Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference

Developer Reference

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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

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 = 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.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.