cggsvp-f(3)

cggsvp.f –

Synopsis

Functions/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)
CGGSVP

Function/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 is INTEGER
 The number of rows of the matrix A. M >= 0.

 P is INTEGER
 The number of rows of the matrix B. P >= 0.

 N is INTEGER
 The number of columns of the matrices A and B. N >= 0.

 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 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 is INTEGER

 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 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 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 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 = -i, 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.

Author

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