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cggsvp.f(3) LAPACK cggsvp.f(3)NAMEcggsvp.f-SYNOPSISFunctions/Subroutines 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) CGGSVPFunction/Subroutine Documentation subroutine cggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, realTOLA, realTOLB, integerK, integerL, complex, dimension( ldu, * )U, integerLDU, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, real, dimension( * )RWORK, complex, dimension( * )TAU, complex, dimension( * )WORK, integerINFO) CGGSVP Purpose: CGGSVP computes unitary matrices U, V and Q such that N-K-L K L U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; 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**H*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**H,B**H)**H. This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine CGGSVD. Parameters: JOBU 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 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B B is COMPLEX array, dimension (LDB,N) On entry, the P-by-N 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 REAL TOLB TOLB is REAL 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. K K is INTEGER L 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 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 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 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 REAL array, dimension (2*N) TAU TAU is COMPLEX array, dimension (N) WORK WORK is COMPLEX array, dimension (max(3*N,M,P)) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Further Details: The subroutine uses LAPACK subroutine CGEQPF 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. Definition at line 259 of file cggsvp.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 cggsvp.f(3)

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