# sggsvp.f(3) [centos man page]

```sggsvp.f(3)							      LAPACK							       sggsvp.f(3)

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

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

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.

Version 3.4.2							  Tue Sep 25 2012						       sggsvp.f(3)```
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