Contents

# ?bdsdc

Computes the singular value decomposition of a real bidiagonal matrix using a divide and conquer method.

## Syntax

Include Files
• mkl.h
Description
The routine computes the Singular Value Decomposition (SVD) of a real
n
-by-
n
(upper or lower) bidiagonal matrix
B
:
B
=
U
*
Σ
*
V
T
, using a divide and conquer method, where
Σ
is a diagonal matrix with non-negative diagonal elements (the singular values of
B
), and
U
and
V
are orthogonal matrices of left and right singular vectors, respectively.
?bdsdc
can be used to compute all singular values, and optionally, singular vectors or singular vectors in compact form.
This rotuine uses
?lasd0
,
?lasd1
,
?lasd2
,
?lasd3
,
?lasd4
,
?lasd5
,
?lasd6
,
?lasd7
,
?lasd8
,
?lasd9
,
?lasda
,
?lasdq
,
?lasdt
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Must be
'U'
or
'L'
.
If
uplo
=
'U'
,
B
is an upper bidiagonal matrix.
If
uplo
=
'L'
,
B
is a lower bidiagonal matrix.
compq
Must be
'N'
,
'P'
, or
'I'
.
If
compq
=
'N'
, compute singular values only.
If
compq
=
'P'
, compute singular values and compute singular vectors in compact form.
If
compq
=
'I'
, compute singular values and singular vectors.
d
,
e
Arrays:
d
contains the
n
diagonal elements of the bidiagonal matrix
B
. The size of
d
must be at least max(1,
n
).
e
contains the off-diagonal elements of the bidiagonal matrix
B
. The size of
e
must be at least max(1,
n
).
ldu
The leading dimension of the output array
u
;
ldu
1.
If singular vectors are desired, then
ldu
max(1,
n
)
, regardless of the value of
matrix_layout
.
ldvt
The leading dimension of the output array
vt
;
ldvt
1.
If singular vectors are desired, then
ldvt
max(1,
n
)
, regardless of the value of
matrix_layout
.
Output Parameters
d
If
info
= 0
, overwritten by the singular values of
B
.
e
On exit,
e
is overwritten.
u
,
vt
,
q
Arrays:
u
(size
ldu
*
n
)
,
vt
(size
ldvt
*
n
)
,
q
(size
n
*(11 + 2*
smlsiz
+ 8*int(log
2
(
n
/(
smlsiz
+1)))) where
smlsiz
is returned by
ilaenv
and is equal to maximum size of the subproblems at the bottom of the computation tree ).
.
If
compq
=
'I'
, then on exit
u
contains the left singular vectors of the bidiagonal matrix
B
, unless
info
0
(
see
info
). For other values of
compq
,
u
is not referenced.
if
compq
=
'I'
, then on exit
vt
T
contains the right singular vectors of the bidiagonal matrix
B
, unless
info
0
(
see
info
). For other values of
compq
,
vt
is not referenced.
If
compq
=
'P'
, then on exit, if
info
= 0
,
q
and
iq
contain the left and right singular vectors in a compact form. Specifically,
q
contains all the
float
(for
sbdsdc
) or
double
(for
dbdsdc
) data for singular vectors. For other values of
compq
,
q
is not referenced.
iq
Array:
iq
(size
n
*(3 + 3*int(log
2
(
n
/(
smlsiz
+1)))) where
smlsiz
is returned by
ilaenv
and is equal to maximum size of the subproblems at the bottom of the computation tree.)
.
If
compq
=
'P'
, then on exit, if
info
= 0
,
q
and
iq
contain the left and right singular vectors in a compact form. Specifically,
iq
contains all the
lapack_int
data for singular vectors. For other values of
compq
,
iq
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
, the algorithm failed to compute a singular value. The update process of divide and conquer 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