NAME

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 is INTEGER


          The number of rows of the matrix A.  M >= 0.



          P is INTEGER


          The number of rows of the matrix B.  P >= 0.



          N is INTEGER


          The number of columns of the matrices A and B.  N >= 0.



          A is REAL array, dimension (LDA,N)


          The M-by-N matrix A.



          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 is REAL array, dimension (LDA,N)


          The N-by-N orthogonal matrix Q.



          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 is REAL array, dimension (LDB,N)


          On entry, the P-by-N matrix A.



          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 is REAL array, dimension (LDB,P)


          The P-by-P orthogonal matrix Z.



          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

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