# zggsvp3.f - Man Page

SRC/zggsvp3.f

## Synopsis

### Functions/Subroutines

subroutine zggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)
ZGGSVP3

## Function/Subroutine Documentation

### subroutine zggsvp3 (character jobu, character jobv, character jobq, integer m, integer p, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision tola, double precision tolb, integer k, integer l, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) iwork, double precision, dimension( * ) rwork, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZGGSVP3

Purpose:

``` ZGGSVP3 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
ZGGSVD3.```
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

```          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 COMPLEX*16 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 COMPLEX*16 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)*MAZHEPS,
TOLB = MAX(P,N)*norm(B)*MAZHEPS.
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**H,B**H)**H.```

U

```          U is COMPLEX*16 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

```          V is COMPLEX*16 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

```          Q is COMPLEX*16 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 DOUBLE PRECISION array, dimension (2*N)`

TAU

`          TAU is COMPLEX*16 array, dimension (N)`

WORK

```          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.```

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.

Further Details:

```  The subroutine uses LAPACK subroutine ZGEQP3 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.

ZGGSVP3 replaces the deprecated subroutine ZGGSVP.```

Definition at line 275 of file zggsvp3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zggsvp3(3) is an alias of zggsvp3.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK