Contents

# ?ggsvp

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

## Syntax

Include Files
• mkl.h
Description
This routine is deprecated; use
ggsvp3
.
The routine computes orthogonal matrices
U
,
V
and
Q
such that
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804