
NAMEzggsvp.f SYNOPSISFunctions/Subroutinessubroutine 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) Function/Subroutine Documentationsubroutine zggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, double precisionTOLA, double precisionTOLB, integerK, integerL, complex*16, dimension( ldu, * )U, integerLDU, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, double precision, dimension( * )RWORK, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)ZGGSVP Purpose:ZGGSVP computes unitary matrices U, V and Q such that NKL K L U**H*A*Q = K ( 0 A12 A13 ) if MKL >= 0; L ( 0 0 A23 ) MKL ( 0 0 0 ) NKL K L = K ( 0 A12 A13 ) if MKL < 0; MK ( 0 0 A23 ) NKL K L V**H*B*Q = L ( 0 0 B13 ) PL ( 0 0 0 ) where the KbyK matrix A12 and LbyL matrix B13 are nonsingular upper triangular; A23 is LbyL upper triangular if MKL >= 0, otherwise A23 is (MK)byL upper trapezoidal. K+L = the effective numerical rank of the (M+P)byN matrix (A**H,B**H)**H. This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine ZGGSVD. JOBU
Author:
JOBU is CHARACTER*1 = 'U': Unitary matrix U is computed; = 'N': U is not computed.JOBV JOBV is CHARACTER*1 = 'V': Unitary matrix V is computed; = 'N': V is not computed.JOBQ JOBQ is CHARACTER*1 = 'Q': Unitary matrix Q is computed; = 'N': Q is not computed.M M is INTEGER The number of rows of the matrix A. M >= 0.P P is INTEGER The number of rows of the matrix B. P >= 0.N N is INTEGER The number of columns of the matrices A and B. N >= 0.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B B is COMPLEX*16 array, dimension (LDB,N) On entry, the PbyN matrix B. On exit, B contains the triangular matrix described in the Purpose section.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,P).TOLA TOLA is DOUBLE PRECISIONTOLB TOLB is DOUBLE PRECISION 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)*MAZHEPS, TOLB = MAX(P,N)*norm(B)*MAZHEPS. The size of TOLA and TOLB may affect the size of backward errors of the decomposition.K K is INTEGERL L is INTEGER On exit, K and L specify the dimension of the subblocks described in Purpose section. K + L = effective numerical rank of (A**H,B**H)**H.U U is COMPLEX*16 array, dimension (LDU,M) If JOBU = 'U', U contains the unitary matrix U. If JOBU = 'N', U is not referenced.LDU LDU is INTEGER The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.V V is COMPLEX*16 array, dimension (LDV,P) If JOBV = 'V', V contains the unitary matrix V. If JOBV = 'N', V is not referenced.LDV LDV is INTEGER The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.Q Q is COMPLEX*16 array, dimension (LDQ,N) If JOBQ = 'Q', Q contains the unitary matrix Q. If JOBQ = 'N', Q is not referenced.LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.IWORK IWORK is INTEGER array, dimension (N)RWORK RWORK is DOUBLE PRECISION array, dimension (2*N)TAU TAU is COMPLEX*16 array, dimension (N)WORK WORK is COMPLEX*16 array, dimension (max(3*N,M,P))INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
The subroutine uses LAPACK subroutine ZGEQPF 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. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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