sggsvp - compute orthogonal matrices
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(*) 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, 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 C INTERFACE #include <sunperf.h> 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);
Oracle Solaris Studio Performance Library sggsvp(3P) NAME sggsvp - compute orthogonal matrices SYNOPSIS 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(*) 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, 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 C INTERFACE #include <sunperf.h> 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); PURPOSE sggsvp computes orthogonal 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 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 General- ized Singular Value Decomposition (GSVD), see subroutine SGGSVD. ARGUMENTS JOBU (input) = 'U': Orthogonal matrix U is computed; = 'N': U is not computed. JOBV (input) = 'V': Orthogonal matrix V is computed; = 'N': V is not computed. JOBQ (input) = 'Q': Orthogonal 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 contains 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 contains the triangular matrix described in the Purpose 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 subblock 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 the description of TOLA. K (output) On exit, K and L specify the dimension of the subblocks described in Purpose. K + L = effective numerical rank of (A',B')'. L (output) See the description of K. U (output) If JOBU = 'U', U contains the orthogonal 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 (output) If JOBV = 'V', V contains the orthogonal 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 (output) If JOBQ = 'Q', Q contains the orthogonal 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) 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 illegal value. FURTHER DETAILS The subroutine uses LAPACK subroutine SGEQPF for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix. It may be replaced by a better rank determination strategy. 7 Nov 2015 sggsvp(3P)