NAME

TESTING/EIG/sgqrts.f

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine sgqrts (integer n, integer m, integer p, 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)

SGQRTS

Purpose:



 SGQRTS tests SGGQRF, which computes the GQR factorization of an


 N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.

Parameters



          N is INTEGER


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



          M is INTEGER


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



          P is INTEGER


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



          A is REAL array, dimension (LDA,M)


          The N-by-M matrix A.



          AF is REAL array, dimension (LDA,N)


          Details of the GQR factorization of A and B, as returned


          by SGGQRF, see SGGQRF for further details.



          Q is REAL array, dimension (LDA,N)


          The M-by-M 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 SGGQRF.



          B is REAL array, dimension (LDB,P)


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



          BF is REAL array, dimension (LDB,N)


          Details of the GQR factorization of A and B, as returned


          by SGGQRF, see SGGQRF 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(N,M,P)**2.

RWORK



          RWORK is REAL array, dimension (max(N,M,P))

RESULT



          RESULT is REAL array, dimension (4)


          The test ratios:


            RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)


            RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)


            RESULT(3) = norm( I - Q'*Q ) / ( M*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 174 of file sgqrts.f.

Author

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