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Visible to Intel only — GUID: GUID-D82ECBB0-F5BF-43DA-BBC8-C96C28EF9D3B
?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, 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 C2 + S2 = 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 v1t is computed. Otherwise, v1t is not computed.
- jobv2t
-
CHARACTER. If equals Y, then v2t is computed. Otherwise, v2t is not computed.
- trans
-
CHARACTER
- = 'T':
- x, u1, u2, v1t, v2t are stored in row-major order.
- otherwise
- x, u1, u2, v1t, v2t are stored in column-major order.
- signs
-
CHARACTER
- = 'O':
- The lower-left block is made nonpositive (the "other" convention).
- otherwise
- The upper-right block is made nonpositive (the "default" convention).
- 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)), ..., cos(theta(r)) ), and
S = diag( sin(theta(1)), ..., sin(theta(r)) ).
- 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 v1T or unitary matrix v1H.
- 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 v2T or unitary matrix v2H.
- work
-
On exit,
- If info = 0,
- work(1) returns the optimal lwork.
- If info > 0,
- For ?orcsd, work(2:r) contains the values phi(1), ..., phi(r-1) that, together with theta(1), ..., theta(r) define the matrix in intermediate bidiagonal-block form remaining after nonconvergence. info specifies the number of nonzero phi's.
- rwork
-
On exit,
- If info = 0,
- rwork(1) returns the optimal lrwork.
- If info > 0,
- For ?uncsd, rwork(2:r) contains the values phi(1), ..., phi(r-1) that, together with theta(1), ..., theta(r) define the matrix in intermediate bidiagonal-block form remaining after nonconvergence. info specifies the number of nonzero phi's.
- 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.
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 v1t is computed. Must be 'Y' or 'O'.
- jobv2t
-
Indicates whether v2t is computed. Must be 'Y' or 'O'.
- trans
-
Must be 'N' or 'T'.
- signs
-
Must be 'O' or 'D'.