dggsvp.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dggsvp (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO)
DGGSVP

## Function/Subroutine Documentation

### subroutine dggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precisionTOLA, double precisionTOLB, integerK, integerL, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)

DGGSVP

Purpose:

``` DGGSVP 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
DGGSVD.
```

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
```

TOLB

```          TOLB is DOUBLE PRECISION

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
```

WORK

```          WORK is DOUBLE PRECISION 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 DGEQPF 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 dggsvp.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.