Add eigensolver support for Hermitian and Symmetric

[luraess]

Add ROCMatrix-specific generalized eigensolver support for Hermitian and Symmetric inputs.

This makes calls like eigen(Hermitian(A_gpu), Hermitian(B_gpu)) dispatch to rocSOLVER instead of falling through to the generic LinearAlgebra path.

Changes

• Add high-level sygvd! / hegvd! rocSOLVER wrappers.
• Add eigen(A, B) methods for Symmetric and Hermitian ROC matrices.
• Respect wrapper uplo, matching Base LinearAlgebra behavior.
• Map positive solver info to LinearAlgebra.PosDefException.
• Added the mixed real wrapper support and tests.

Testing

Added regression coverage for generalized Symmetric and Hermitian ROCMatrix eigensolver calls.

Fixes #903.

[luraess]

Note that mixed Hermitian/Symmetric support is intentionally real-only, because complex Symmetric is not a Hermitian definite problem.

[github-actions]

AMDGPU.jl Benchmarks

Details

Benchmark suite	Current: f3cab5f	Previous: 790ffef	Ratio
amdgpu/synchronization/context/device	640 ns	600 ns	1.07
amdgpu/synchronization/stream/blocking	270 ns	250 ns	1.08
amdgpu/synchronization/stream/nonblocking	360 ns	330 ns	1.09
array/accumulate/Float32/1d	86321 ns	85181 ns	1.01
array/accumulate/Float32/dims=1	316234 ns	346495 ns	0.91
array/accumulate/Float32/dims=1L	135832 ns	135832 ns	1
array/accumulate/Float32/dims=2	129322 ns	133722 ns	0.97
array/accumulate/Float32/dims=2L	2810031 ns	2807449 ns	1.00
array/accumulate/Int64/1d	97761 ns	97751 ns	1.00
array/accumulate/Int64/dims=1	243523 ns	327884 ns	0.74
array/accumulate/Int64/dims=1L	167762 ns	167762 ns	1
array/accumulate/Int64/dims=2	122592 ns	128652 ns	0.95
array/accumulate/Int64/dims=2L	2985303 ns	2987542 ns	1.00
array/broadcast	90451 ns	85431 ns	1.06
array/construct	1700 ns	1640 ns	1.04
array/copy	39070 ns	37090 ns	1.05
array/copyto!/cpu_to_gpu	183192 ns	119302 ns	1.54
array/copyto!/gpu_to_cpu	115372 ns	183102 ns	0.63
array/copyto!/gpu_to_gpu	60751 ns	73881 ns	0.82
array/iteration/findall/bool	180053 ns	180732 ns	1.00
array/iteration/findall/int	190923 ns	199623 ns	0.96
array/iteration/findfirst/bool	117472 ns	121852 ns	0.96
array/iteration/findfirst/int	115881 ns	114861 ns	1.01
array/iteration/findmin/1d	169572 ns	170243 ns	1.00
array/iteration/findmin/2d	153793 ns	155382 ns	0.99
array/iteration/logical	354545 ns	355195 ns	1.00
array/iteration/scalar	289114 ns	290084 ns	1.00
array/permutedims/2d	74651 ns	75151 ns	0.99
array/permutedims/3d	73881 ns	74541 ns	0.99
array/permutedims/4d	77241 ns	77212 ns	1.00
array/random/rand/Float32	51311 ns	50610 ns	1.01
array/random/rand/Int64	56261 ns	57201 ns	0.98
array/random/rand!/Float32	86801 ns	95971 ns	0.90
array/random/rand!/Int64	91372 ns	86611 ns	1.05
array/random/randn/Float32	88711 ns	99462 ns	0.89
array/random/randn!/Float32	96751 ns	108421 ns	0.89
array/reductions/mapreduce/Float32/1d	133152 ns	133292 ns	1.00
array/reductions/mapreduce/Float32/dims=1	95081 ns	95621 ns	0.99
array/reductions/mapreduce/Float32/dims=1L	774411 ns	778531 ns	0.99
array/reductions/mapreduce/Float32/dims=2	96862 ns	97572 ns	0.99
array/reductions/mapreduce/Float32/dims=2L	298724 ns	308705 ns	0.97
array/reductions/mapreduce/Int64/1d	134031 ns	134702 ns	1.00
array/reductions/mapreduce/Int64/dims=1	95001 ns	96291 ns	0.99
array/reductions/mapreduce/Int64/dims=1L	779552 ns	785001 ns	0.99
array/reductions/mapreduce/Int64/dims=2	96271 ns	96932 ns	0.99
array/reductions/mapreduce/Int64/dims=2L	300325 ns	308475 ns	0.97
array/reductions/reduce/Float32/1d	133271 ns	133372 ns	1.00
array/reductions/reduce/Float32/dims=1	94912 ns	95181 ns	1.00
array/reductions/reduce/Float32/dims=1L	775042 ns	775611 ns	1.00
array/reductions/reduce/Float32/dims=2	96642 ns	97251 ns	0.99
array/reductions/reduce/Float32/dims=2L	297444 ns	297585 ns	1.00
array/reductions/reduce/Int64/1d	133852 ns	135242 ns	0.99
array/reductions/reduce/Int64/dims=1	95081 ns	95041 ns	1.00
array/reductions/reduce/Int64/dims=1L	777551 ns	781271 ns	1.00
array/reductions/reduce/Int64/dims=2	96071 ns	96491 ns	1.00
array/reductions/reduce/Int64/dims=2L	307385 ns	302104 ns	1.02
array/reverse/1d	43201 ns	42991 ns	1.00
array/reverse/1dL	74871 ns	75381 ns	0.99
array/reverse/1dL_inplace	111402 ns	167852 ns	0.66
array/reverse/1d_inplace	141082 ns	72911 ns	1.93
array/reverse/2d	50621 ns	51030 ns	0.99
array/reverse/2dL	101831 ns	101682 ns	1.00
array/reverse/2dL_inplace	126222 ns	107362 ns	1.18
array/reverse/2d_inplace	143612 ns	85981 ns	1.67
array/sorting/1d	341685 ns	342214 ns	1.00
integration/byval/reference	38940 ns	39040 ns	1.00
integration/byval/slices=1	40101 ns	40281 ns	1.00
integration/byval/slices=2	159702 ns	146872 ns	1.09
integration/byval/slices=3	238554 ns	238173 ns	1.00
integration/volumerhs	5036353 ns	5024071 ns	1.00
kernel/indexing	129452 ns	67700 ns	1.91
kernel/indexing_checked	69131 ns	64401 ns	1.07
kernel/launch	1290 ns	1350 ns	0.96
kernel/rand	196543 ns	198943 ns	0.99
latency/import	1585085821 ns	1577477738 ns	1.00
latency/precompile	36331778672 ns	36338831604 ns	1.00
latency/ttfp	2158035653 ns	2145912756 ns	1.01

This comment was automatically generated by workflow using github-action-benchmark.