Support softmax for row_vector, matrix types + code simplifications

[jachymb]

Summary

This refactors the softmax and log_softmax functions in the following ways:

• both vector and row_vector are now supported instead of just vector
• matrix type is also supported and the softmax is applied row-wise. (i.e. the return value is effectively a row_stochastic_matrix for modelling purposes)
• refactored the relevant code to utilize Eigen functionalities instead of some for loops and some other bits here and there, simplifying the code and improving clarity. I am honestly not a C++ guru, but I believe these shouldn't have any negative impact on performance.

Tests

• Added test for the new types
• Added a test for the edge case when some of the values is -inf

Side Effects

None to my knowledge.

Release notes

softmax and log_softmax now support row_vector and matrix (applied row-wise)

Checklist

• Copyright holder: Me, jachymb@gmail.com
  - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
  - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested

[jachymb]

I think it's some server error, not actual test failure.

[SteveBronder]

@serban-nicusor-toptal Can you take a look at https://jenkins.flatironinstitute.org/blue/organizations/jenkins/Stan%2FMath/detail/PR-3313/4/pipeline/ ?

I'm not sure what is going on with the nohup permissions there

EDIT: Fixed

[jachymb]

@SteveBronder may I ask for a rerun pls?

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_regr/gp_regr.stan	0.1	0.09	1.11	9.76% faster
gp_regr/gen_gp_data.stan	0.03	0.02	1.12	10.98% faster
arK/arK.stan	2.0	1.72	1.17	14.19% faster
eight_schools/eight_schools.stan	0.06	0.05	1.15	12.83% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	9.63	8.43	1.14	12.49% faster
pkpd/one_comp_mm_elim_abs.stan	21.06	18.59	1.13	11.71% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.27	0.24	1.12	10.61% faster
sir/sir.stan	76.72	67.2	1.14	12.41% faster
gp_pois_regr/gp_pois_regr.stan	3.06	2.8	1.09	8.27% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.89	2.69	1.07	6.86% faster
irt_2pl/irt_2pl.stan	4.8	4.15	1.16	13.61% faster
arma/arma.stan	0.32	0.29	1.1	8.88% faster
garch/garch.stan	0.54	0.42	1.27	21.04% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.15	12.91% faster
performance.compilation	239.08	230.47	1.04	3.6% faster
Mean result: 1.1300492258145844

---

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

[SteveBronder]

@jachymb Did you use an AI to write this? We have not adopted an AI policy yet but it's nice to let us know. If you wrote this I'm happy to help you fix it up. There are a number of odds and ends in this PR which will take some cleaning up and if it's an AI then I'll most likely just close it.

[jachymb]

@SteveBronder Yeah, I used claude code, but reviewed every line of code until I felt it makes a good sense. I'd say my c++ knowledge is only intermediate, I mostly work with other languages. If you point me to topics where you think it should be approached differently or some resources I should first go through, I'd be happy to learn about that.