# 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

Univ. of Colorado Denver

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