sggsvp.f man page

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

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 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

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

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**T,B**T)**T.

U

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

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

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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sggsvp(3) is an alias of sggsvp.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK