Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?orcsd/?uncsd
Computes the CS decomposition of a block-partitioned orthogonal/unitary matrix.
Syntax
call sorcsd ( jobu1 , jobu2 , jobv1t , jobv2t , trans , signs , m , p , q , x11 , ldx11 , x12 , ldx12 , x21 , ldx21 , x22 , ldx22 , theta , u1 , ldu1 , u2 , ldu2 , v1t , ldv1t , v2t , ldv2t , work , lwork , iwork , info )
call dorcsd ( jobu1 , jobu2 , jobv1t , jobv2t , trans , signs , m , p , q , x11 , ldx11 , x12 , ldx12 , x21 , ldx21 , x22 , ldx22 , theta , u1 , ldu1 , u2 , ldu2 , v1t , ldv1t , v2t , ldv2t , work , lwork , iwork , info )
call cuncsd ( jobu1 , jobu2 , jobv1t , jobv2t , trans , signs , m , p , q , x11 , ldx11 , x12 , ldx12 , x21 , ldx21 , x22 , ldx22 , theta , u1 , ldu1 , u2 , ldu2 , v1t , ldv1t , v2t , ldv2t , work , lwork , rwork , lrwork , iwork , info )
call zuncsd ( jobu1 , jobu2 , jobv1t , jobv2t , trans , signs , m , p , q , x11 , ldx11 , x12 , ldx12 , x21 , ldx21 , x22 , ldx22 , theta , u1 , ldu1 , u2 , ldu2 , v1t , ldv1t , v2t , ldv2t , work , lwork , rwork , lrwork , iwork , info )
call orcsd ( x11 , x12 , x21 , x22 , theta , u1 , u2 , v1t , v2t [ , jobu1 ] [ , jobu2 ] [ , jobv1t ] [ , jobv2t ] [ , trans ] [ , signs ] [ , info ] )
call uncsd ( x11 , x12 , x21 , x22 , theta , u1 , u2 , v1t , v2t [ , jobu1 ] [ , jobu2 ] [ , jobv1t ] [ , jobv2t ] [ , trans ] [ , signs ] [ , info ] )
Include Files
mkl.fi , mkl_lapack.f90
Description
The routines ?orcsd / ?uncsd compute the CS decomposition of an m -by- m partitioned orthogonal matrix X :
or unitary matrix:
x11 is p -by- q . The orthogonal/unitary matrices u1 , u2 , v1 , and v2 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
jobu1
CHARACTER . If equals Y , then u1 is computed. Otherwise, u1 is not computed.
jobu2
CHARACTER . If equals Y , then u2 is computed. Otherwise, u2 is not computed.
jobv1t
CHARACTER . If equals Y , then v1:code:`t` is computed. Otherwise, v1:code:`t` is not computed.
jobv2t
CHARACTER . If equals Y , then v2:code:`t` is computed. Otherwise, v2:code:`t` is not computed.
- trans
-
CHARACTER
- signs
-
CHARACTER
m
INTEGER . The number of rows and columns of the matrix X .
p
INTEGER . The number of rows in x11 and x12 . 0 ≤p≤m .
q
INTEGER . The number of columns in x11 and x21 . 0 ≤q≤m .
- x11 , x12 , x21 , x22
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd 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
INTEGER . 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
INTEGER . The leading dimension of the array u1 . If jobu1 = ‘ Y ‘, ldu1≥ max(1,p) .
ldu2
INTEGER . The leading dimension of the array u2 . If jobu2 = ‘ Y ‘, ldu2≥ max(1,m-p) .
ldv1t
INTEGER . The leading dimension of the array v1t . If jobv1t = ‘ Y ‘, ldv1t≥ max(1,q) .
ldv2t
INTEGER . The leading dimension of the array v2t . If jobv2t = ‘ Y ‘, ldv2t≥ max(1,m-q) .
- work
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd Workspace array, size ( max(1,lwork) ).
lwork
INTEGER . The size of the work array. Constraints:
If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla .
- rwork
-
REAL for cuncsd DOUBLE PRECISION for zuncsd Workspace array, size ( max(1,lrwork) ).
lrwork
INTEGER . The size of the rwork array. Constraints:
If lrwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the rwork array, returns this value as the first entry of the rwork array, and no error message related to lrwork is issued by xerbla .
iwork
INTEGER . Workspace array, dimension m .
Output Parameters
- theta
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd
Array, size ( r ) , in which r = min(p,m-p,q,m-q) .
C = diag( cos(theta(1)[0]), ..., cos(theta(r)[r - 1]) ) , and
S = diag( sin(theta(1)[0]), ..., sin(theta(r)[r - 1]) ) .
- u1
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd
Array, size ( p ) .
If jobu1 = ‘ Y ‘, u1 contains the p -by- p orthogonal/unitary matrix u1 .
- u2
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd
Array, size ( ldu2 , m - p ) .
If jobu2 = ‘ Y ‘, u2 contains the ( m - p )-by-( m - p ) orthogonal/unitary matrix u2 .
- v1t
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd
Array, size ( ldv1t ,*) .
If jobv1t = ‘ Y ‘, v1t contains the q -by- q orthogonal matrix v1:code:`T` or unitary matrix v1:code:`H` .
- v2t
-
REAL for sorcsd DOUBLE PRECISION for dorcsd COMPLEX for cuncsd DOUBLE COMPLEX for zuncsd
Array, size ( ldv2t , m - q ) .
If jobv2t = ‘ Y ‘, v2t contains the ( m - q )-by-( m - q ) orthogonal matrix v2:code:`T` or unitary matrix v2:code:`H` .
- work
-
On exit,
- rwork
-
On exit,
info
INTEGER .
= 0: successful exit
< 0: if info = -i , the i -th argument has an illegal value
> 0: ?orcsd / ?uncsd did not converge. See the description of work above for details.
Return Values
No return value, info is an Output Parameter.
Fortran 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions .
Specific details for the routine ?orcsd/?uncsd interface are as follows:
x11
Holds the block of matrix X of size ( p , q ).
x12
Holds the block of matrix X of size ( p , m - q ).
x21
Holds the block of matrix X of size ( m - p , q ).
x22
Holds the block of matrix X of size ( m - p , m - q ).
theta
Holds the vector of length r = min(p,m-p,q,m-q) .
u1
Holds the matrix of size ( p , p ).
u2
Holds the matrix of size ( m - p , m - p ).
v1t
Holds the matrix of size ( q , q ).
v2t
Holds the matrix of size ( m - q , m - q ).
jobsu1
Indicates whether u1 is computed. Must be ‘Y’ or ‘O’ .
jobsu2
Indicates whether u2 is computed. Must be ‘Y’ or ‘O’ .
jobv1t
Indicates whether v1:code:`t` is computed. Must be ‘Y’ or ‘O’ .
jobv2t
Indicates whether v2:code:`t` is computed. Must be ‘Y’ or ‘O’ .
trans
Must be ‘N’ or ‘T’ .
signs
Must be ‘O’ or ‘D’ .