# zgrqts.f - Man Page

TESTING/EIG/zgrqts.f

## Synopsis

### Functions/Subroutines

subroutine zgrqts (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)
ZGRQTS

## Function/Subroutine Documentation

### subroutine zgrqts (integer m, integer p, integer n, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) taua, complex*16, dimension( ldb, * ) b, complex*16, dimension( ldb, * ) bf, complex*16, dimension( ldb, * ) z, complex*16, dimension( ldb, * ) t, complex*16, dimension( ldb, * ) bwk, integer ldb, complex*16, dimension( * ) taub, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( 4 ) result)

ZGRQTS

Purpose:

``` ZGRQTS tests ZGGRQF, which computes the GRQ factorization of an
M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.```
Parameters

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)
The M-by-N matrix A.```

AF

```          AF is COMPLEX*16 array, dimension (LDA,N)
Details of the GRQ factorization of A and B, as returned
by ZGGRQF, see CGGRQF for further details.```

Q

```          Q is COMPLEX*16 array, dimension (LDA,N)
The N-by-N unitary matrix Q.```

R

`          R is COMPLEX*16 array, dimension (LDA,MAX(M,N))`

LDA

```          LDA is INTEGER
The leading dimension of the arrays A, AF, R and Q.
LDA >= max(M,N).```

TAUA

```          TAUA is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by DGGQRC.```

B

```          B is COMPLEX*16 array, dimension (LDB,N)
On entry, the P-by-N matrix A.```

BF

```          BF is COMPLEX*16 array, dimension (LDB,N)
Details of the GQR factorization of A and B, as returned
by ZGGRQF, see CGGRQF for further details.```

Z

```          Z is DOUBLE PRECISION array, dimension (LDB,P)
The P-by-P unitary matrix Z.```

T

`          T is COMPLEX*16 array, dimension (LDB,max(P,N))`

BWK

`          BWK is COMPLEX*16 array, dimension (LDB,N)`

LDB

```          LDB is INTEGER
The leading dimension of the arrays B, BF, Z and T.
LDB >= max(P,N).```

TAUB

```          TAUB is COMPLEX*16 array, dimension (min(P,N))
The scalar factors of the elementary reflectors, as returned
by DGGRQF.```

WORK

`          WORK is COMPLEX*16 array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The dimension of the array WORK, LWORK >= max(M,P,N)**2.```

RWORK

`          RWORK is DOUBLE PRECISION array, dimension (M)`

RESULT

```          RESULT is DOUBLE PRECISION array, dimension (4)
The test ratios:
RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 174 of file zgrqts.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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