SUBROUTINE SGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, * TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO) CHARACTER * 1 JOBU, JOBV, JOBQ INTEGER M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO INTEGER IWORK(*) REAL TOLA, TOLB REAL A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*), Q(LDQ,*), TAU(*), WORK(*) SUBROUTINE SGGSVP_64( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, * TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO) CHARACTER * 1 JOBU, JOBV, JOBQ INTEGER*8 M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO INTEGER*8 IWORK(*) REAL TOLA, TOLB REAL A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*), Q(LDQ,*), TAU(*), WORK(*)
SUBROUTINE GGSVP( JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B, [LDB], * TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK], [TAU], * [WORK], [INFO]) CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ INTEGER :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO INTEGER, DIMENSION(:) :: IWORK REAL :: TOLA, TOLB REAL, DIMENSION(:) :: TAU, WORK REAL, DIMENSION(:,:) :: A, B, U, V, Q SUBROUTINE GGSVP_64( JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B, * [LDB], TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK], * [TAU], [WORK], [INFO]) CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ INTEGER(8) :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL :: TOLA, TOLB REAL, DIMENSION(:) :: TAU, WORK REAL, DIMENSION(:,:) :: A, B, U, V, Q
void sggsvp(char jobu, char jobv, char jobq, int m, int p, int n, float *a, int lda, float *b, int ldb, float tola, float tolb, int *k, int *l, float *u, int ldu, float *v, int ldv, float *q, int ldq, int *info);
void sggsvp_64(char jobu, char jobv, char jobq, long m, long p, long n, float *a, long lda, float *b, long ldb, float tola, float tolb, long *k, long *l, float *u, long ldu, float *v, long ldv, float *q, long ldq, long *info);
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 nonsingular 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 transpose of Z.
This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine SGGSVD.