , , 4, Uk = b, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 377+0i 435+0i 382s [2,] 406+0i 464+0i 382s 382s , , 5, Uk = b, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 493+0i 551+0i 382s [2,] 522+0i 580+0i 382s 382s , , 1, Uk = c, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 30+0i 90+0i 382s [2,] 60+0i 120+0i 382s 382s , , 2, Uk = c, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 150+0i 210+0i 382s [2,] 180+0i 240+0i 382s 382s , , 3, Uk = c, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 270+0i 330+0i 382s [2,] 300+0i 360+0i 382s 382s , , 4, Uk = c, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 390+0i 450+0i 382s [2,] 420+0i 480+0i 382s 382s , , 5, Uk = c, Vk = B2, Wk = 5 382s 382s V 382s U' [,1] [,2] 382s [1,] 510+0i 570+0i 382s [2,] 540+0i 600+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > einstein.tensor(A,U="U'",mark(B,"k"),V="Vk",W="Wk") 382s Uk 382s U' a b c 382s [1,] 1945+0i 2045+0i 2145+0i 382s [2,] 2090+0i 2200+0i 2310+0i 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > einstein.tensor(A,U="U'",mark(B,"k"),V="Vk",W="Wk",1/10) 382s Uk 382s U' a b c 382s [1,] 194.5+0i 204.5+0i 214.5+0i 382s [2,] 209.0+0i 220.0+0i 231.0+0i 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > einstein.tensor(A,U="U'",mark(B,"k"),V="Vk",W="Wk",diag=to.tensor(c(1,1/10,1/100),c(Uk=3))) 382s Uk 382s U' a b c 382s [1,] 1945+0i 204.5+0i 21.45+0i 382s [2,] 2090+0i 220.0+0i 23.10+0i 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > 382s > ftable(einstein.tensor(A,U="U'",B)) 382s U a b c 382s U' 382s U'1 1945+0i 2045+0i 2145+0i 382s U'2 2090+0i 2200+0i 2310+0i 382s > ftable(einstein.tensor(A,U="U'",mark(B,"k"))) 382s Wk 1 2 3 4 5 382s U' V W Uk Vk 382s U'1 V1 W1 a B1 1+0i 7+0i 13+0i 19+0i 25+0i 382s B2 4+0i 10+0i 16+0i 22+0i 28+0i 382s b B1 2+0i 8+0i 14+0i 20+0i 26+0i 382s B2 5+0i 11+0i 17+0i 23+0i 29+0i 382s c B1 3+0i 9+0i 15+0i 21+0i 27+0i 382s B2 6+0i 12+0i 18+0i 24+0i 30+0i 382s W2 a B1 5+0i 35+0i 65+0i 95+0i 125+0i 382s B2 20+0i 50+0i 80+0i 110+0i 140+0i 382s b B1 10+0i 40+0i 70+0i 100+0i 130+0i 382s B2 25+0i 55+0i 85+0i 115+0i 145+0i 382s c B1 15+0i 45+0i 75+0i 105+0i 135+0i 382s B2 30+0i 60+0i 90+0i 120+0i 150+0i 382s W3 a B1 9+0i 63+0i 117+0i 171+0i 225+0i 382s B2 36+0i 90+0i 144+0i 198+0i 252+0i 382s b B1 18+0i 72+0i 126+0i 180+0i 234+0i 382s B2 45+0i 99+0i 153+0i 207+0i 261+0i 382s c B1 27+0i 81+0i 135+0i 189+0i 243+0i 382s B2 54+0i 108+0i 162+0i 216+0i 270+0i 382s W4 a B1 13+0i 91+0i 169+0i 247+0i 325+0i 382s B2 52+0i 130+0i 208+0i 286+0i 364+0i 382s b B1 26+0i 104+0i 182+0i 260+0i 338+0i 382s B2 65+0i 143+0i 221+0i 299+0i 377+0i 382s c B1 39+0i 117+0i 195+0i 273+0i 351+0i 382s B2 78+0i 156+0i 234+0i 312+0i 390+0i 382s W5 a B1 17+0i 119+0i 221+0i 323+0i 425+0i 382s B2 68+0i 170+0i 272+0i 374+0i 476+0i 382s b B1 34+0i 136+0i 238+0i 340+0i 442+0i 382s B2 85+0i 187+0i 289+0i 391+0i 493+0i 382s c B1 51+0i 153+0i 255+0i 357+0i 459+0i 382s B2 102+0i 204+0i 306+0i 408+0i 510+0i 382s V2 W1 a B1 3+0i 21+0i 39+0i 57+0i 75+0i 382s B2 12+0i 30+0i 48+0i 66+0i 84+0i 382s b B1 6+0i 24+0i 42+0i 60+0i 78+0i 382s B2 15+0i 33+0i 51+0i 69+0i 87+0i 382s c B1 9+0i 27+0i 45+0i 63+0i 81+0i 382s B2 18+0i 36+0i 54+0i 72+0i 90+0i 382s W2 a B1 7+0i 49+0i 91+0i 133+0i 175+0i 382s B2 28+0i 70+0i 112+0i 154+0i 196+0i 382s b B1 14+0i 56+0i 98+0i 140+0i 182+0i 382s B2 35+0i 77+0i 119+0i 161+0i 203+0i 382s c B1 21+0i 63+0i 105+0i 147+0i 189+0i 382s B2 42+0i 84+0i 126+0i 168+0i 210+0i 382s W3 a B1 11+0i 77+0i 143+0i 209+0i 275+0i 382s B2 44+0i 110+0i 176+0i 242+0i 308+0i 382s b B1 22+0i 88+0i 154+0i 220+0i 286+0i 382s B2 55+0i 121+0i 187+0i 253+0i 319+0i 382s c B1 33+0i 99+0i 165+0i 231+0i 297+0i 382s B2 66+0i 132+0i 198+0i 264+0i 330+0i 382s W4 a B1 15+0i 105+0i 195+0i 285+0i 375+0i 382s B2 60+0i 150+0i 240+0i 330+0i 420+0i 382s b B1 30+0i 120+0i 210+0i 300+0i 390+0i 382s B2 75+0i 165+0i 255+0i 345+0i 435+0i 382s c B1 45+0i 135+0i 225+0i 315+0i 405+0i 382s B2 90+0i 180+0i 270+0i 360+0i 450+0i 382s W5 a B1 19+0i 133+0i 247+0i 361+0i 475+0i 382s B2 76+0i 190+0i 304+0i 418+0i 532+0i 382s b B1 38+0i 152+0i 266+0i 380+0i 494+0i 382s B2 95+0i 209+0i 323+0i 437+0i 551+0i 382s c B1 57+0i 171+0i 285+0i 399+0i 513+0i 382s B2 114+0i 228+0i 342+0i 456+0i 570+0i 382s U'2 V1 W1 a B1 2+0i 14+0i 26+0i 38+0i 50+0i 382s B2 8+0i 20+0i 32+0i 44+0i 56+0i 382s b B1 4+0i 16+0i 28+0i 40+0i 52+0i 382s B2 10+0i 22+0i 34+0i 46+0i 58+0i 382s c B1 6+0i 18+0i 30+0i 42+0i 54+0i 382s B2 12+0i 24+0i 36+0i 48+0i 60+0i 382s W2 a B1 6+0i 42+0i 78+0i 114+0i 150+0i 382s B2 24+0i 60+0i 96+0i 132+0i 168+0i 382s b B1 12+0i 48+0i 84+0i 120+0i 156+0i 382s B2 30+0i 66+0i 102+0i 138+0i 174+0i 382s c B1 18+0i 54+0i 90+0i 126+0i 162+0i 382s B2 36+0i 72+0i 108+0i 144+0i 180+0i 382s W3 a B1 10+0i 70+0i 130+0i 190+0i 250+0i 382s B2 40+0i 100+0i 160+0i 220+0i 280+0i 382s b B1 20+0i 80+0i 140+0i 200+0i 260+0i 382s B2 50+0i 110+0i 170+0i 230+0i 290+0i 382s c B1 30+0i 90+0i 150+0i 210+0i 270+0i 382s B2 60+0i 120+0i 180+0i 240+0i 300+0i 382s W4 a B1 14+0i 98+0i 182+0i 266+0i 350+0i 382s B2 56+0i 140+0i 224+0i 308+0i 392+0i 382s b B1 28+0i 112+0i 196+0i 280+0i 364+0i 382s B2 70+0i 154+0i 238+0i 322+0i 406+0i 382s c B1 42+0i 126+0i 210+0i 294+0i 378+0i 382s B2 84+0i 168+0i 252+0i 336+0i 420+0i 382s W5 a B1 18+0i 126+0i 234+0i 342+0i 450+0i 382s B2 72+0i 180+0i 288+0i 396+0i 504+0i 382s b B1 36+0i 144+0i 