Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?lasdq

Computes the SVD of a real bidiagonal matrix with diagonal
d
 and off-diagonal
e
. Used by
?bdsdc
.

Syntax

void slasdq
(
char
*uplo
,
lapack_int
*sqre
,
lapack_int
*n
,
lapack_int
*ncvt
,
lapack_int
*nru
,
lapack_int
*ncc
,
float
*d
,
float
*e
,
float
*vt
,
lapack_int
*ldvt
,
float
*u
,
lapack_int
*ldu
,
float
*c
,
lapack_int
*ldc
,
float
*work
,
lapack_int
*info
);
void dlasdq
(
char
*uplo
,
lapack_int
*sqre
,
lapack_int
*n
,
lapack_int
*ncvt
,
lapack_int
*nru
,
lapack_int
*ncc
,
double
*d
,
double
*e
,
double
*vt
,
lapack_int
*ldvt
,
double
*u
,
lapack_int
*ldu
,
double
*c
,
lapack_int
*ldc
,
double
*work
,
lapack_int
*info
);
Include Files
  • mkl.h
Description
The routine
?lasdq
 computes the singular value decomposition (
SVD
) of a real (upper or lower) bidiagonal matrix with diagonal
d
 and off-diagonal
e
, accumulating the transformations if desired. If
B
 is the input bidiagonal matrix, the algorithm computes orthogonal matrices
Q
 and
P
 such that
B
 =
Q
*
S
*
P
T
. The singular values
S
 are overwritten on
d
.
The input matrix
U
 is changed to
U
*
Q
 if desired.
The input matrix
VT
 is changed to
P
T
*
VT
 if desired.
The input matrix
C
 is changed to
Q
T
*
C
 if desired.
Input Parameters
uplo
On entry,
uplo
 specifies whether the input bidiagonal matrix is upper or lower bidiagonal.
If
uplo
 =
'U'
 or
'u'
,
B
 is upper bidiagonal;
If
uplo
 =
'L'
 or
'l'
,
B
 is lower bidiagonal.
sqre
= 0: then the input matrix is
n
-by-
n
.
= 1: then the input matrix is
n
-by-(
n
+1) if
uplu
 =
'U'
 and (
n
+1)-by-
n
 if
uplu
=
'L'
. The bidiagonal matrix has
n
 =
nl
 +
nr
 + 1
 rows and
m
 =
n
 +
sqre
≥
n
 columns.
n
On entry,
n
 specifies the number of rows and columns in the matrix.
n
 must be at least 0.
ncvt
On entry,
ncvt
 specifies the number of columns of the matrix
VT
.
ncvt
 must be at least 0.
nru
On entry,
nru
 specifies the number of rows of the matrix
U
.
nru
 must be at least 0.
ncc
On entry,
ncc
 specifies the number of columns of the matrix
C
.
ncc
 must be at least 0.
d
Array,
DIMENSION
 (
n
). On entry,
d
 contains the diagonal entries of the bidiagonal matrix.
e
Array,
DIMENSION
 is (
n
-1) if
sqre
 = 0
 and
n
 if
sqre
 = 1
. On entry, the entries of
e
 contain the off-diagonal entries of the bidiagonal matrix.
vt
Array,
DIMENSION
 (
ldvt
,
ncvt
). On entry, contains a matrix which on exit has been premultiplied by
P
T
, dimension
n
-by-
ncvt
 if
sqre
 = 0
 and (
n
+1)-by-
ncvt
 if
sqre
 = 1
 (not referenced if
ncvt
=0).
ldvt
On entry,
ldvt
 specifies the leading dimension of
vt
 as declared in the calling (sub) program.
ldvt
 must be at least 1. If
ncvt
 is nonzero,
ldvt
 must also be at least
n
.
u
Array,
DIMENSION
 (
ldu
,
n
). On entry, contains a matrix which on exit has been postmultiplied by
Q
, dimension
nru
-by-
n
 if
sqre
 = 0
 and
nru
-by-(
n
+1) if
sqre
 = 1
 (not referenced if
nru
=0).
ldu
On entry,
ldu
 specifies the leading dimension of
u
 as declared in the calling (sub) program.
ldu
 must be at least
max(1,
nru
 )
 .
c
Array,
DIMENSION
 (
ldc
,
ncc
). On entry, contains an
n
-by-
ncc
 matrix which on exit has been premultiplied by
Q'
, dimension
n
-by-
ncc
 if
sqre
 = 0
 and (
n
+1)-by-
ncc
 if
sqre
 = 1
 (not referenced if
ncc
=0).
ldc
On entry,
ldc
 specifies the leading dimension of
C
 as declared in the calling (sub) program.
ldc
 must be at least 1. If
ncc
 is non-zero,
ldc
 must also be at least
n
.
work
Array,
DIMENSION
 (4
n
). This is a workspace array. Only referenced if one of
ncvt
,
nru
, or
ncc
 is nonzero, and if
n
 is at least 2.
Output Parameters
d
On normal exit,
d
 contains the singular values in ascending order.
e
On normal exit,
e
 will contain 0. If the algorithm does not converge,
d
 and
e
 will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input.
vt
On exit, the matrix has been premultiplied by
P
'.
u
On exit, the matrix has been postmultiplied by
Q
.
c
On exit, the matrix has been premultiplied by
Q
'.
info
On exit, a value of 0 indicates a successful exit. If
info
 < 0
, argument number -
info
 is illegal. If
info
 > 0
, the algorithm did not converge, and
info
 specifies how many superdiagonals did not converge.

Product and Performance Information

1

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