Contents
zggsvp - compute unitary matrices U, V and Q such that N-
K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
SUBROUTINE ZGGSVP(JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA,
TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK,
INFO)
CHARACTER * 1 JOBU, JOBV, JOBQ
DOUBLE COMPLEX A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*),
Q(LDQ,*), TAU(*), WORK(*)
INTEGER M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER IWORK(*)
DOUBLE PRECISION TOLA, TOLB
DOUBLE PRECISION RWORK(*)
SUBROUTINE ZGGSVP_64(JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA,
TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK,
INFO)
CHARACTER * 1 JOBU, JOBV, JOBQ
DOUBLE COMPLEX A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*),
Q(LDQ,*), TAU(*), WORK(*)
INTEGER*8 M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION TOLA, TOLB
DOUBLE PRECISION RWORK(*)
F95 INTERFACE
SUBROUTINE GGSVP(JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B, [LDB],
TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK], [RWORK],
[TAU], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ
COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, U, V, Q
INTEGER :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8) :: TOLA, TOLB
REAL(8), DIMENSION(:) :: RWORK
SUBROUTINE GGSVP_64(JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B,
[LDB], TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK],
[RWORK], [TAU], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ
COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, U, V, Q
INTEGER(8) :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8) :: TOLA, TOLB
REAL(8), DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void zggsvp(char jobu, char jobv, char jobq, int m, int p,
int n, doublecomplex *a, int lda, doublecomplex
*b, int ldb, double tola, double tolb, int *k, int
*l, doublecomplex *u, int ldu, doublecomplex *v,
int ldv, doublecomplex *q, int ldq, int *info);
void zggsvp_64(char jobu, char jobv, char jobq, long m, long
p, long n, doublecomplex *a, long lda, doublecom-
plex *b, long ldb, double tola, double tolb, long
*k, long *l, doublecomplex *u, long ldu, doub-
lecomplex *v, long ldv, doublecomplex *q, long
ldq, long *info);
zggsvp computes unitary matrices U, V and Q such that
L ( 0 0 A23 )
M-K-L ( 0 0 0 )
N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )
N-K-L K L
V'*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )
where the K-by-K matrix A12 and L-by-L matrix B13 are non-
singular upper triangular; A23 is L-by-L upper triangular if
M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal.
K+L = the effective numerical rank of the (M+P)-by-N matrix
(A',B')'. Z' denotes the conjugate transpose of Z.
This decomposition is the preprocessing step for computing
the Generalized Singular Value Decomposition (GSVD), see
subroutine ZGGSVD.
JOBU (input)
= 'U': Unitary matrix U is computed;
= 'N': U is not computed.
JOBV (input)
= 'V': Unitary matrix V is computed;
= 'N': V is not computed.
JOBQ (input)
= 'Q': Unitary matrix Q is computed;
= 'N': Q is not computed.
M (input) The number of rows of the matrix A. M >= 0.
P (input) The number of rows of the matrix B. P >= 0.
N (input) The number of columns of the matrices A and B. N
>= 0.
A (input/output)
On entry, the M-by-N matrix A. On exit, A con-
tains the triangular (or trapezoidal) matrix
described in the Purpose section.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
B (input/output)
On entry, the P-by-N matrix B. On exit, B con-
tains the triangular matrix described in the Pur-
pose section.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,P).
TOLA (input)
TOLA and TOLB are the thresholds to determine the
effective numerical rank of matrix B and a sub-
block of A. Generally, they are set to TOLA =
MAX(M,N)*norm(A)*MACHEPS, TOLB =
MAX(P,N)*norm(B)*MACHEPS. The size of TOLA and
TOLB may affect the size of backward errors of the
decomposition.
TOLB (input)
See description of TOLA.
K (output)
On exit, K and L specify the dimension of the sub-
blocks described in Purpose section. K + L =
effective numerical rank of (A',B')'.
L (output)
See the description of K.
U (input) If JOBU = 'U', U contains the unitary matrix U.
If JOBU = 'N', U is not referenced.
LDU (input)
The leading dimension of the array U. LDU >=
max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
V (input) If JOBV = 'V', V contains the unitary matrix V.
If JOBV = 'N', V is not referenced.
LDV (input)
The leading dimension of the array V. LDV >=
max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
Q (input) If JOBQ = 'Q', Q contains the unitary matrix Q.
If JOBQ = 'N', Q is not referenced.
LDQ (input)
The leading dimension of the array Q. LDQ >=
max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK (workspace)
dimension(N)
RWORK (workspace)
dimension(2*N)
TAU (workspace)
dimension(N)
WORK (workspace)
dimension(MAX(3*N,M,P))
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
The subroutine uses LAPACK subroutine CGEQPF for the QR fac-
torization with column pivoting to detect the effective
numerical rank of the a matrix. It may be replaced by a
better rank determination strategy.