252+0i 360+0i 468+0i 382s B2 90+0i 198+0i 306+0i 414+0i 522+0i 382s c B1 54+0i 162+0i 270+0i 378+0i 486+0i 382s B2 108+0i 216+0i 324+0i 432+0i 540+0i 382s V2 W1 a B1 4+0i 28+0i 52+0i 76+0i 100+0i 382s B2 16+0i 40+0i 64+0i 88+0i 112+0i 382s b B1 8+0i 32+0i 56+0i 80+0i 104+0i 382s B2 20+0i 44+0i 68+0i 92+0i 116+0i 382s c B1 12+0i 36+0i 60+0i 84+0i 108+0i 382s B2 24+0i 48+0i 72+0i 96+0i 120+0i 382s W2 a B1 8+0i 56+0i 104+0i 152+0i 200+0i 382s B2 32+0i 80+0i 128+0i 176+0i 224+0i 382s b B1 16+0i 64+0i 112+0i 160+0i 208+0i 382s B2 40+0i 88+0i 136+0i 184+0i 232+0i 382s c B1 24+0i 72+0i 120+0i 168+0i 216+0i 382s B2 48+0i 96+0i 144+0i 192+0i 240+0i 382s W3 a B1 12+0i 84+0i 156+0i 228+0i 300+0i 382s B2 48+0i 120+0i 192+0i 264+0i 336+0i 382s b B1 24+0i 96+0i 168+0i 240+0i 312+0i 382s B2 60+0i 132+0i 204+0i 276+0i 348+0i 382s c B1 36+0i 108+0i 180+0i 252+0i 324+0i 382s B2 72+0i 144+0i 216+0i 288+0i 360+0i 382s W4 a B1 16+0i 112+0i 208+0i 304+0i 400+0i 382s B2 64+0i 160+0i 256+0i 352+0i 448+0i 382s b B1 32+0i 128+0i 224+0i 320+0i 416+0i 382s B2 80+0i 176+0i 272+0i 368+0i 464+0i 382s c B1 48+0i 144+0i 240+0i 336+0i 432+0i 382s B2 96+0i 192+0i 288+0i 384+0i 480+0i 382s W5 a B1 20+0i 140+0i 260+0i 380+0i 500+0i 382s B2 80+0i 200+0i 320+0i 440+0i 560+0i 382s b B1 40+0i 160+0i 280+0i 400+0i 520+0i 382s B2 100+0i 220+0i 340+0i 460+0i 580+0i 382s c B1 60+0i 180+0i 300+0i 420+0i 540+0i 382s B2 120+0i 240+0i 360+0i 480+0i 600+0i 382s > ftable(einstein.tensor(A,U="U'",mark(B,"k"),V="Vk",W="Wk")) 382s Uk a b c 382s U' 382s U'1 1945+0i 2045+0i 2145+0i 382s U'2 2090+0i 2200+0i 2310+0i 382s > ftable(einstein.tensor(A,U="U'",mark(B,"k"),V="Vk",W="Wk",1/10)) 382s Uk a b c 382s U' 382s U'1 194.5+0i 204.5+0i 214.5+0i 382s U'2 209.0+0i 220.0+0i 231.0+0i 382s > ftable(einstein.tensor(A,U="U'",mark(B,"k"),V="Vk",W="Wk",diag=to.tensor(c(1,1/10,1/100),c(Uk=3)))) 382s Uk a b c 382s U' 382s U'1 1945.00+0i 204.50+0i 21.45+0i 382s U'2 2090.00+0i 220.00+0i 23.10+0i 382s > 382s > # %e% [[]] 382s > dim(A[[U=~M]]) 382s M V W 382s 2 2 5 382s > A[[U=~M]] %e% B 382s U 382s M a b c 382s [1,] 1945+0i 2045+0i 2145+0i 382s [2,] 2090+0i 2200+0i 2310+0i 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > A[[U=~M,V=~"L"]] %e% B 382s , , U = a, V = B1 382s 382s L 382s M [,1] [,2] 382s [1,] 825+0i 955+0i 382s [2,] 890+0i 1020+0i 382s 382s , , U = b, V = B1 382s 382s L 382s M [,1] [,2] 382s [1,] 870+0i 1010+0i 382s [2,] 940+0i 1080+0i 382s 382s , , U = c, V = B1 382s 382s L 382s M [,1] [,2] 382s [1,] 915+0i 1065+0i 382s [2,] 990+0i 1140+0i 382s 382s , , U = a, V = B2 382s 382s L 382s M [,1] [,2] 382s [1,] 960+0i 1120+0i 382s [2,] 1040+0i 1200+0i 382s 382s , , U = b, V = B2 382s 382s L 382s M [,1] [,2] 382s [1,] 1005+0i 1175+0i 382s [2,] 1090+0i 1260+0i 382s 382s , , U = c, V = B2 382s 382s L 382s M [,1] [,2] 382s [1,] 1050+0i 1230+0i 382s [2,] 1140+0i 1320+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > 382s > # firstnames/secondnames 382s > #firstnames(secondnames(names(A),"2"),"2") 382s > contraname(names(A)) 382s [1] "^U" "^V" "^W" 382s > 382s > dim(A) 382s U V W 382s 2 2 5 382s > dim(B) 382s U V W 382s 3 2 5 382s > 382s > add.tensor(A,A)/2-A 382s , , 1 382s 382s V 382s U [,1] [,2] 382s [1,] 0+0i 0+0i 382s [2,] 0+0i 0+0i 382s 382s , , 2 382s 382s V 382s U [,1] [,2] 382s [1,] 0+0i 0+0i 382s [2,] 0+0i 0+0i 382s 382s , , 3 382s 382s V 382s U [,1] [,2] 382s [1,] 0+0i 0+0i 382s [2,] 0+0i 0+0i 382s 382s , , 4 382s 382s V 382s U [,1] [,2] 382s [1,] 0+0i 0+0i 382s [2,] 0+0i 0+0i 382s 382s , , 5 382s 382s V 382s U [,1] [,2] 382s [1,] 0+0i 0+0i 382s [2,] 0+0i 0+0i 382s 382s attr(,"class") 382s [1] "tensor" 382s > norm.tensor(add.tensor(A,A)/2-A) 382s [1] 0 382s > 382s > tmp <- add.tensor( A,A[[U=~K]] ,op="-") 382s > dim(tmp) 382s U V W K 382s 2 2 5 2 382s > ftable(tmp) 382s K K1 K2 382s U V W 382s U1 V1 W1 0+0i -1+0i 382s W2 0+0i -1+0i 382s W3 0+0i -1+0i 382s W4 0+0i -1+0i 382s W5 0+0i -1+0i 382s V2 W1 0+0i -1+0i 382s W2 0+0i -1+0i 382s W3 0+0i -1+0i 382s W4 0+0i -1+0i 382s W5 0+0i -1+0i 382s U2 V1 W1 1+0i 0+0i 382s W2 1+0i 0+0i 382s W3 1+0i 0+0i 382s W4 1+0i 0+0i 382s W5 1+0i 0+0i 382s V2 W1 1+0i 0+0i 382s W2 1+0i 0+0i 382s W3 1+0i 0+0i 382s W4 1+0i 0+0i 382s W5 1+0i 0+0i 382s > 382s > A %e% A 382s [1] 2870+0i 382s > norm.tensor(reorder(A,c(2,3,1)) - A) 382s [1] 0 382s > 382s > # Dragging 382s > 382s > g <- to.tensor(c(1,2,0,1),c(i=2,j=2)) 382s > A <- to.tensor(rnorm(8),c(a=2,b=2,c=2)) 382s > A2 <- drag.tensor(A,g,c("b","c")) 382s > A2 382s , , 1 382s 382s ^b 382s a [,1] [,2] 382s [1,] -1.997813 5.216444 382s [2,] 0.701076 -2.253076 382s 382s , , 2 382s 382s ^b 382s a [,1] [,2] 382s [1,] 3.432017 -8.334954 382s [2,] -1.124918 4.904314 382s 382s attr(,"class") 382s [1] "tensor" 382s > names(A2) 382s [1] "a" "^b" "^c" 382s > as.covariate(names(A2)) 382s [1] "a" "b" "c" 382s > as.contravariate(names(A2)) 382s [1] "^a" "^b" "^c" 382s > is.covariate(A2) 382s [1] TRUE FALSE FALSE 382s > is.contravariate(A2) 382s [1] FALSE TRUE TRUE 382s > riemann.tensor(A2,g) 382s , , 1, 1, 1 382s 382s ^b 382s a [,1] [,2] 382s [1,] -1.997813 5.216444 382s [2,] 0.701076 -2.253076 382s 382s , , 2, 1, 1 382s 382s ^b 382s a [,1] [,2] 382s [1,] 3.432017 -8.334954 382s [2,] -1.124918 4.904314 382s 382s , , 1, 2, 1 382s 382s ^b 382s a [,1] [,2] 382s [1,] -3.995625 10.432888 382s [2,] 1.402152 -4.506152 382s 382s , , 2, 2, 1 382s 382s ^b 382s a [,1] [,2] 