Add matrix/vector array reshaping helpers

[fatimmajumder]

Summary

Fixes #3233.

This PR adds the remaining reshaping helpers requested in the issue:

• to_matrix(std::vector<Eigen::Matrix<T, Eigen::Dynamic, 1>>) for array-of-column-vector reshaping
• to_vector_array(matrix)
• to_row_vector_array(matrix)

The existing array-of-row-vector to_matrix overload was already present, so this PR leaves that behavior unchanged and adds tests for it.

The implemented semantics are:

• array of column vectors -> matrix columns, with result(i, j) = x[j](i)
• matrix -> vector array returns one column vector per matrix column
• matrix -> row-vector array returns one row vector per matrix row

Empty top-level arrays follow existing to_matrix behavior and return 0 x 0. Zero-length contained vectors preserve the inferable dimension.

Tests

Passed locally:

./runTests.py test/unit/math/prim/fun/to_matrix_test.cpp test/unit/math/prim/fun/to_vector_array_test.cpp test/unit/math/prim/fun/to_row_vector_array_test.cpp

Also passed targeted header tests:

make stan/math/prim/fun/to_matrix.hpp-test
make stan/math/prim/fun/to_vector_array.hpp-test
make stan/math/prim/fun/to_row_vector_array.hpp-test
make stan/math/prim/fun.hpp-test

I did not run the complete make test-headers; I started it, but it was traversing unrelated forward-mode headers, so I stopped it and ran the targeted header isolation tests above instead.

Side Effects

No intentional side effects.

I intentionally did not add ragged-vector validation because the existing array-of-row-vector overload does not appear to validate ragged inputs either, and I did not want to introduce a new policy for only one direction of the reshape.

Release notes

Adds reshaping helpers for converting between matrices and arrays of Eigen vectors/row vectors.

Checklist

• Copyright holder: Fatim Majumder
• The basic tests are passing
• The code is written in idiomatic C++ and changes are documented in the doxygen

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_regr/gp_regr.stan	0.1	0.1	0.95	-5.43% slower
gp_regr/gen_gp_data.stan	0.02	0.03	0.94	-6.19% slower
arK/arK.stan	1.89	2.0	0.94	-6.21% slower
eight_schools/eight_schools.stan	0.06	0.06	0.94	-5.88% slower
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	9.06	9.42	0.96	-3.96% slower
pkpd/one_comp_mm_elim_abs.stan	19.84	20.72	0.96	-4.43% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.25	0.26	0.95	-4.83% slower
sir/sir.stan	73.34	76.47	0.96	-4.27% slower
gp_pois_regr/gp_pois_regr.stan	2.9	2.97	0.97	-2.61% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.81	2.87	0.98	-2.33% slower
irt_2pl/irt_2pl.stan	4.43	5.03	0.88	-13.52% slower
arma/arma.stan	0.32	0.33	0.97	-3.14% slower
garch/garch.stan	0.46	0.47	0.97	-3.48% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	0.98	-2.56% slower
performance.compilation	240.11	231.89	1.04	3.42% faster
Mean result: 0.9591845925615083

---

Jenkins Console Log
Blue Ocean
Commit hash: e0729e1cdec40e8ec3da60b40b20a2cfc223fc94

---

Machine information

No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
Thread(s) per core: 2
Core(s) per socket: 20
Socket(s): 2
NUMA node(s): 2
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz
Stepping: 4
CPU MHz: 2400.000
CPU max MHz: 3700.0000
CPU min MHz: 1000.0000
BogoMIPS: 4800.00
Virtualization: VT-x
L1d cache: 1.3 MiB
L1i cache: 1.3 MiB
L2 cache: 40 MiB
L3 cache: 55 MiB
NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
Vulnerability Gather data sampling: Mitigation; Microcode
Vulnerability Itlb multihit: KVM: Mitigation: Split huge pages
Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable
Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Meltdown: Mitigation; PTI
Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Mitigation; IBRS
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Vmscape: Mitigation; IBPB before exit to userspace
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++:
g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang:
clang version 10.0.0-4ubuntu1
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin