sgrqts.f - Man Page

TESTING/EIG/sgrqts.f

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine sgrqts (integer m, integer p, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) taua, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, real, dimension( ldb, * ) z, real, dimension( ldb, * ) t, real, dimension( ldb, * ) bwk, integer ldb, real, dimension( * ) taub, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 4 ) result)

SGRQTS

Purpose:

``` SGRQTS tests SGGRQF, 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 REAL array, dimension (LDA,N)
The M-by-N matrix A.```

AF

```          AF is REAL array, dimension (LDA,N)
Details of the GRQ factorization of A and B, as returned
by SGGRQF, see SGGRQF for further details.```

Q

```          Q is REAL array, dimension (LDA,N)
The N-by-N orthogonal matrix Q.```

R

`          R is REAL 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 REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by SGGQRC.```

B

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

BF

```          BF is REAL array, dimension (LDB,N)
Details of the GQR factorization of A and B, as returned
by SGGRQF, see SGGRQF for further details.```

Z

```          Z is REAL array, dimension (LDB,P)
The P-by-P orthogonal matrix Z.```

T

`          T is REAL array, dimension (LDB,max(P,N))`

BWK

`          BWK is REAL 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 REAL array, dimension (min(P,N))
The scalar factors of the elementary reflectors, as returned
by SGGRQF.```

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

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

RWORK

`          RWORK is REAL array, dimension (M)`

RESULT

```          RESULT is REAL 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 175 of file sgrqts.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

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