382s [1,] 6.864035 -16.669908 382s [2,] -2.249835 9.808628 382s 382s , , 1, 1, 2 382s 382s ^b 382s a [,1] [,2] 382s [1,] 0 0 382s [2,] 0 0 382s 382s , , 2, 1, 2 382s 382s ^b 382s a [,1] [,2] 382s [1,] 0 0 382s [2,] 0 0 382s 382s , , 1, 2, 2 382s 382s ^b 382s a [,1] [,2] 382s [1,] -1.997813 5.216444 382s [2,] 0.701076 -2.253076 382s 382s , , 2, 2, 2 382s 382s ^b 382s a [,1] [,2] 382s [1,] 3.432017 -8.334954 382s [2,] -1.124918 4.904314 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > 382s > # ####################### 382s > 382s > d1 <- c(a=2,b=2) 382s > d2 <- c("a'"=2,"b'"=2) 382s > m <- to.tensor(1:4,d1) 382s > V <- delta.tensor(d1)+one.tensor(c(d1,d2)) 382s > V 382s , , 1, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 2 1 382s [2,] 1 1 382s 382s , , 2, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 1 1 382s [2,] 2 1 382s 382s , , 1, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 1 2 382s [2,] 1 1 382s 382s , , 2, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 1 1 382s [2,] 1 2 382s 382s attr(,"class") 382s [1] "tensor" 382s > X <- (power.tensor(V,c("a","b"),c("a'","b'"),p=1/2) %e% 382s + to.tensor(rnorm(1000*2*2),c(i=1000,d2))) + m 382s > # The mean 382s > mean.tensor(X,along="i") 382s b 382s a [,1] [,2] 382s [1,] 1.049987 3.066707 382s [2,] 1.990994 4.025764 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > # Full tensorial covariance: 382s > var.tensor(X,along="i") 382s , , 1, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 2.039425 1.039642 382s [2,] 1.060075 1.004232 382s 382s , , 2, 1 382s 382s b 382s a [,1] [,2] 382s [1,] 1.060075 1.0417556 382s [2,] 2.042461 0.9857423 382s 382s , , 1, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 1.039642 2.050543 382s [2,] 1.041756 1.046732 382s 382s , , 2, 2 382s 382s b 382s a [,1] [,2] 382s [1,] 1.0042320 1.046732 382s [2,] 0.9857423 1.956060 382s 382s attr(,"class") 382s [1] "tensor" 382s > # Variance of the slices X[[b=1]] and X[[b=2]] : 382s > var.tensor(X,along="i",by="b") 382s , , 1 382s 382s a' 382s a [,1] [,2] 382s [1,] 2.039425 1.060075 382s [2,] 1.060075 2.042461 382s 382s , , 2 382s 382s a' 382s a [,1] [,2] 382s [1,] 2.050543 1.046732 382s [2,] 1.046732 1.956060 382s 382s attr(,"class") 382s [1] "tensor" 382s > # Covariance of the slices X[[b=1]] and X[[b=2]] : 382s > var.tensor(X[[b=1]],X[[a=~"a'",b=2]],along="i") 382s a' 382s a [,1] [,2] 382s [1,] 1.039642 1.0042320 382s [2,] 1.041756 0.9857423 382s attr(,"class") 382s [1] "tensor" "matrix" 382s > 382s > 382s > ## ######################### 382s > 382s > Var <- function(x,along) { 382s + one <- one.tensor(dim(x)[along]) 382s + M <- one/(one%e%one) 382s + z <- x- M %e% x 382s + einstein.tensor( z,mark(z),by=names(M)) %e% M 382s + 382s + } 382s > 382s > A <- to.tensor(rnorm(4000),c(i=2,j=2,s=1000)) 382s > 382s > dim(A)["s"] 382s s 382s 1000 382s > Var(A,"s") 382s , , 1, 1 382s 382s j 382s i [,1] [,2] 382s [1,] 0.8632351 0.01671362 382s [2,] -0.0105442 0.01923930 382s 382s , , 2, 1 382s 382s j 382s i [,1] [,2] 382s [1,] -0.0105442 -0.025024729 382s [2,] 1.0003179 -0.005157977 382s 382s , , 1, 2 382s 382s j 382s i [,1] [,2] 382s [1,] 0.01671362 0.95200584 382s [2,] -0.02502473 -0.01240971 382s 382s , , 2, 2 382s 382s j 382s i [,1] [,2] 382s [1,] 0.019239302 -0.01240971 382s [2,] -0.005157977 1.02441163 382s 382s attr(,"class") 382s [1] "tensor" 382s > delta.tensor(c(i=2,j=2)) 382s , , 1, 1 382s 382s j 382s i [,1] [,2] 382s [1,] 1 0 382s [2,] 0 0 382s 382s , , 2, 1 382s 382s j 382s i [,1] [,2] 382s [1,] 0 0 382s [2,] 1 0 382s 382s , , 1, 2 382s 382s j 382s i [,1] [,2] 382s [1,] 0 1 382s [2,] 0 0 382s 382s , , 2, 2 382s 382s j 382s i [,1] [,2] 382s [1,] 0 0 382s [2,] 0 1 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > Var(A,"s")-delta.tensor(c(i=2,j=2)) 382s , , 1, 1 382s 382s j 382s i [,1] [,2] 382s [1,] -0.1367649 0.01671362 382s [2,] -0.0105442 0.01923930 382s 382s , , 2, 1 382s 382s j 382s i [,1] [,2] 382s [1,] -0.0105442041 -0.025024729 382s [2,] 0.0003178862 -0.005157977 382s 382s , , 1, 2 382s 382s j 382s i [,1] [,2] 382s [1,] 0.01671362 -0.04799416 382s [2,] -0.02502473 -0.01240971 382s 382s , , 2, 2 382s 382s j 382s i [,1] [,2] 382s [1,] 0.019239302 -0.01240971 382s [2,] -0.005157977 0.02441163 382s 382s attr(,"class") 382s [1] "tensor" 382s > 382s > 382s > 382s > 382s autopkgtest [20:29:31]: test run-unit-test: -----------------------] 383s autopkgtest [20:29:32]: test run-unit-test: - - - - - - - - - - results - - - - - - - - - - 383s run-unit-test PASS 383s autopkgtest [20:29:32]: test pkg-r-autopkgtest: preparing testbed 384s Reading package lists... 385s Building dependency tree... 385s Reading state information... 