DArray: Add SVD algorithm

[jpsamaroo]

Written by Claude Opus and Sonnet

[github-actions]

Dagger benchmarks: dirty vs master

	master	dirty	master / dirty
array/dagger/N=1024 (block 512)/add (X + X)	3.66 ± 0.11 ms	3.82 ± 0.23 ms	0.959 ± 0.065
array/dagger/N=1024 (block 512)/alloc (rand)	3.25 ± 0.82 ms	3.19 ± 0.1 ms	1.02 ± 0.26
array/dagger/N=1024 (block 512)/broadcast (X .+ 1)	2.36 ± 0.079 ms	2.41 ± 0.045 ms	0.979 ± 0.038
array/dagger/N=1024 (block 512)/map (sin.(X))	5.06 ± 0.18 ms	5.15 ± 0.12 ms	0.983 ± 0.042
array/dagger/N=1024 (block 512)/norm	1.19 ± 0.13 ms	1.22 ± 0.33 ms	0.98 ± 0.28
array/dagger/N=1024 (block 512)/reduce (sum)	2.44 ± 0.82 ms	2.04 ± 0.12 ms	1.2 ± 0.41
array/dagger/N=1024 (block 512)/transpose (permutedims)	4.79 ± 0.45 ms	4.16 ± 0.48 ms	1.15 ± 0.17
array/dagger/N=256 (block 256)/add (X + X)	1.3 ± 0.17 ms	1.4 ± 0.43 ms	0.928 ± 0.31
array/dagger/N=256 (block 256)/alloc (rand)	1.37 ± 0.057 ms	1.35 ± 0.13 ms	1.02 ± 0.11
array/dagger/N=256 (block 256)/broadcast (X .+ 1)	0.527 ± 0.069 ms	0.559 ± 0.11 ms	0.943 ± 0.22
array/dagger/N=256 (block 256)/map (sin.(X))	1.03 ± 0.15 ms	0.956 ± 0.11 ms	1.08 ± 0.2
array/dagger/N=256 (block 256)/norm	0.543 ± 0.12 ms	0.51 ± 0.06 ms	1.07 ± 0.27
array/dagger/N=256 (block 256)/reduce (sum)	1.02 ± 0.23 ms	1.18 ± 0.35 ms	0.864 ± 0.33
array/dagger/N=256 (block 256)/transpose (permutedims)	0.984 ± 0.094 ms	0.859 ± 0.14 ms	1.15 ± 0.21
linalg/dagger/N=1024 (block 512)/cholesky	16.8 ± 0.44 ms	23.4 ± 3.4 ms	0.718 ± 0.11
linalg/dagger/N=1024 (block 512)/lu	1.2 ± 0.013 s	1.23 ± 0.011 s	0.976 ± 0.014
linalg/dagger/N=1024 (block 512)/matmul (A*A)	30.2 ± 3.3 ms	29.7 ± 2.2 ms	1.02 ± 0.13
linalg/dagger/N=1024 (block 512)/matvec (A*x)	2.86 ± 0.16 ms	2.91 ± 0.38 ms	0.982 ± 0.14
linalg/dagger/N=1024 (block 512)/qr	0.189 ± 0.018 s	0.18 ± 0.0044 s	1.05 ± 0.1
linalg/dagger/N=1024 (block 512)/solve (A\b via lu)	1.9 ± 0.0039 s	1.98 ± 0.028 s	0.96 ± 0.014
linalg/dagger/N=1024 (block 512)/syrk (A'*A)	28.7 ± 3.5 ms	0.033 ± 0.0041 s	0.872 ± 0.15
linalg/dagger/N=256 (block 256)/cholesky	2.73 ± 1.2 ms	2.75 ± 0.27 ms	0.992 ± 0.45
linalg/dagger/N=256 (block 256)/lu	0.171 ± 0.04 s	0.167 ± 0.01 s	1.03 ± 0.25
linalg/dagger/N=256 (block 256)/matmul (A*A)	2.22 ± 0.11 ms	2.34 ± 0.48 ms	0.95 ± 0.2
linalg/dagger/N=256 (block 256)/matvec (A*x)	1.41 ± 1 ms	1.33 ± 0.096 ms	1.06 ± 0.76
linalg/dagger/N=256 (block 256)/qr	5.35 ± 0.51 ms	5.1 ± 0.85 ms	1.05 ± 0.2
linalg/dagger/N=256 (block 256)/solve (A\b via lu)	0.362 ± 0.032 s	0.37 ± 0.023 s	0.98 ± 0.11
linalg/dagger/N=256 (block 256)/syrk (A'*A)	3.95 ± 0.23 ms	4.85 ± 2.7 ms	0.815 ± 0.46
stencil/dagger/N=1024 (block 512)/alloc (neighbors Wrap)	21.6 ± 5.4 ms	22.1 ± 4.1 ms	0.977 ± 0.31
stencil/dagger/N=1024 (block 512)/assign (const)	1.76 ± 0.043 ms	1.68 ± 0.18 ms	1.05 ± 0.11
stencil/dagger/N=1024 (block 512)/multi-expr	3.94 ± 0.13 ms	3.61 ± 0.16 ms	1.09 ± 0.059
stencil/dagger/N=1024 (block 512)/neighbors (Clamp)	20.2 ± 5.6 ms	22.4 ± 1.7 ms	0.905 ± 0.26
stencil/dagger/N=1024 (block 512)/neighbors (Pad)	23 ± 2.4 ms	19 ± 0.63 ms	1.21 ± 0.13
stencil/dagger/N=1024 (block 512)/neighbors (Reflect)	20.8 ± 3.3 ms	21.7 ± 6.1 ms	0.96 ± 0.31
stencil/dagger/N=1024 (block 512)/neighbors (Wrap)	22.6 ± 1.8 ms	20.4 ± 4.5 ms	1.11 ± 0.26
stencil/dagger/N=1024 (block 512)/update (+)	1.93 ± 0.031 ms	1.94 ± 0.11 ms	0.995 ± 0.057
stencil/dagger/N=256 (block 256)/alloc (neighbors Wrap)	4.51 ± 0.33 ms	4.53 ± 0.55 ms	0.995 ± 0.14
stencil/dagger/N=256 (block 256)/assign (const)	0.708 ± 0.064 ms	0.69 ± 0.36 ms	1.03 ± 0.54
stencil/dagger/N=256 (block 256)/multi-expr	1.45 ± 0.093 ms	1.4 ± 0.089 ms	1.03 ± 0.093
stencil/dagger/N=256 (block 256)/neighbors (Clamp)	4.3 ± 0.14 ms	3.93 ± 0.48 ms	1.09 ± 0.14
stencil/dagger/N=256 (block 256)/neighbors (Pad)	3.6 ± 0.11 ms	3.9 ± 0.32 ms	0.921 ± 0.081
stencil/dagger/N=256 (block 256)/neighbors (Reflect)	3.97 ± 0.59 ms	3.98 ± 0.35 ms	0.997 ± 0.17
stencil/dagger/N=256 (block 256)/neighbors (Wrap)	3.98 ± 0.25 ms	3.89 ± 0.66 ms	1.02 ± 0.19
stencil/dagger/N=256 (block 256)/update (+)	1.01 ± 0.27 ms	0.809 ± 0.081 ms	1.25 ± 0.35
time_to_load	0.787 ± 0.011 s	0.804 ± 0.011 s	0.978 ± 0.019

Plots

⚠️ Regressions (> 25.0%)

• linalg/dagger/N=1024 (block 512)/cholesky: +39.3%

Full results and plots (download the benchmark-results artifact).