gesvd

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ID 772045

Date 6/24/2024

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gesvd

Computes the singular value decomposition of a general rectangular matrix. This routine belongs to the oneapi::mkl::lapack namespace.

Description
API

Description

The routine computes the singular value decomposition (SVD) of a real/complex m-by-n matrix A, optionally computing the left and/or right singular vectors. The SVD is written as:

A = U*Σ*VT for real routines
A = U*Σ*VH for complex routines

where Σ is an m-by-n diagonal matrix, U is an m-by-m orthogonal/unitary matrix, and V is an n-by-n orthogonal/unitary matrix. The diagonal elements of Σ are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m, n) columns of U and V are the left and right singular vectors of A.

API

Syntax

namespace oneapi::mkl::lapack {
  void gesvd(sycl::queue &queue,
  mkl::jobsvd jobu,
  mkl::jobsvd jobvt,
  std::int64_t m,
  std::int64_t n,
  sycl::buffer<T> &a,
  std::int64_t lda,
  sycl::buffer<RealT> &s,
  sycl::buffer<T> &u,
  std::int64_t ldu,
  sycl::buffer<T> &vt,
  std::int64_t ldvt,
  sycl::buffer<T> &scratchpad,
  std::int64_t scratchpad_size)
}

gesvd supports the following precision and devices.

T	Devices Supported
`float`	CPU
`double`	CPU
`std::complex<float>`	CPU
`std::complex<double>`	CPU

Input Parameters

queue

Device queue where calculations will be performed.

jobu

Must be jobsvd::vectors, job::somevec, jobsvd::vectorsina, or job::novec. Specifies options for computing all or part of the matrix U.

If jobu = jobsvd::vectors, all m columns of U are returned in the buffer u;

if jobu = job::somevec, the first min(m, n) columns of U (the left singular vectors) are returned in the buffer u;

if jobu = jobsvd::vectorsina, the first min(m, n) columns of U (the left singular vectors) are overwritten on the buffer a;

if jobu = job::novec, no columns of U (no left singular vectors) are computed.

jobvt

Must be jobsvd::vectors, job::somevec, jobsvd::vectorsina, or job::novec. Specifies options for computing all or part of the matrix VT/VH.

If jobvt = jobsvd::vectors, all n columns of VT/VH are returned in the buffer vt;

if jobvt = job::somevec, the first min(m, n) columns of VT/VH (the left singular vectors) are returned in the buffer vt;

if jobvt = jobsvd::vectorsina, the first min(m, n) columns of VT/VH (the left singular vectors) are overwritten on the buffer a;

if jobvt = job::novec, no columns of VT/VH (no left singular vectors) are computed.

jobvt and jobu cannot both be jobsvd::vectorsina.

m

The number of rows in the matrix A (0 ≤ m).

n

The number of columns in the matrix A (0 ≤ n).

a

Buffer holding arraya, size (lda,*). The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

ldu

The leading dimension of u.

ldvt

The leading dimension of vt.

scratchpad

Pointer to scratchpad memory to be used by the routine for storing intermediate results.

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by the gesvd_scratchpad_size function.

Output Parameters

a

On exit,

If jobu = jobsvd::vectorsina, a is overwritten with the first min(m,n) columns of U (the left singular vectors stored columnwise);

If jobvt = jobsvd::vectorsina, a is overwritten with the first min(m, n) rows of V^T/V^H (the right singular vectors stored rowwise);

If jobu ≠ jobsvd::vectorsina and jobvt ≠ jobsvd::vectorsina, the contents of a are destroyed.

s

Array containing the singular values, size at least max(1, min(m,n)). Contains the singular values of A sorted so that s(i) ≥ s(i+1).

u

Array containing U; the second dimension of u must be at least max(1, m) if jobu = jobsvd::vectors, and at least max(1, min(m, n)) if jobu = job::somevec.

If jobu = jobsvd::vectors, u contains the m-by-m orthogonal/unitary matrix U.

If jobu = job::somevec, u contains the first min(m, n) columns of U (the left singular vectors stored column-wise).

If jobu = job::novec or jobsvd::vectorsina, u is not referenced.

vt

Array containing V^T; the second dimension of vt must be at least max(1, n).

If jobvt = jobsvd::vectors, vt contains the n-by-n orthogonal/unitary matrix V^T/V^H.

If jobvt = job::somevec, vt contains the first min(m, n) rows of V^T/V^H (the right singular vectors stored row-wise).

If jobvt = job::novec or jobsvd::vectorsina, vt is not referenced.

Exceptions

Exception	Description
`mkl::lapack::exception`	This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If `info = -i`, the `i`-th parameter had an illegal value. If `info = i`, then if bdsqr did not converge, `i` specifies how many superdiagonals of the intermediate bidiagonal form `B` did not converge to zero, and `scratchpad(2:min(m,n))` contains the unconverged superdiagonal elements of an upper bidiagonal matrix `B` whose diagonal is in `s` (not necessarily sorted). `B` satisfies `A = UBVT`, so it has the same singular values as `A`, and singular vectors related by `U` and `V`^T. If `info` is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.

Exception

Description

mkl::lapack::exception

This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object:

If info = -i, the i-th parameter had an illegal value.

If info = i, then if bdsqr did not converge, i specifies how many superdiagonals of the intermediate bidiagonal form B did not converge to zero, and scratchpad(2:min(m,n)) contains the unconverged superdiagonal elements of an upper bidiagonal matrix B whose diagonal is in s (not necessarily sorted). B satisfies A = U*B*VT, so it has the same singular values as A, and singular vectors related by U and V^T.

If info is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.

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oneMKL - Data Parallel C++ Developer Reference

gesvd

Description

API