385s Starting pkgProblemResolver with broken count: 0 385s Starting 2 pkgProblemResolver with broken count: 0 385s Done 385s The following additional packages will be installed: 385s build-essential cpp cpp-13 cpp-13-aarch64-linux-gnu cpp-aarch64-linux-gnu 385s dctrl-tools g++ g++-13 g++-13-aarch64-linux-gnu g++-aarch64-linux-gnu gcc 385s gcc-13 gcc-13-aarch64-linux-gnu gcc-aarch64-linux-gnu gfortran gfortran-13 385s gfortran-13-aarch64-linux-gnu gfortran-aarch64-linux-gnu icu-devtools 385s libasan8 libatomic1 libblas-dev libbz2-dev libc-dev-bin libc6-dev libcc1-0 385s libcrypt-dev libgcc-13-dev libgfortran-13-dev libhwasan0 libicu-dev libisl23 385s libitm1 libjpeg-dev libjpeg-turbo8-dev libjpeg8-dev liblapack-dev liblsan0 385s liblzma-dev libmpc3 libncurses-dev libnsl-dev libpcre2-16-0 libpcre2-32-0 385s libpcre2-dev libpcre2-posix3 libpkgconf3 libpng-dev libreadline-dev 385s libstdc++-13-dev libtirpc-dev libtsan2 libubsan1 linux-libc-dev pkg-config 385s pkg-r-autopkgtest pkgconf pkgconf-bin r-base-dev rpcsvc-proto zlib1g-dev 385s Suggested packages: 385s cpp-doc gcc-13-locales cpp-13-doc debtags gcc-13-doc gcc-multilib 385s manpages-dev autoconf automake libtool flex bison gdb gcc-doc 385s gdb-aarch64-linux-gnu gfortran-doc gfortran-13-doc libcoarrays-dev 385s liblapack-doc glibc-doc icu-doc liblzma-doc ncurses-doc readline-doc 385s libstdc++-13-doc texlive-base texlive-latex-base texlive-plain-generic 385s texlive-fonts-recommended texlive-fonts-extra texlive-extra-utils 385s texlive-latex-recommended texlive-latex-extra texinfo 385s Recommended packages: 385s bzip2-doc manpages manpages-dev libc-devtools libpng-tools 385s The following NEW packages will be installed: 385s autopkgtest-satdep build-essential cpp cpp-13 cpp-13-aarch64-linux-gnu 385s cpp-aarch64-linux-gnu dctrl-tools g++ g++-13 g++-13-aarch64-linux-gnu 385s g++-aarch64-linux-gnu gcc gcc-13 gcc-13-aarch64-linux-gnu 385s gcc-aarch64-linux-gnu gfortran gfortran-13 gfortran-13-aarch64-linux-gnu 385s gfortran-aarch64-linux-gnu icu-devtools libasan8 libatomic1 libblas-dev 385s libbz2-dev libc-dev-bin libc6-dev libcc1-0 libcrypt-dev libgcc-13-dev 385s libgfortran-13-dev libhwasan0 libicu-dev libisl23 libitm1 libjpeg-dev 385s libjpeg-turbo8-dev libjpeg8-dev liblapack-dev liblsan0 liblzma-dev libmpc3 385s libncurses-dev libnsl-dev libpcre2-16-0 libpcre2-32-0 libpcre2-dev 385s libpcre2-posix3 libpkgconf3 libpng-dev libreadline-dev libstdc++-13-dev 385s libtirpc-dev libtsan2 libubsan1 linux-libc-dev pkg-config pkg-r-autopkgtest 385s pkgconf pkgconf-bin r-base-dev rpcsvc-proto zlib1g-dev 386s 0 upgraded, 62 newly installed, 0 to remove and 0 not upgraded. 386s Need to get 92.9 MB/92.9 MB of archives. 386s After this operation, 343 MB of additional disk space will be used. 386s Get:1 /tmp/autopkgtest.VN3CAc/2-autopkgtest-satdep.deb autopkgtest-satdep arm64 0 [724 B] 386s Get:2 http://ftpmaster.internal/ubuntu noble/main arm64 libc-dev-bin arm64 2.39-0ubuntu2 [19.7 kB] 386s Get:3 http://ftpmaster.internal/ubuntu noble/main arm64 linux-libc-dev arm64 6.8.0-11.11 [1569 kB] 386s Get:4 http://ftpmaster.internal/ubuntu noble/main arm64 libcrypt-dev arm64 1:4.4.36-4 [136 kB] 386s Get:5 http://ftpmaster.internal/ubuntu noble/main arm64 libtirpc-dev arm64 1.3.4+ds-1build1 [232 kB] 386s Get:6 http://ftpmaster.internal/ubuntu noble/main arm64 libnsl-dev arm64 1.3.0-3 [71.9 kB] 386s Get:7 http://ftpmaster.internal/ubuntu noble/main arm64 rpcsvc-proto arm64 1.4.2-0ubuntu6 [65.4 kB] 386s Get:8 http://ftpmaster.internal/ubuntu noble/main arm64 libc6-dev arm64 2.39-0ubuntu2 [1596 kB] 386s Get:9 http://ftpmaster.internal/ubuntu noble/main arm64 libisl23 arm64 0.26-3 [713 kB] 386s Get:10 http://ftpmaster.internal/ubuntu noble/main arm64 libmpc3 arm64 1.3.1-1 [55.3 kB] 386s Get:11 http://ftpmaster.internal/ubuntu noble/main arm64 cpp-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [10.3 MB] 387s Get:12 http://ftpmaster.internal/ubuntu noble/main arm64 cpp-13 arm64 13.2.0-17ubuntu2 [1028 B] 387s Get:13 http://ftpmaster.internal/ubuntu noble/main arm64 cpp-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [5316 B] 387s Get:14 http://ftpmaster.internal/ubuntu noble/main arm64 cpp arm64 4:13.2.0-7ubuntu1 [22.4 kB] 387s Get:15 http://ftpmaster.internal/ubuntu noble/main arm64 libcc1-0 arm64 14-20240303-1ubuntu1 [44.7 kB] 387s Get:16 http://ftpmaster.internal/ubuntu noble/main arm64 libitm1 arm64 14-20240303-1ubuntu1 [27.7 kB] 387s Get:17 http://ftpmaster.internal/ubuntu noble/main arm64 libatomic1 arm64 14-20240303-1ubuntu1 [11.4 kB] 387s Get:18 http://ftpmaster.internal/ubuntu noble/main arm64 libasan8 arm64 14-20240303-1ubuntu1 [2919 kB] 387s Get:19 http://ftpmaster.internal/ubuntu noble/main arm64 liblsan0 arm64 14-20240303-1ubuntu1 [1282 kB] 387s Get:20 http://ftpmaster.internal/ubuntu noble/main arm64 libtsan2 arm64 14-20240303-1ubuntu1 [2687 kB] 387s Get:21 http://ftpmaster.internal/ubuntu noble/main arm64 libubsan1 arm64 14-20240303-1ubuntu1 [1151 kB] 387s Get:22 http://ftpmaster.internal/ubuntu noble/main arm64 libhwasan0 arm64 14-20240303-1ubuntu1 [1597 kB] 387s Get:23 http://ftpmaster.internal/ubuntu noble/main arm64 libgcc-13-dev arm64 13.2.0-17ubuntu2 [2464 kB] 387s Get:24 http://ftpmaster.internal/ubuntu noble/main arm64 gcc-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [20.1 MB] 387s Get:25 http://ftpmaster.internal/ubuntu noble/main arm64 gcc-13 arm64 13.2.0-17ubuntu2 [467 kB] 387s Get:26 http://ftpmaster.internal/ubuntu noble/main arm64 gcc-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [1198 B] 387s Get:27 http://ftpmaster.internal/ubuntu noble/main arm64 gcc arm64 4:13.2.0-7ubuntu1 [5018 B] 387s Get:28 http://ftpmaster.internal/ubuntu noble/main arm64 libstdc++-13-dev arm64 13.2.0-17ubuntu2 [2322 kB] 387s Get:29 http://ftpmaster.internal/ubuntu noble/main arm64 g++-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [11.7 MB] 388s Get:30 http://ftpmaster.internal/ubuntu noble/main arm64 g++-13 arm64 13.2.0-17ubuntu2 [14.4 kB] 388s Get:31 http://ftpmaster.internal/ubuntu noble/main