Update dpnp.linalg.matrix_power() implementation

[vlad-perevezentsev]

This PR updates a dpnp.linalg.matrix_power() function to raise an input square matrix to the power n using dpnp.linalg.inv() and dpnp.matmul()
The changes are related to support of all types.

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View rendered docs @ https://intelpython.github.io/dpnp/index.html

[vlad-perevezentsev]

This table shows the performance of dpnp.linalg.matrix_power() function on Iris Xe

Results for floating and complexfloating types when n>0 (call dpnp.matmul()) are worse than in numpy on CPU.

@vtavana do you know about this or is it a regression?

In [1]: import dpnp
 
In [2]: import numpy
 
In [3]: na = numpy.random.randint(-10**4, 10**4, size=(4096,4096))
 
In [4]: a = numpy.array(na,dtype='f4')
 
In [5]: a_dp = dpnp.array(a, device='cpu')
 
In [6]: %timeit res = numpy.matmul(a,a)
334 ms ± 4.88 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
 
In [7]: %timeit res = dpnp.matmul(a_dp,a_dp)
380 ms ± 18.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

[vtavana]

@vtavana do you know about this or is it a regression?

There is always some sort of variation in timing on Iris Xe. However, for this case NumPy falls back on SEGMM but dpnp falls back on SGEMM_64. and their timing is different

In [9]: %timeit numpy.matmul(a,a)
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a3a68,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a3a70,0x7fabaffff010,4096) 512.61ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 509.24ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 501.30ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 514.48ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 517.97ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 486.50ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 496.99ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM(N,N,4096,4096,4096,0x7ffc219a38a8,0x7fac93ada010,4096,0x7fac93ada010,4096,0x7ffc219a38b0,0x7fabaffff010,4096) 512.76ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
506 ms ± 10.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [10]: %timeit dpnp.matmul(a_dp,a_dp)
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac2fffdcd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac2fffdce0,0x7fabe4000000,4096) 499.49ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac3a41acd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac3a41ace0,0x7fabe4000000,4096) 501.18ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac39c19cd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac39c19ce0,0x7fabe4000000,4096) 508.51ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac2fffdcd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac2fffdce0,0x7fabe4000000,4096) 504.49ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac3a41acd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac3a41ace0,0x7fabe4000000,4096) 536.80ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac39c19cd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac39c19ce0,0x7fabe4000000,4096) 532.84ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac2fffdcd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac2fffdce0,0x7fabe4000000,4096) 508.24ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
MKL_VERBOSE SGEMM_64(N,N,4096,4096,4096,0x7fac3a41acd8,0x7fac40000000,4096,0x7fac40000000,4096,0x7fac3a41ace0,0x7fabe4000000,4096) 519.75ms CNR:OFF Dyn:1 FastMM:1 TID:0  NThr:6
517 ms ± 13.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)