Contents

# ?gesvdx

Computes the SVD and left and right singular vectors for a matrix.

## Syntax

Include Files
• mkl.h
Description
?gesvdx
computes the singular value decomposition (SVD) of a real or complex m-by-n matrix
A
, optionally computing the left and right singular vectors. The SVD is written
A
=
U
*
Σ
* transpose(
V
)
where
Σ
is an
m
-by-
n
matrix which is zero except for its min(
m
,
n
) diagonal elements,
U
is an
m
-by-
m
matrix, and
V
is an
n
-by-
n
matrix. The matrices
U
and
V
are orthogonal for real
A
, and unitary for complex
A
. 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
.
?gesvdx
uses an eigenvalue problem for obtaining the SVD, which allows for the computation of a subset of singular values and vectors. See
?bdsvdx
for details.
Note that the routine returns
V
T
, not
V
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
jobu
Specifies options for computing all or part of the matrix
U
:
= 'V': the first min(
m
,
n
) columns of
U
(the left singular vectors) or as specified by
range
are returned in the array
u
;
= 'N': no columns of
U
(no left singular vectors) are computed.
jobvt
Specifies options for computing all or part of the matrix
V
T
:
= 'V': the first min(
m
,
n
) rows of
V
T
(the right singular vectors) or as specified by
range
are returned in the array
vt
;
= 'N': no rows of
V
T
(no right singular vectors) are computed.
range
= 'A': find all singular values.
= 'V': all singular values in the half-open interval (
vl
,
vu
] are found.
= 'I': the
il
-th through
iu
-th singular values are found.
m
The number of rows of the input matrix
A
.
m
0.
n
The number of columns of the input matrix
A
.
n
0.
a
Array, size
lda
*
n
On entry, the
m
-by-
n
matrix
A
.
lda
The leading dimension of the array
a
.
lda
max(1,
m
).
vl
vl
0.
vu
If
range
='V', the lower and upper bounds of the interval to be searched for singular values.
vu
>
vl
. Not referenced if
range
= 'A' or 'I'.
il
iu
If
range
='I', the indices (in ascending order) of the smallest and largest singular values to be returned. 1
il
iu
min(
m
,
n
), if min(
m
,
n
) > 0. Not referenced if
range
= 'A' or 'V'.
ldu
The leading dimension of the array
u
.
ldu
1; if
jobu
= 'V',
ldu
m
.
ldvt
The leading dimension of the array
vt
.
ldvt
1; if
jobvt
= 'V',
ldvt
ns
(see above).
Output Parameters
a
On exit, the contents of
a
are destroyed.
ns
The total number of singular values found,
0
ns
min(
m
,
n
).
If
range
= 'A',
ns
= min(
m
,
n
); if
range
= 'I',
ns
=
iu
-
il
+ 1.
s
Array, size (min(
m
,
n
))
The singular values of
A
, sorted so that
s
[
i
]
s
[
i
+ 1]
.
u
Array, size
ldu
*
ucol
If
jobu
= 'V',
u
contains columns of
U
(the left singular vectors, stored columnwise) as specified by
range
; if
jobu
= 'N',
u
is not referenced.
Make sure that
ucol
ns
; if
range
= 'V', the exact value of
ns
is not known in advance and an upper bound must be used.
vt
Array, size
ldvt
*
n
If
jobvt
= 'V',
vt
contains the rows of
V
T
(the right singular vectors, stored rowwise) as specified by
range
; if
jobvt
= 'N',
vt
is not referenced.
Make sure that
ldvt
ns
; if
range
= 'V', the exact value of
ns
is not known in advance and an upper bound must be used.
superb
Array, size (12*min(
m
,
n
)).
If
info
= 0, the first
ns
elements of
superb
are zero. If
info
> 0, then
superb
contains the indices of the eigenvectors that failed to converge in
?bdsvdx
/
?stevx
.
Return Values
This function returns a value
info
.
= 0: successful exit.
< 0: if info = -
i
, the
i
-th argument had an illegal value.
> 0: if info =
i
, then
i
eigenvectors failed to converge in
?bdsvdx
/
?stevx
. if info =
n
*2 + 1, an internal error occurred in
?bdsvdx
.

#### Product and Performance Information

1

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