Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?orcsd/?uncsd

Computes the CS decomposition of a block-partitioned orthogonal/unitary matrix.

Syntax

lapack_int LAPACKE_sorcsd
(
int
matrix_layout
,
char
jobu1
,
char
jobu2
,
char
jobv1t
,
char
jobv2t
,
char
trans
,
char
signs
,
lapack_int
m
,
lapack_int
p
,
lapack_int
q
,
float*
x11
,
lapack_int
ldx11
,
float*
x12
,
lapack_int
ldx12
,
float*
x21
,
lapack_int
ldx21
,
float*
x22
,
lapack_int
ldx22
,
float*
theta
,
float*
u1
,
lapack_int
ldu1
,
float*
u2
,
lapack_int
ldu2
,
float*
v1t
,
lapack_int
ldv1t
,
float*
v2t
,
lapack_int
ldv2t
);
lapack_int LAPACKE_dorcsd
(
int
matrix_layout
,
char
jobu1
,
char
jobu2
,
char
jobv1t
,
char
jobv2t
,
char
trans
,
char
signs
,
lapack_int
m
,
lapack_int
p
,
lapack_int
q
,
double*
x11
,
lapack_int
ldx11
,
double*
x12
,
lapack_int
ldx12
,
double*
x21
,
lapack_int
ldx21
,
double*
x22
,
lapack_int
ldx22
,
double*
theta
,
double*
u1
,
lapack_int
ldu1
,
double*
u2
,
lapack_int
ldu2
,
double*
v1t
,
lapack_int
ldv1t
,
double*
v2t
,
lapack_int
ldv2t
);
lapack_int LAPACKE_cuncsd
(
int
matrix_layout
,
char
jobu1
,
char
jobu2
,
char
jobv1t
,
char
jobv2t
,
char
trans
,
char
signs
,
lapack_int
m
,
lapack_int
p
,
lapack_int
q
,
lapack_complex_float*
x11
,
lapack_int
ldx11
,
lapack_complex_float*
x12
,
lapack_int
ldx12
,
lapack_complex_float*
x21
,
lapack_int
ldx21
,
lapack_complex_float*
x22
,
lapack_int
ldx22
,
float*
theta
,
lapack_complex_float*
u1
,
lapack_int
ldu1
,
lapack_complex_float*
u2
,
lapack_int
ldu2
,
lapack_complex_float*
v1t
,
lapack_int
ldv1t
,
lapack_complex_float*
v2t
,
lapack_int
ldv2t
);
lapack_int LAPACKE_zuncsd
(
int
matrix_layout
,
char
jobu1
,
char
jobu2
,
char
jobv1t
,
char
jobv2t
,
char
trans
,
char
signs
,
lapack_int
m
,
lapack_int
p
,
lapack_int
q
,
lapack_complex_double*
x11
,
lapack_int
ldx11
,
lapack_complex_double*
x12
,
lapack_int
ldx12
,
lapack_complex_double*
x21
,
lapack_int
ldx21
,
lapack_complex_double*
x22
,
lapack_int
ldx22
,
double*
theta
,
lapack_complex_double*
u1
,
lapack_int
ldu1
,
lapack_complex_double*
u2
,
lapack_int
ldu2
,
lapack_complex_double*
v1t
,
lapack_int
ldv1t
,
lapack_complex_double*
v2t
,
lapack_int
ldv2t
);
Include Files
  • mkl.h
Description
The routines
?orcsd
/
?uncsd
 compute the CS decomposition of an
m
-by-
m
 partitioned orthogonal matrix
X
:
Equation
or unitary matrix:
Equation
x
11
 is
p
-by-
q
. The orthogonal/unitary matrices
u
1
,
u
2
,
v
1
, and
v
2
 are
p
-by-
p
,
(m-p)
-by-
(m-p)
,
q
-by-
q
,
(m-q)
-by-
(m-q)
, respectively.
C
 and
S
 are
r
-by-
r
