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cuncsd-f(3)

cuncsd.f –

Synopsis

Functions/Subroutines

recursive subroutine 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)
CUNCSD

Function/Subroutine Documentation

recursive subroutine cuncsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, characterSIGNS, integerM, integerP, integerQ, complex, dimension( ldx11, * )X11, integerLDX11, complex, dimension( ldx12, * )X12, integerLDX12, complex, dimension( ldx21, * )X21, integerLDX21, complex, dimension( ldx22, * )X22, integerLDX22, real, dimension( * )THETA, complex, dimension( ldu1, * )U1, integerLDU1, complex, dimension( ldu2, * )U2, integerLDU2, complex, dimension( ldv1t, * )V1T, integerLDV1T, complex, dimension( ldv2t, * )V2T, integerLDV2T, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerINFO)

CUNCSD

Purpose:

 CUNCSD computes the CS decomposition of an M-by-M partitioned
 unitary matrix X:
 [ I 0 0 | 0 0 0 ]
 [ 0 C 0 | 0 -S 0 ]
 [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**H
 X = [-----------] = [---------] [---------------------] [---------] .
 [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]
 [ 0 S 0 | 0 C 0 ]
 [ 0 0 I | 0 0 0 ]
 X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P,
 (M-P)-by-(M-P), Q-by-Q, and (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).

 

Parameters:

JOBU1

 JOBU1 is CHARACTER
 = 'Y': U1 is computed;
 otherwise: U1 is not computed.

JOBU2

 JOBU2 is CHARACTER
 = 'Y': U2 is computed;
 otherwise: U2 is not computed.

JOBV1T

 JOBV1T is CHARACTER
 = 'Y': V1T is computed;
 otherwise: V1T is not computed.

JOBV2T

 JOBV2T is CHARACTER
 = 'Y': V2T is computed;
 otherwise: V2T is not computed.

TRANS

 TRANS is CHARACTER
 = 'T': X, U1, U2, V1T, and V2T are stored in row-major
 order;
 otherwise: X, U1, U2, V1T, and V2T are stored in column-
 major order.

SIGNS

 SIGNS is CHARACTER
 = 'O': The lower-left block is made nonpositive (the
 "other" convention);
 otherwise: The upper-right block is made nonpositive (the
 "default" convention).

M

 M is INTEGER
 The number of rows and columns in X.

P

 P is INTEGER
 The number of rows in X11 and X12. 0 <= P <= M.

Q

 Q is INTEGER
 The number of columns in X11 and X21. 0 <= Q <= M.

X11

 X11 is COMPLEX array, dimension (LDX11,Q)
 On entry, part of the unitary matrix whose CSD is desired.

LDX11

 LDX11 is INTEGER
 The leading dimension of X11. LDX11 >= MAX(1,P).

X12

 X12 is COMPLEX array, dimension (LDX12,M-Q)
 On entry, part of the unitary matrix whose CSD is desired.

LDX12

 LDX12 is INTEGER
 The leading dimension of X12. LDX12 >= MAX(1,P).

X21

 X21 is COMPLEX array, dimension (LDX21,Q)
 On entry, part of the unitary matrix whose CSD is desired.

LDX21

 LDX21 is INTEGER
 The leading dimension of X11. LDX21 >= MAX(1,M-P).

X22

 X22 is COMPLEX array, dimension (LDX22,M-Q)
 On entry, part of the unitary matrix whose CSD is desired.

LDX22

 LDX22 is INTEGER
 The leading dimension of X11. LDX22 >= MAX(1,M-P).

THETA

 THETA is REAL array, dimension (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

 U1 is COMPLEX array, dimension (P)
 If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.

LDU1

 LDU1 is INTEGER
 The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
 MAX(1,P).

U2

 U2 is COMPLEX array, dimension (M-P)
 If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
 matrix U2.

LDU2

 LDU2 is INTEGER
 The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
 MAX(1,M-P).

V1T

 V1T is COMPLEX array, dimension (Q)
 If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
 matrix V1**H.

LDV1T

 LDV1T is INTEGER
 The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
 MAX(1,Q).

V2T

 V2T is COMPLEX array, dimension (M-Q)
 If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
 matrix V2**H.

LDV2T

 LDV2T is INTEGER
 The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
 MAX(1,M-Q).

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER
 The dimension of the array WORK.
 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

 RWORK is REAL array, dimension MAX(1,LRWORK)
 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
 If INFO > 0 on exit, 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.

LRWORK

 LRWORK is INTEGER
 The dimension of the array RWORK.
 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 work array, and no error
 message related to LRWORK is issued by XERBLA.

IWORK

 IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))

INFO

 INFO is INTEGER
 = 0: successful exit.
 < 0: if INFO = -i, the i-th argument had an illegal value.
 > 0: CBBCSD did not converge. See the description of RWORK
 above for details.

 

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 316 of file cuncsd.f.

Author

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