arm64 g++-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [962 B] 388s Get:32 http://ftpmaster.internal/ubuntu noble/main arm64 g++ arm64 4:13.2.0-7ubuntu1 [1082 B] 388s Get:33 http://ftpmaster.internal/ubuntu noble/main arm64 build-essential arm64 12.10ubuntu1 [4932 B] 388s Get:34 http://ftpmaster.internal/ubuntu noble/main arm64 dctrl-tools arm64 2.24-3build2 [65.2 kB] 388s Get:35 http://ftpmaster.internal/ubuntu noble/main arm64 libgfortran-13-dev arm64 13.2.0-17ubuntu2 [478 kB] 388s Get:36 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [10.8 MB] 388s Get:37 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran-13 arm64 13.2.0-17ubuntu2 [10.3 kB] 388s Get:38 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [1022 B] 388s Get:39 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran arm64 4:13.2.0-7ubuntu1 [1164 B] 388s Get:40 http://ftpmaster.internal/ubuntu noble/main arm64 icu-devtools arm64 74.2-1ubuntu1 [209 kB] 388s Get:41 http://ftpmaster.internal/ubuntu noble/main arm64 libblas-dev arm64 3.12.0-3 [111 kB] 388s Get:42 http://ftpmaster.internal/ubuntu noble/main arm64 libbz2-dev arm64 1.0.8-5ubuntu1 [35.8 kB] 388s Get:43 http://ftpmaster.internal/ubuntu noble/main arm64 libicu-dev arm64 74.2-1ubuntu1 [11.9 MB] 388s Get:44 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg-turbo8-dev arm64 2.1.5-2ubuntu1 [304 kB] 388s Get:45 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg8-dev arm64 8c-2ubuntu11 [1484 B] 388s Get:46 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg-dev arm64 8c-2ubuntu11 [1482 B] 388s Get:47 http://ftpmaster.internal/ubuntu noble/main arm64 liblapack-dev arm64 3.12.0-3 [4293 kB] 388s Get:48 http://ftpmaster.internal/ubuntu noble/main arm64 libncurses-dev arm64 6.4+20240113-1ubuntu1 [385 kB] 388s Get:49 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-16-0 arm64 10.42-4ubuntu1 [195 kB] 388s Get:50 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-32-0 arm64 10.42-4ubuntu1 [183 kB] 388s Get:51 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-posix3 arm64 10.42-4ubuntu1 [6654 B] 388s Get:52 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-dev arm64 10.42-4ubuntu1 [679 kB] 388s Get:53 http://ftpmaster.internal/ubuntu noble/main arm64 libpkgconf3 arm64 1.8.1-2 [31.2 kB] 388s Get:54 http://ftpmaster.internal/ubuntu noble/main arm64 zlib1g-dev arm64 1:1.3.dfsg-3ubuntu1 [895 kB] 388s Get:55 http://ftpmaster.internal/ubuntu noble/main arm64 libpng-dev arm64 1.6.43-1 [266 kB] 388s Get:56 http://ftpmaster.internal/ubuntu noble/main arm64 libreadline-dev arm64 8.2-3 [177 kB] 388s Get:57 http://ftpmaster.internal/ubuntu noble/main arm64 pkgconf-bin arm64 1.8.1-2 [20.4 kB] 388s Get:58 http://ftpmaster.internal/ubuntu noble/main arm64 pkgconf arm64 1.8.1-2 [16.7 kB] 388s Get:59 http://ftpmaster.internal/ubuntu noble/main arm64 pkg-config arm64 1.8.1-2 [7170 B] 388s Get:60 http://ftpmaster.internal/ubuntu noble/main arm64 liblzma-dev arm64 5.4.5-0.3 [209 kB] 388s Get:61 http://ftpmaster.internal/ubuntu noble/universe arm64 r-base-dev all 4.3.2-1build1 [4336 B] 388s Get:62 http://ftpmaster.internal/ubuntu noble/universe arm64 pkg-r-autopkgtest all 20231212ubuntu1 [6448 B] 389s Fetched 92.9 MB in 3s (31.6 MB/s) 389s Selecting previously unselected package libc-dev-bin. 389s (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 76354 files and directories currently installed.) 389s Preparing to unpack .../00-libc-dev-bin_2.39-0ubuntu2_arm64.deb ... 389s Unpacking libc-dev-bin (2.39-0ubuntu2) ... 389s Selecting previously unselected package linux-libc-dev:arm64. 389s Preparing to unpack .../01-linux-libc-dev_6.8.0-11.11_arm64.deb ... 389s Unpacking linux-libc-dev:arm64 (6.8.0-11.11) ... 389s Selecting previously unselected package libcrypt-dev:arm64. 389s Preparing to unpack .../02-libcrypt-dev_1%3a4.4.36-4_arm64.deb ... 389s Unpacking libcrypt-dev:arm64 (1:4.4.36-4) ... 389s Selecting previously unselected package libtirpc-dev:arm64. 389s Preparing to unpack .../03-libtirpc-dev_1.3.4+ds-1build1_arm64.deb ... 389s Unpacking libtirpc-dev:arm64 (1.3.4+ds-1build1) ... 389s Selecting previously unselected package libnsl-dev:arm64. 389s Preparing to unpack .../04-libnsl-dev_1.3.0-3_arm64.deb ... 389s Unpacking libnsl-dev:arm64 (1.3.0-3) ... 389s Selecting previously unselected package rpcsvc-proto. 389s Preparing to unpack .../05-rpcsvc-proto_1.4.2-0ubuntu6_arm64.deb ... 389s Unpacking rpcsvc-proto (1.4.2-0ubuntu6) ... 389s Selecting previously unselected package libc6-dev:arm64. 390s Preparing to unpack .../06-libc6-dev_2.39-0ubuntu2_arm64.deb ... 390s Unpacking libc6-dev:arm64 (2.39-0ubuntu2) ... 390s Selecting previously unselected package libisl23:arm64. 390s Preparing to unpack .../07-libisl23_0.26-3_arm64.deb ... 390s Unpacking libisl23:arm64 (0.26-3) ... 390s Selecting previously unselected package libmpc3:arm64. 390s Preparing to unpack .../08-libmpc3_1.3.1-1_arm64.deb ... 390s Unpacking libmpc3:arm64 (1.3.1-1) ... 390s Selecting previously unselected package cpp-13-aarch64-linux-gnu. 390s Preparing to unpack .../09-cpp-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 390s Unpacking cpp-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 390s Selecting previously unselected package cpp-13. 390s Preparing to unpack .../10-cpp-13_13.2.0-17ubuntu2_arm64.deb ... 390s Unpacking cpp-13 (13.2.0-17ubuntu2) ... 