Contents

# ?orcsd2by1/?uncsd2by1

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

## Syntax

Include Files
• mkl.h
Description
The routines
?orcsd2by1
/
?uncsd2by1
compute the CS decomposition of an
m
-by-
q
matrix
X
with orthonormal columns that has been partitioned into a 2-by-1 block structure: 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 equal to 'Y', then
u
1
is computed. Otherwise,
u
1
is not computed.
jobu2
If equal to 'Y', then
u
2
is computed. Otherwise,
u
2
is not computed.
jobv1t
If equal to 'Y', then
v
1
t
is computed. Otherwise,
v
1
t
is not computed.
m
The number of rows and columns of the matrix
X
.
p
The number of rows in
x
11
.
0
p
m
.
q
The number of columns in
x
11
.
0
q
m
.
x11
Array, size
(
ldx11
*
q
)
.
On entry, the part of the orthogonal matrix whose CSD is desired.
ldx11
The leading dimension of the array
x11
.
ldx11
max(1,
p
)
.
x21
Array, size
(
ldx21
*
q
)
.
On entry, the part of the orthogonal matrix whose CSD is desired.
ldx21
The leading dimension of the array
X
.
ldx21
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
)
.
Output Parameters
theta
Array,
size
r
, in which
r
= min(
p
,
m-p
,
q
,
m-q
)
.
C
= diag( cos(
theta
(1)), ..., cos(
theta
(r)) )
, and
S
= diag( sin(
theta
(1)), ..., sin(
theta
(r)) )
.
u1
Array, size
(
ldu1
*
p
)
.
If
jobu1
= '
Y
',
u1
contains the
p
-by-
p
orthogonal/unitary matrix
u
1
.
u2
Array, size
(
ldu2
*(
m
-
p
))
.
If
jobu2
= '
Y
',
u2
contains the (
m
-
p
)-by-(
m
-
p
) orthogonal/unitary matrix
u
2
.
v1t
Array, size
(
ldv1t
*
q
)
.
If
jobv1t
= '
Y
',
v1t
contains the
q
-by-
q
orthogonal matrix
v
1
T
or unitary matrix
v
1
H
.
Return Values
This function returns a value
info
.
= 0: successful exit
< 0: if
info
= -
i
, the
i
-th argument has an illegal value
> 0:
?orcsd2by1
/
?uncsd2by1
did not converge.

#### Product and Performance Information

1

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