Previous: cggsvd Up: ../lapack-c.html Next: cgtcon

NAME CGGSVP - compute unitary matrices U, V and Q such that U'*A*Q = ( 0 A12 A13 ) K , V'*B*Q = ( 0 0 B13 ) L ( 0 0 A23 ) L ( 0 0 0 ) P-L ( 0 0 0 ) M-K-L N-K-L K L N-K-L K L where the K-by-K matrix A12 and L-by-L matrix B13 are non- singular upper triangular SYNOPSIS SUBROUTINE CGGSVP( 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 JOBQ, JOBU, JOBV INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P REAL TOLA, TOLB INTEGER IWORK( * ) REAL RWORK( * ) COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * ) PURPOSE CGGSVP computes unitary matrices U, V and Q such that A23 is upper trapezoidal. K+L = the effective 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 CGGSVD. ARGUMENTS JOBU (input) CHARACTER*1 = 'U': Unitary matrix U is computed; = 'N': U is not computed. JOBV (input) CHARACTER*1 = 'V': Unitary matrix V is computed; = 'N': V is not computed. JOBQ (input) CHARACTER*1 = 'Q': Unitary matrix Q is computed; = 'N': Q is not computed. M (input) INTEGER The number of rows of the matrix A. M >= 0. P (input) INTEGER The number of rows of the matrix B. P >= 0. N (input) INTEGER The number of columns of the matrices A and B. N >= 0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). B (input/output) COMPLEX array, dimension (LDB,N) On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose sec- tion. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,P). TOLA (input) REAL TOLB (input) REAL TOLA and TOLB are the thres- holds to determine the effective 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 decom- position. K (output) INTEGER L (output) INTEGER On exit, K and L specify the dimension of the subblocks described in Purpose section. K + L = effective numerical rank of (A',B')'. U (output) COMPLEX array, dimension (LDU,M) If JOBU = 'U', U contains the unitary matrix U. If JOBU = 'N', U is not referenced. LDU (input) INTEGER The leading dimension of the array U. LDU >= max(1,M). V (output) COMPLEX array, dimension (LDV,M) If JOBV = 'V', V contains the unitary matrix V. If JOBV = 'N', V is not referenced. LDV (input) INTEGER The leading dimension of the array V. LDV >= max(1,P). Q (output) COMPLEX array, dimension (LDQ,N) If JOBQ = 'Q', Q contains the unitary matrix Q. If JOBQ = 'N', Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= max(1,N). IWORK (workspace) INTEGER array, dimension (N) RWORK (workspace) REAL array, dimension (2*N) TAU (workspace) COMPLEX array, dimension (N) WORK (workspace) COMPLEX array, dimension (MAX(3*N,M,P)) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. FURTHER DETAILS 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.