 nonnegative diagonal matrices satisfying
C
2
 +
S
2
 =
I
, in which
r
 = min(
p
,
m-p
,
q
,
m-q
)
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
jobu1
If equals
Y
, then
u
1
 is computed. Otherwise,
u
1
 is not computed.
jobu2
If equals
Y
, then
u
2
 is computed. Otherwise,
u
2
 is not computed.
jobv1t
If equals
Y
, then
v
1
t
 is computed. Otherwise,
v
1
t
 is not computed.
jobv2t
If equals
Y
, then
v
2
t
 is computed. Otherwise,
v
2
t
 is not computed.
trans
= '
T
':
x
,
u
1
,
u
2
,
v
1
t
,
v
2
t
 are stored in row-major order.
otherwise
x
,
u
1
,
u
2
,
v
1
t
,
v
2
t
 are stored in column-major order.
signs
= '
O
':
The lower-left block is made nonpositive (the "other" convention).
otherwise
The upper-right block is made nonpositive (the "default" convention).
m
The number of rows and columns of the matrix
X
.
p
The number of rows in
x
11
 and
x
12
.
0
≤
p
≤
m
.
q
The number of columns in
x
11
 and
x
21
.
0
≤
q
≤
m
.
x11
,
x12
,
x21
,
x22
Arrays of size
x11
 (
ldx11
,
q
),
x12
 (
ldx12
,
m
 -
q
),
x21
 (
ldx21
,
q
), and
x22
 (
ldx22
,
m
 -
q
).
Contain the parts of the orthogonal/unitary matrix whose CSD is desired.
ldx11
,
ldx12
,
ldx21
,
ldx22
The leading dimensions of the parts of array
X
.
ldx11
≥
 max(1,
p
),
ldx12
≥
 max(1,
p
),
ldx21
≥
 max(1,
m
 -
p
),
ldx22
≥
 max(1,
m
 -
p
).
ldu1
The leading dimension of the array
u
1
. If
jobu1
 = '
Y
',
ldu1
≥
 max(1,
p
)
.
ldu2
The leading dimension of the array
u
2
. If
jobu2
 = '
Y
',
ldu2
≥
 max(1,
m
-
p
)
.
ldv1t
The leading dimension of the array
v1t
. If
jobv1t
 = '
Y
',
ldv1t
≥
 max(1,
q
)
.
ldv2t
The leading dimension of the array
v2t
. If
jobv2t
 = '
Y
',
ldv2t
≥
 max(1,
m
-
q
)
.
Output Parameters
theta
Array,
size
r
, in which
r
 = min(
p
,
m-p
,
q
,
m-q
)
.
C
 = diag( cos(
theta
[0]
), ..., cos(
theta
[
r
 - 1]
) )
, and
S
 = diag( sin(
theta
[0]
), ..., sin(
theta
[
r
 - 1]
) )
.
u1
Array,
size at least max(1,
ldu1
*
p
)
.
If
jobu1
 = '
Y
',
u1
 contains the
p
-by-
p
 orthogonal/unitary matrix
u
1
.
u2
Array, size
at least max(1,
ldu2
*(
m
 -
p
))
.
If
jobu2
 = '
Y
',
u2
 contains the (
m
-
p
)-by-(
m
-
p
) orthogonal/unitary matrix
u
2
.
v1t
Array, size
at least max(1,
ldv1t
*
q
)
 .
If
jobv1t
 = '
Y
',
v1t
 contains the
q
-by-
q
 orthogonal matrix
v
1
T
 or unitary matrix
v
1
H
.
v2t
Array, size
at least max(1,
ldv2t
*(
m
 -
q
))
.
If
jobv2t
 = '
Y
',
v2t
 contains the (
m
-
q
)-by-(
m
-
q
) orthogonal matrix
v
2
T
 or unitary matrix
v
2
H
.
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.
> 0:
?orcsd
/
?uncsd
 did not converge.