390s Selecting previously unselected package cpp-aarch64-linux-gnu. 390s Preparing to unpack .../11-cpp-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 390s Unpacking cpp-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 390s Selecting previously unselected package cpp. 390s Preparing to unpack .../12-cpp_4%3a13.2.0-7ubuntu1_arm64.deb ... 390s Unpacking cpp (4:13.2.0-7ubuntu1) ... 390s Selecting previously unselected package libcc1-0:arm64. 390s Preparing to unpack .../13-libcc1-0_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libcc1-0:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libitm1:arm64. 390s Preparing to unpack .../14-libitm1_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libitm1:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libatomic1:arm64. 390s Preparing to unpack .../15-libatomic1_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libatomic1:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libasan8:arm64. 390s Preparing to unpack .../16-libasan8_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libasan8:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package liblsan0:arm64. 390s Preparing to unpack .../17-liblsan0_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking liblsan0:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libtsan2:arm64. 390s Preparing to unpack .../18-libtsan2_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libtsan2:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libubsan1:arm64. 390s Preparing to unpack .../19-libubsan1_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libubsan1:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libhwasan0:arm64. 390s Preparing to unpack .../20-libhwasan0_14-20240303-1ubuntu1_arm64.deb ... 390s Unpacking libhwasan0:arm64 (14-20240303-1ubuntu1) ... 390s Selecting previously unselected package libgcc-13-dev:arm64. 390s Preparing to unpack .../21-libgcc-13-dev_13.2.0-17ubuntu2_arm64.deb ... 390s Unpacking libgcc-13-dev:arm64 (13.2.0-17ubuntu2) ... 391s Selecting previously unselected package gcc-13-aarch64-linux-gnu. 391s Preparing to unpack .../22-gcc-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 391s Unpacking gcc-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 391s Selecting previously unselected package gcc-13. 391s Preparing to unpack .../23-gcc-13_13.2.0-17ubuntu2_arm64.deb ... 391s Unpacking gcc-13 (13.2.0-17ubuntu2) ... 391s Selecting previously unselected package gcc-aarch64-linux-gnu. 391s Preparing to unpack .../24-gcc-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 391s Unpacking gcc-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 391s Selecting previously unselected package gcc. 391s Preparing to unpack .../25-gcc_4%3a13.2.0-7ubuntu1_arm64.deb ... 391s Unpacking gcc (4:13.2.0-7ubuntu1) ... 391s Selecting previously unselected package libstdc++-13-dev:arm64. 391s Preparing to unpack .../26-libstdc++-13-dev_13.2.0-17ubuntu2_arm64.deb ... 391s Unpacking libstdc++-13-dev:arm64 (13.2.0-17ubuntu2) ... 391s Selecting previously unselected package g++-13-aarch64-linux-gnu. 391s Preparing to unpack .../27-g++-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 391s Unpacking g++-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 391s Selecting previously unselected package g++-13. 391s Preparing to unpack .../28-g++-13_13.2.0-17ubuntu2_arm64.deb ... 391s Unpacking g++-13 (13.2.0-17ubuntu2) ... 391s Selecting previously unselected package g++-aarch64-linux-gnu. 391s Preparing to unpack .../29-g++-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 391s Unpacking g++-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 391s Selecting previously unselected package g++. 391s Preparing to unpack .../30-g++_4%3a13.2.0-7ubuntu1_arm64.deb ... 391s Unpacking g++ (4:13.2.0-7ubuntu1) ... 392s Selecting previously unselected package build-essential. 392s Preparing to unpack .../31-build-essential_12.10ubuntu1_arm64.deb ... 392s Unpacking build-essential (12.10ubuntu1) ... 392s Selecting previously unselected package dctrl-tools. 392s Preparing to unpack .../32-dctrl-tools_2.24-3build2_arm64.deb ... 392s Unpacking dctrl-tools (2.24-3build2) ... 392s Selecting previously unselected package libgfortran-13-dev:arm64. 392s Preparing to unpack .../33-libgfortran-13-dev_13.2.0-17ubuntu2_arm64.deb ... 392s Unpacking libgfortran-13-dev:arm64 (13.2.0-17ubuntu2) ... 392s Selecting previously unselected package gfortran-13-aarch64-linux-gnu. 392s Preparing to unpack .../34-gfortran-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 392s Unpacking gfortran-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 392s Selecting previously unselected package gfortran-13. 392s Preparing to unpack .../35-gfortran-13_13.2.0-17ubuntu2_arm64.deb ... 392s Unpacking gfortran-13 (13.2.0-17ubuntu2) ... 392s Selecting previously unselected package gfortran-aarch64-linux-gnu. 392s Preparing to unpack .../36-gfortran-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 392s Unpacking gfortran-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 392s Selecting previously unselected package gfortran. 392s Preparing to unpack .../37-gfortran_4%3a13.2.0-7ubuntu1_arm64.deb ... 392s Unpacking gfortran (4:13.2.0-7ubuntu1) ... 392s Selecting previously unselected package icu-devtools. 392s Preparing to unpack .../38-icu-devtools_74.2-1ubuntu1_arm64.deb ... 