Contents

?gesdd

Computes the singular value decomposition of a general rectangular matrix using a divide and conquer method.

Syntax

Include Files
• mkl.h
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.
If singular vectors are desired, it uses a divide-and-conquer algorithm. The SVD is written
A
=
U
*
Σ
*
V
T
for real routines,
A
=
U
*
Σ
*
V
H
for complex routines,
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
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
.
Note that the routine returns
vt
=
V
T
(for real flavors) or
vt
=
V
H
(for complex flavors), not
V
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
jobz
Must be
'A'
,
'S'
,
'O'
, or
'N'
.
Specifies options for computing all or part of the matrices
U
and
V
.
If
jobz
=
'A'
, all
m
columns of
U
and all
n
rows of
V
T
or
V
H
are returned in the arrays
u
and
vt
;
if
jobz
=
'S'
, the first min(
m
,
n
) columns of
U
and the first min(
m
,
n
) rows of
V
T
or
V
H
are returned in the arrays
u
and
vt
;
if
jobz
=
'O'
, then
if
m

n
, the first
n
columns of
U
are overwritten in the array
a
and all rows of
V
T
or
V
H
are returned in the array
vt
;
if
m
<
n
, all columns of
U
are returned in the array
u
and the first
m
rows of
V
T
or
V
H
are overwritten in the array
a
;
if
jobz
=
'N'
, no columns of
U
or rows of
V
T
or
V
H
are computed.
m
The number of rows of the matrix
A
(
m
0
).
n
The number of columns in
A
(
n
0).
a
a
(size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout)
is an array containing the
m
-by-
n
matrix
A
.
lda
The leading dimension of the array
a
. Must be at least max(1,
m
)
for column major layout and at least max(1,
n
) for row major layout
.
ldu
,
ldvt
The leading dimensions of the output arrays
u
and
vt
, respectively.
The minimum size of
ldu
is
jobz
m
n
m
<
n
'N'
1
1
'A'
m
m
'S'
m
for column major layout;
n
for row major layout
m
'O'
1
m
The minimum size of
ldvt
is
jobz
m
n
m
<
n
'N'
1
1
'A'
n
n
'S'
n
m
for column major layout;
n
for row major layout
'O'
n
1
Output Parameters
a
On exit:
If
jobz
=
'O'
, then if
m

n
,
a
is overwritten with the first
n
columns of
U
(the left singular vectors, stored columnwise). If
m
<
n
,
a
is overwritten with the first
m
rows of
V
T
(the right singular vectors, stored rowwise);
If
jobz
'O'
, the contents of
a
are destroyed.
s
Array, size at least max(1, min(
m
,
n
)). Contains the singular values of
A
sorted so that
s
(i)

s
(i+1)
.
u
,
vt
Arrays:
Array
u
is of size:
jobz
m
n
m
<
n
'N'
1
1
'A'
max(1,
ldu
*
m
)
max(1,
ldu
*
m
)
'S'
max(1,
ldu
*
n
) for column major layout; max(1,
ldu
*
m
) for row major layout
max(1,
ldu
*
m
)
'O'
1
max(1,
ldu
*
m
)
If
jobz
=
'A'
or
jobz
=
'O'
and
m
<
n
,
u
contains the
m
-by-
m
orthogonal/unitary matrix
U
.
If
jobz
=
'S'
,
u
contains the first min(
m
,
n
) columns of
U
(the left singular vectors, stored columnwise).
If
jobz
=
'O'
and
m
n
, or
jobz
=
'N'
,
u
is not referenced.
Array
vt
is of size:
jobz
m
n
m
<
n
'N'
1
1
'A'
max(1,
ldvt
*
n
)
max(1,
ldvt
*
n
)
'S'
max(1,
ldvt
*
n
)
max(1,
ldvt
*
n
) for column major layout; max(1,
ldvt
*
m
) for row major layout;
'O'
max(1,
ldvt
*
n
)
1
If
jobz
=
'A'
or
jobz
=
'O'
and
m
n
,
vt
contains the
n
-by-
n
orthogonal/unitary matrix
V
T
.
If
jobz
=
'S'
,
vt
contains the first min(
m
,
n
) rows of
V
T
(the right singular vectors, stored rowwise).
If
jobz
=
'O'
and
m
<
n
, or
jobz
=
'N'
,
vt
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.
If
info
=
i
, then
?bdsdc
did not converge, updating process failed.

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