Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?ggsvp

Computes the preprocessing decomposition for the generalized SVD (deprecated).

Syntax

lapack_int LAPACKE_sggsvp
(
int
matrix_layout
,
char
jobu
,
char
jobv
,
char
jobq
,
lapack_int
m
,
lapack_int
p
,
lapack_int
n
,
float*
a
,
lapack_int
lda
,
float*
b
,
lapack_int
ldb
,
float
tola
,
float
tolb
,
lapack_int*
k
,
lapack_int*
l
,
float*
u
,
lapack_int
ldu
,
float*
v
,
lapack_int
ldv
,
float*
q
,
lapack_int
ldq
);
lapack_int LAPACKE_dggsvp
(
int
matrix_layout
,
char
jobu
,
char
jobv
,
char
jobq
,
lapack_int
m
,
lapack_int
p
,
lapack_int
n
,
double*
a
,
lapack_int
lda
,
double*
b
,
lapack_int
ldb
,
double
tola
,
double
tolb
,
lapack_int*
k
,
lapack_int*
l
,
double*
u
,
lapack_int
ldu
,
double*
v
,
lapack_int
ldv
,
double*
q
,
lapack_int
ldq
);
lapack_int LAPACKE_cggsvp
(
int
matrix_layout
,
char
jobu
,
char
jobv
,
char
jobq
,
lapack_int
m
,
lapack_int
p
,
lapack_int
n
,
lapack_complex_float*
a
,
lapack_int
lda
,
lapack_complex_float*
b
,
lapack_int
ldb
,
float
tola
,
float
tolb
,
lapack_int*
k
,
lapack_int*
l
,
lapack_complex_float*
u
,
lapack_int
ldu
,
lapack_complex_float*
v
,
lapack_int
ldv
,
lapack_complex_float*
q
,
lapack_int
ldq
);
lapack_int LAPACKE_zggsvp
(
int
matrix_layout
,
char
jobu
,
char
jobv
,
char
jobq
,
lapack_int
m
,
lapack_int
p
,
lapack_int
n
,
lapack_complex_double*
a
,
lapack_int
lda
,
lapack_complex_double*
b
,
lapack_int
ldb
,
double
tola
,
double
tolb
,
lapack_int*
k
,
lapack_int*
l
,
lapack_complex_double*
u
,
lapack_int
ldu
,
lapack_complex_double*
v
,
lapack_int
ldv
,
lapack_complex_double*
q
,
lapack_int
ldq
);
Include Files
  • mkl.h
Description
This routine is deprecated; use
ggsvp3
.
The routine computes orthogonal matrices
U
,
V
 and
Q
 such that
Equation
Equation
Equation
where the
k
-by-
k
 matrix
A
12
 and
l
-by-
l
 matrix
B
13
 are nonsingular upper triangular;
A
23
 is
l
-by-
l
 upper triangular if
m
-
k
-l
≥
0
, otherwise
A
23
 is (
m
-
k
)-by-
l
 upper trapezoidal. The sum
k
+
l
 is equal to the effective numerical rank of the (
m
+
p
)-by-
n
 matrix (
A
H
,
B
H
)
H
.
This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine ?tgsja.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
jobu
Must be
'U'
 or
'N'
.
If
jobu
 =
'U'
, orthogonal/unitary matrix
U
 is computed.
If
jobu
 =
'N'
,
U
 is not computed.
jobv
Must be
'V'
 or
'N'
.
If
jobv
 =
'V'
, orthogonal/unitary matrix
V
 is computed.
If
jobv
 =
'N'
,
V
 is not computed.
jobq
Must be
'Q'
 or
'N'
.
If
jobq
 =
'Q'
, orthogonal/unitary matrix
Q
 is computed.
If
jobq
 =
'N'
,
Q
 is not computed.
m
The number of rows of the matrix
A
 (
m
≥
 0).
p
The number of rows of the matrix
B
 (
p
≥
 0).
n
The number of columns of the matrices
A
 and
B
 (
n
≥
 0).
a
,
b
Arrays:
a
(size at least max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout)
 contains the
m
-by-
n
 matrix
A
.
b
(size at least max(1,
ldb
*
n
) for column major layout and max(1,
ldb
*
p
) for row major layout)
 contains the
p
-by-
n
 matrix
B
.
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
ldb
The leading dimension of
b
; at least max(1,
p
)
for column major layout and max(1,
n
) for row major layout
.
tola
,
tolb
tola
 and
tolb
 are the thresholds to determine the effective numerical rank of matrix
B
 and a subblock of
A
. Generally, they are set to
tola
 = max(
m
,
n
)*||
A
||*MACHEPS
,
tolb
 = max(
p
,
n
)*||
B
||*MACHEPS
.
The size of
tola
 and
tolb
 may affect the size of backward errors of the decomposition.
ldu
The leading dimension of the output array
u
 .
ldu
≥
 max(1,
m
)
 if
jobu
 =
'U'
;
ldu
≥
 1
 otherwise.
ldv
The leading dimension of the output array
v
 .
ldv
≥
 max(1,
p
)
 if
jobv
 =
'V'
;
ldv
≥
 1
 otherwise.
ldq
The leading dimension of the output array
q
 .
ldq
≥
 max(1,
n
)
 if
jobq
 =
'Q'
;
ldq
≥
 1
 otherwise.
Output Parameters
a
Overwritten by the triangular (or trapezoidal) matrix
described in the
Description
 section
.
b
Overwritten by the triangular matrix
described in the
Description
 section
.
k
,
l
On exit,
k
 and
l
 specify the dimension of subblocks. The sum
k
 +
l
 is equal to effective numerical rank of (
A
H
,
B
H
)
H
.
u
,
v
,
q
Arrays:
If
jobu
 =
'U'
,
u
(size max(1,
ldu
*
m
))
 contains the orthogonal/unitary matrix
U
.
If
jobu
 =
'N'
,
u
 is not referenced.
If
jobv
 =
'V'
,
v
(size max(1,
ldv
*
p
))
 contains the orthogonal/unitary matrix
V
.
If
jobv
 =
'N'
,
v
 is not referenced.
If
jobq
 =
'Q'
,
q
(size max(1,
ldq
*
n
))
 contains the orthogonal/unitary matrix
Q
.
If
jobq
 =
'N'
,
q
 is not referenced.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
 =
-i
, the
i
-th parameter had an illegal value.

Product and Performance Information

1

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