392s Unpacking icu-devtools (74.2-1ubuntu1) ... 392s Selecting previously unselected package libblas-dev:arm64. 392s Preparing to unpack .../39-libblas-dev_3.12.0-3_arm64.deb ... 392s Unpacking libblas-dev:arm64 (3.12.0-3) ... 392s Selecting previously unselected package libbz2-dev:arm64. 392s Preparing to unpack .../40-libbz2-dev_1.0.8-5ubuntu1_arm64.deb ... 392s Unpacking libbz2-dev:arm64 (1.0.8-5ubuntu1) ... 392s Selecting previously unselected package libicu-dev:arm64. 392s Preparing to unpack .../41-libicu-dev_74.2-1ubuntu1_arm64.deb ... 392s Unpacking libicu-dev:arm64 (74.2-1ubuntu1) ... 392s Selecting previously unselected package libjpeg-turbo8-dev:arm64. 392s Preparing to unpack .../42-libjpeg-turbo8-dev_2.1.5-2ubuntu1_arm64.deb ... 392s Unpacking libjpeg-turbo8-dev:arm64 (2.1.5-2ubuntu1) ... 392s Selecting previously unselected package libjpeg8-dev:arm64. 392s Preparing to unpack .../43-libjpeg8-dev_8c-2ubuntu11_arm64.deb ... 392s Unpacking libjpeg8-dev:arm64 (8c-2ubuntu11) ... 392s Selecting previously unselected package libjpeg-dev:arm64. 392s Preparing to unpack .../44-libjpeg-dev_8c-2ubuntu11_arm64.deb ... 392s Unpacking libjpeg-dev:arm64 (8c-2ubuntu11) ... 392s Selecting previously unselected package liblapack-dev:arm64. 392s Preparing to unpack .../45-liblapack-dev_3.12.0-3_arm64.deb ... 392s Unpacking liblapack-dev:arm64 (3.12.0-3) ... 393s Selecting previously unselected package libncurses-dev:arm64. 393s Preparing to unpack .../46-libncurses-dev_6.4+20240113-1ubuntu1_arm64.deb ... 393s Unpacking libncurses-dev:arm64 (6.4+20240113-1ubuntu1) ... 393s Selecting previously unselected package libpcre2-16-0:arm64. 393s Preparing to unpack .../47-libpcre2-16-0_10.42-4ubuntu1_arm64.deb ... 393s Unpacking libpcre2-16-0:arm64 (10.42-4ubuntu1) ... 393s Selecting previously unselected package libpcre2-32-0:arm64. 393s Preparing to unpack .../48-libpcre2-32-0_10.42-4ubuntu1_arm64.deb ... 393s Unpacking libpcre2-32-0:arm64 (10.42-4ubuntu1) ... 393s Selecting previously unselected package libpcre2-posix3:arm64. 393s Preparing to unpack .../49-libpcre2-posix3_10.42-4ubuntu1_arm64.deb ... 393s Unpacking libpcre2-posix3:arm64 (10.42-4ubuntu1) ... 393s Selecting previously unselected package libpcre2-dev:arm64. 393s Preparing to unpack .../50-libpcre2-dev_10.42-4ubuntu1_arm64.deb ... 393s Unpacking libpcre2-dev:arm64 (10.42-4ubuntu1) ... 393s Selecting previously unselected package libpkgconf3:arm64. 393s Preparing to unpack .../51-libpkgconf3_1.8.1-2_arm64.deb ... 393s Unpacking libpkgconf3:arm64 (1.8.1-2) ... 393s Selecting previously unselected package zlib1g-dev:arm64. 393s Preparing to unpack .../52-zlib1g-dev_1%3a1.3.dfsg-3ubuntu1_arm64.deb ... 393s Unpacking zlib1g-dev:arm64 (1:1.3.dfsg-3ubuntu1) ... 393s Selecting previously unselected package libpng-dev:arm64. 393s Preparing to unpack .../53-libpng-dev_1.6.43-1_arm64.deb ... 393s Unpacking libpng-dev:arm64 (1.6.43-1) ... 393s Selecting previously unselected package libreadline-dev:arm64. 393s Preparing to unpack .../54-libreadline-dev_8.2-3_arm64.deb ... 393s Unpacking libreadline-dev:arm64 (8.2-3) ... 393s Selecting previously unselected package pkgconf-bin. 393s Preparing to unpack .../55-pkgconf-bin_1.8.1-2_arm64.deb ... 393s Unpacking pkgconf-bin (1.8.1-2) ... 393s Selecting previously unselected package pkgconf:arm64. 393s Preparing to unpack .../56-pkgconf_1.8.1-2_arm64.deb ... 393s Unpacking pkgconf:arm64 (1.8.1-2) ... 393s Selecting previously unselected package pkg-config:arm64. 393s Preparing to unpack .../57-pkg-config_1.8.1-2_arm64.deb ... 393s Unpacking pkg-config:arm64 (1.8.1-2) ... 393s Selecting previously unselected package liblzma-dev:arm64. 393s Preparing to unpack .../58-liblzma-dev_5.4.5-0.3_arm64.deb ... 393s Unpacking liblzma-dev:arm64 (5.4.5-0.3) ... 393s Selecting previously unselected package r-base-dev. 393s Preparing to unpack .../59-r-base-dev_4.3.2-1build1_all.deb ... 393s Unpacking r-base-dev (4.3.2-1build1) ... 393s Selecting previously unselected package pkg-r-autopkgtest. 393s Preparing to unpack .../60-pkg-r-autopkgtest_20231212ubuntu1_all.deb ... 393s Unpacking pkg-r-autopkgtest (20231212ubuntu1) ... 393s Selecting previously unselected package autopkgtest-satdep. 393s Preparing to unpack .../61-2-autopkgtest-satdep.deb ... 393s Unpacking autopkgtest-satdep (0) ... 393s Setting up linux-libc-dev:arm64 (6.8.0-11.11) ... 393s Setting up libpcre2-16-0:arm64 (10.42-4ubuntu1) ... 393s Setting up libpcre2-32-0:arm64 (10.42-4ubuntu1) ... 393s Setting up libtirpc-dev:arm64 (1.3.4+ds-1build1) ... 393s Setting up libpkgconf3:arm64 (1.8.1-2) ... 393s Setting up rpcsvc-proto (1.4.2-0ubuntu6) ... 393s Setting up libmpc3:arm64 (1.3.1-1) ... 393s Setting up libatomic1:arm64 (14-20240303-1ubuntu1) ... 393s Setting up icu-devtools (74.2-1ubuntu1) ... 393s Setting up pkgconf-bin (1.8.1-2) ... 393s Setting up liblzma-dev:arm64 (5.4.5-0.3) ... 393s Setting up libubsan1:arm64 (14-20240303-1ubuntu1) ... 393s Setting up libpcre2-posix3:arm64 (10.42-4ubuntu1) ... 393s Setting up libnsl-dev:arm64 (1.3.0-3) ... 393s Setting up libhwasan0:arm64 (14-20240303-1ubuntu1) ... 393s Setting up libcrypt-dev:arm64 (1:4.4.36-4) ... 393s Setting up libasan8:arm64 (14-20240303-1ubuntu1) ... 393s Setting up libtsan2:arm64 (14-20240303-1ubuntu1) ... 393s Setting up libisl23:arm64 (0.26-3) ... 