dougiesquire opened a new issue, #21095:
URL: https://github.com/apache/incubator-mxnet/issues/21095
## Description
I'm quite possibly misunderstanding something, but
`mxnet.np.random.multivariate_normal` seems to produce unexpected values
relative to, for example, `numpy.random.multivariate_normal` for some
covariance matrices.
## To Reproduce
The following code demonstrates the unexpected behaviour by comparing
distributions created using the `numpy`, `jax` and `mxnet`
`random.multivariate_normal` functions:
```python
import numpy as np
from mxnet import np as mxnp
import jax
import matplotlib.pyplot as plt
mean = np.array([0., 0.])
cov = np.array([[0.2, 0.2],[0.2, 20]])
mean_mxnp = mxnp.array(mean)
cov_mxnp = mxnp.array(cov)
mvn_np = np.random.multivariate_normal(mean, cov, size=10000)
mvn_mxnp = mxnp.random.multivariate_normal(mean_mxnp, cov_mxnp,
size=10000).asnumpy()
mvn_jax = np.array(jax.random.multivariate_normal(jax.random.PRNGKey(0),
mean, cov, shape=(10000,)))
fig = plt.figure(figsize=(14, 4))
ax = fig.subplots(1, len(mean), sharey=True)
for idx in range(len(mean)):
ax[idx].hist(mvn_np[:,idx], bins=100, alpha=0.5, label="numpy.random")
ax[idx].hist(mvn_mxnp[:,idx], bins=100, alpha=0.5,
label="mxnet.np.random")
ax[idx].hist(mvn_jax[:,idx], bins=100, alpha=0.5, label="jax.random")
ax[idx].set_xlabel(f"var{idx}")
ax[idx].set_ylabel(f"Count")
ax[idx].legend()
ax[idx].grid()
```
Which generates:
<img width="840" alt="Screen Shot 2022-07-15 at 11 05 00 am"
src="https://user-images.githubusercontent.com/42455466/179126206-69329608-276e-423a-9de6-a76dbc763793.png";>
You can see that the `var0` distribution from
`mxnet.random.multivariate_normal` (left panel) is incorrect. This seems to
occur when `cov[0,0]` is small, though I haven't tested this very thoroughly.
## Environment
Note, I've replaced some directory path details below with "..."
<details>
<summary>Environment Information</summary>
```
----------Python Info----------
Version : 3.10.4
Compiler : GCC 10.3.0
Build : ('main', 'Mar 24 2022 17:38:57')
Arch : ('64bit', 'ELF')
------------Pip Info-----------
Version : 22.1.2
Directory : /.../pip
----------MXNet Info-----------
Version : 1.9.1
Directory : /.../mxnet
Commit hash file "/.../mxnet/COMMIT_HASH" not found. Not installed from
pre-built package or built from source.
Library : ['/.../mxnet/libmxnet.so']
Build features:
✖ CUDA
✖ CUDNN
✖ NCCL
✖ CUDA_RTC
✖ TENSORRT
✔ CPU_SSE
✔ CPU_SSE2
✔ CPU_SSE3
✖ CPU_SSE4_1
✖ CPU_SSE4_2
✖ CPU_SSE4A
✖ CPU_AVX
✖ CPU_AVX2
✔ OPENMP
✖ SSE
✖ F16C
✖ JEMALLOC
✔ BLAS_OPEN
✖ BLAS_ATLAS
✖ BLAS_MKL
✖ BLAS_APPLE
✔ LAPACK
✔ MKLDNN
✔ OPENCV
✖ CAFFE
✖ PROFILER
✔ DIST_KVSTORE
✖ CXX14
✖ INT64_TENSOR_SIZE
✔ SIGNAL_HANDLER
✖ DEBUG
✖ TVM_OP
----------System Info----------
Platform : Linux-4.18.0-372.13.1.el8.nci.x86_64-x86_64-with-glibc2.28
system : Linux
node : gadi-login-08.gadi.nci.org.au
release : 4.18.0-372.13.1.el8.nci.x86_64
version : #1 SMP Mon Jul 4 08:46:44 AEST 2022
----------Hardware Info----------
machine : x86_64
processor : x86_64
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
CPU(s): 48
On-line CPU(s) list: 0-47
Thread(s) per core: 1
Core(s) per socket: 24
Socket(s): 2
NUMA node(s): 4
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Platinum 8268 CPU @ 2.90GHz
Stepping: 7
CPU MHz: 2900.000
CPU max MHz: 3900.0000
CPU min MHz: 1200.0000
BogoMIPS: 5800.00
L1d cache: 32K
L1i cache: 32K
L2 cache: 1024K
L3 cache: 36608K
NUMA node0 CPU(s): 0-3,7,8,12-14,18-20
NUMA node1 CPU(s): 4-6,9-11,15-17,21-23
NUMA node2 CPU(s): 24-27,31,32,36-38,42-44
NUMA node3 CPU(s): 28-30,33-35,39-41,45-47
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 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 intel_ppin ssbd mba ibrs ibpb
stibp ibrs_enhanced fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid 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 avx512_vnni md_clear flush_l1d arch_capabilities
----------Network Test----------
Setting timeout: 10
Timing for MXNet: https://github.com/apache/incubator-mxnet, DNS: 0.0250
sec, LOAD: 0.6436 sec.
Error open Gluon Tutorial(en): http://gluon.mxnet.io, HTTP Error 404: Not
Found, DNS finished in 0.407116174697876 sec.
Error open Gluon Tutorial(cn): https://zh.gluon.ai, <urlopen error [SSL:
CERTIFICATE_VERIFY_FAILED] certificate verify failed: certificate has expired
(_ssl.c:997)>, DNS finished in 1.2768752574920654 sec.
Timing for FashionMNIST:
https://apache-mxnet.s3-accelerate.dualstack.amazonaws.com/gluon/dataset/fashion-mnist/train-labels-idx1-ubyte.gz,
DNS: 0.1059 sec, LOAD: 0.7920 sec.
Timing for PYPI: https://pypi.python.org/pypi/pip, DNS: 0.0096 sec, LOAD:
0.9369 sec.
Error open Conda: https://repo.continuum.io/pkgs/free/, HTTP Error 403:
Forbidden, DNS finished in 0.01588129997253418 sec.
----------Environment----------
CC="icc"
CXX="icpc"
OMP_NUM_THREADS="1"
KMP_DUPLICATE_LIB_OK="True"
KMP_INIT_AT_FORK="FALSE"
```
</details>
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![https://user-images.githubusercontent.com/42455466/179126206-69329608-276e-423a-9de6-a76dbc763793.png"](https://user-images.githubusercontent.com/42455466/179126206-69329608-276e-423a-9de6-a76dbc763793.png"){kind=link}