SGGSVP (3) Linux Manual Page

NAME

sggsvp.f –

SYNOPSIS

Functions/Subroutines

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)
SGGSVP

Function/Subroutine Documentation

subroutine sggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, realTOLA, realTOLB, integerK, integerL, real, dimension( ldu, * )U, integerLDU, real, dimension( ldv, * )V, integerLDV, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)

SGGSVP

Purpose:


SGGSVP computes orthogonal matrices U, V and Q such that
                                               N -
                                           K - L K L U **T *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 **T *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**T,B**T)**T. 
 This decomposition is the preprocessing step for computing the
 Generalized Singular Value Decomposition (GSVD), see subroutine
 SGGSVD.

Parameters:

JOBU

          JOBU is CHARACTER*1
          = 'U':  Orthogonal matrix U is computed;
          = 'N':  U is not computed.

JOBV

          JOBV is CHARACTER*1
          = 'V':  Orthogonal matrix V is computed;
          = 'N':  V is not computed.

JOBQ

          JOBQ is CHARACTER*1
          = 'Q':  Orthogonal 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 REAL 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 REAL 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**T,B**T)**T.

          U is REAL array, dimension (LDU,M)
          If JOBU = 'U', U contains the orthogonal 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 REAL array, dimension (LDV,P)
          If JOBV = 'V', V contains the orthogonal 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 REAL array, dimension (LDQ,N)
          If JOBQ = 'Q', Q contains the orthogonal 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)

TAU

          TAU is REAL array, dimension (N)

WORK

          WORK is REAL 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 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.

Definition at line 253 of file sggsvp.f.

Author

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