393s Setting up libc-dev-bin (2.39-0ubuntu2) ... 393s Setting up libcc1-0:arm64 (14-20240303-1ubuntu1) ... 393s Setting up liblsan0:arm64 (14-20240303-1ubuntu1) ... 393s Setting up libblas-dev:arm64 (3.12.0-3) ... 393s update-alternatives: using /usr/lib/aarch64-linux-gnu/blas/libblas.so to provide /usr/lib/aarch64-linux-gnu/libblas.so (libblas.so-aarch64-linux-gnu) in auto mode 393s Setting up dctrl-tools (2.24-3build2) ... 393s Setting up libitm1:arm64 (14-20240303-1ubuntu1) ... 393s Setting up cpp-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 393s Setting up pkgconf:arm64 (1.8.1-2) ... 393s Setting up cpp-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 393s Setting up liblapack-dev:arm64 (3.12.0-3) ... 393s update-alternatives: using /usr/lib/aarch64-linux-gnu/lapack/liblapack.so to provide /usr/lib/aarch64-linux-gnu/liblapack.so (liblapack.so-aarch64-linux-gnu) in auto mode 393s Setting up pkg-config:arm64 (1.8.1-2) ... 393s Setting up libgcc-13-dev:arm64 (13.2.0-17ubuntu2) ... 393s Setting up libc6-dev:arm64 (2.39-0ubuntu2) ... 393s Setting up libgfortran-13-dev:arm64 (13.2.0-17ubuntu2) ... 393s Setting up libicu-dev:arm64 (74.2-1ubuntu1) ... 393s Setting up libstdc++-13-dev:arm64 (13.2.0-17ubuntu2) ... 393s Setting up libbz2-dev:arm64 (1.0.8-5ubuntu1) ... 393s Setting up libjpeg-turbo8-dev:arm64 (2.1.5-2ubuntu1) ... 393s Setting up libncurses-dev:arm64 (6.4+20240113-1ubuntu1) ... 393s Setting up libpcre2-dev:arm64 (10.42-4ubuntu1) ... 393s Setting up cpp-13 (13.2.0-17ubuntu2) ... 393s Setting up gcc-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 393s Setting up libreadline-dev:arm64 (8.2-3) ... 393s Setting up gcc-13 (13.2.0-17ubuntu2) ... 393s Setting up zlib1g-dev:arm64 (1:1.3.dfsg-3ubuntu1) ... 393s Setting up cpp (4:13.2.0-7ubuntu1) ... 393s Setting up libjpeg8-dev:arm64 (8c-2ubuntu11) ... 393s Setting up g++-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 393s Setting up gcc-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 393s Setting up g++-13 (13.2.0-17ubuntu2) ... 393s Setting up libpng-dev:arm64 (1.6.43-1) ... 393s Setting up libjpeg-dev:arm64 (8c-2ubuntu11) ... 393s Setting up gfortran-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 393s Setting up gcc (4:13.2.0-7ubuntu1) ... 393s Setting up gfortran-13 (13.2.0-17ubuntu2) ... 393s Setting up g++-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 393s Setting up gfortran-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 393s Setting up gfortran (4:13.2.0-7ubuntu1) ... 393s update-alternatives: using /usr/bin/gfortran to provide /usr/bin/f95 (f95) in auto mode 393s update-alternatives: warning: skip creation of /usr/share/man/man1/f95.1.gz because associated file /usr/share/man/man1/gfortran.1.gz (of link group f95) doesn't exist 393s update-alternatives: using /usr/bin/gfortran to provide /usr/bin/f77 (f77) in auto mode 393s update-alternatives: warning: skip creation of /usr/share/man/man1/f77.1.gz because associated file /usr/share/man/man1/gfortran.1.gz (of link group f77) doesn't exist 393s Setting up g++ (4:13.2.0-7ubuntu1) ... 393s update-alternatives: using /usr/bin/g++ to provide /usr/bin/c++ (c++) in auto mode 393s Setting up build-essential (12.10ubuntu1) ... 393s Setting up r-base-dev (4.3.2-1build1) ... 393s Setting up pkg-r-autopkgtest (20231212ubuntu1) ... 393s Setting up autopkgtest-satdep (0) ... 393s Processing triggers for man-db (2.12.0-3) ... 394s Processing triggers for install-info (7.1-3) ... 394s Processing triggers for libc-bin (2.39-0ubuntu2) ... 397s (Reading database ... 79913 files and directories currently installed.) 397s Removing autopkgtest-satdep (0) ... 397s autopkgtest [20:29:46]: test pkg-r-autopkgtest: /usr/share/dh-r/pkg-r-autopkgtest 397s autopkgtest [20:29:46]: test pkg-r-autopkgtest: [----------------------- 398s Test: Try to load the R library tensorA 398s 398s R version 4.3.2 (2023-10-31) -- "Eye Holes" 398s Copyright (C) 2023 The R Foundation for Statistical Computing 398s Platform: aarch64-unknown-linux-gnu (64-bit) 398s 398s R is free software and comes with ABSOLUTELY NO WARRANTY. 398s You are welcome to redistribute it under certain conditions. 398s Type 'license()' or 'licence()' for distribution details. 398s 398s R is a collaborative project with many contributors. 398s Type 'contributors()' for more information and 398s 'citation()' on how to cite R or R packages in publications. 398s 398s Type 'demo()' for some demos, 'help()' for on-line help, or 398s 'help.start()' for an HTML browser interface to help. 398s Type 'q()' to quit R. 398s 398s > library('tensorA') 398s 398s Attaching package: ‘tensorA’ 398s 398s The following object is masked from ‘package:base’: 398s 398s norm 398s 398s > 398s > 398s Other tests are currently unsupported! 398s They will be progressively added. 398s autopkgtest [20:29:47]: test pkg-r-autopkgtest: -----------------------] 399s pkg-r-autopkgtest PASS 399s autopkgtest [20:29:48]: test pkg-r-autopkgtest: - - - - - - - - - - results - - - - - - - - - - 399s autopkgtest [20:29:48]: @@@@@@@@@@@@@@@@@@@@ summary 399s run-unit-test PASS 399s pkg-r-autopkgtest PASS 417s Creating nova instance adt-noble-arm64-r-cran-tensora-20240316-202309-juju-7f2275-prod-proposed-migration-environment-3 from image adt/ubuntu-noble-arm64-server-20240314.img (UUID 7faf5f09-d335-4346-a441-4eab2f9c04fe)...