[BUG] torch.linalg.lstsq returning wrong result.

[nandometzger]

🐛 Describe the bug

I noticed that torch.linalg.lstsq is returning the wrong results for this sample which I attached here for reproducibility: https://drive.google.com/drive/folders/1rLJRrOmR_YdD-t_-7B85xAEJMveD8ER-?usp=drive_link

import torch
pred = torch.load("pred.pt")
GT = torch.load("GT.pt")

I want to solve for the parameters of affine invariant transformation, basically recovering the scale s and shift `t. Therefore my A matrix is

A = torch.stack([pred, torch.ones_like(pred)], dim=1)

With torch.linalg.lstsq, I get:

s, t = torch.linalg.lstsq(A, GT).solution
print("scale", s.item(), "shift", t.item())

scale 0.0009792937198653817 shift 7.378799182333751e-06

With the transparent (torch.linalg.inv) implementation:

s, t = torch.linalg.inv(A.t() @ A) @ A.t() @ GT
print("scale", s.item(), "shift", t.item()) 

scale -0.008498617447912693 shift 1.2577897310256958

I know for a fact that in my data the scale must be negative, therefore I am very confident that the torch.linalg.lstsq is wrong.

All code in one piece:

import torch

pred = torch.load("pred.pt")
GT = torch.load("GT.pt")
A = torch.stack([pred, torch.ones_like(pred)], dim=1)

s, t = torch.linalg.lstsq(A, GT).solution
print("lstsq: scale", s.item(), "shift", t.item())

s, t = torch.linalg.inv(A.t() @ A) @ A.t() @ GT
print("inv: scale", s.item(), "shift", t.item()) 

Versions

Collecting environment information... PyTorch version: 2.0.1+cu117 Is debug build: False CUDA used to build PyTorch: 11.7 ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04 LTS (x86_64) GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0 Clang version: 14.0.0-1ubuntu1.1 CMake version: version 3.29.2 Libc version: glibc-2.35

Python version: 3.10.12 | packaged by conda-forge | (main, Jun 23 2023, 22:40:32) [GCC 12.3.0] (64-bit runtime) Python platform: Linux-5.15.0-106-generic-x86_64-with-glibc2.35 Is CUDA available: True CUDA runtime version: Could not collect CUDA_MODULE_LOADING set to: LAZY GPU models and configuration: GPU 0: NVIDIA GeForce RTX 3090 Ti Nvidia driver version: 535.161.08 cuDNN version: Probably one of the following: /usr/lib/x86_64-linux-gnu/libcudnn.so.8.9.7 /usr/lib/x86_64-linux-gnu/libcudnn_adv_infer.so.8.9.7 /usr/lib/x86_64-linux-gnu/libcudnn_adv_train.so.8.9.7 /usr/lib/x86_64-linux-gnu/libcudnn_cnn_infer.so.8.9.7 /usr/lib/x86_64-linux-gnu/libcudnn_cnn_train.so.8.9.7 /usr/lib/x86_64-linux-gnu/libcudnn_ops_infer.so.8.9.7 /usr/lib/x86_64-linux-gnu/libcudnn_ops_train.so.8.9.7 HIP runtime version: N/A MIOpen runtime version: N/A Is XNNPACK available: True

CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Address sizes: 48 bits physical, 48 bits virtual Byte Order: Little Endian CPU(s): 16 On-line CPU(s) list: 0-15 Vendor ID: AuthenticAMD Model name: AMD Ryzen 7 5800X 8-Core Processor CPU family: 25 Model: 33 Thread(s) per core: 2 Core(s) per socket: 8 Socket(s): 1 Stepping: 2 Frequency boost: enabled CPU max MHz: 3800.0000 CPU min MHz: 2200.0000 BogoMIPS: 7599.93 Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip pku ospke vaes vpclmulqdq rdpid overflow_recov succor smca fsrm Virtualization: AMD-V L1d cache: 256 KiB (8 instances) L1i cache: 256 KiB (8 instances) L2 cache: 4 MiB (8 instances) L3 cache: 32 MiB (1 instance) NUMA node(s): 1 NUMA node0 CPU(s): 0-15 Vulnerability Gather data sampling: Not affected Vulnerability Itlb multihit: Not affected Vulnerability L1tf: Not affected Vulnerability Mds: Not affected Vulnerability Meltdown: Not affected Vulnerability Mmio stale data: Not affected Vulnerability Retbleed: Not affected Vulnerability Spec rstack overflow: Mitigation; safe RET, no microcode Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl and seccomp Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; Retpolines; IBPB conditional; IBRS_FW; STIBP always-on; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Not affected

Versions of relevant libraries: [pip3] numpy==1.26.4 [pip3] torch==2.0.1 [pip3] torchvision==0.15.2 [pip3] triton==2.0.0 [conda] No relevant packages

cc @jianyuh @nikitaved @pearu @mruberry @walterddr @xwang233 @Lezcano

[lezcano]

Any chance you can provide a self-contained repro without external downloads? I don't feel comfortable downloading an external file.

That being said I bet it's because the matrix A is not full rank and:

• If the inputs are in cuda, the default does not support non-fullrank matrices. Even more, we don't have any CUDA driver that supports them.
• You might need to adjust rcond to your data, potentially lowering it
• You might need to run the computation on float64 to get extra precision.

[ezyang]

@lezcano We should add some explicit instructions on the docs on how to check the condition number of the matrix and tell if it is "too larger" or not. We can't do this automatically for perf but we can at least tell people how to check it.

[lezcano]

Been there done that: https://pytorch.org/docs/stable/notes/numerical_accuracy.html#linear-algebra-torch-linalg