NAME

TESTING/EIG/cgrqts.f

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

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

CGRQTS

Purpose:



 CGRQTS tests CGGRQF, 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 COMPLEX array, dimension (LDA,N)


          The M-by-N matrix A.



          AF is COMPLEX array, dimension (LDA,N)


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


          by CGGRQF, see CGGRQF for further details.



          Q is COMPLEX array, dimension (LDA,N)


          The N-by-N unitary matrix Q.



          R is COMPLEX 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 array, dimension (min(M,N))


          The scalar factors of the elementary reflectors, as returned


          by SGGQRC.



          B is COMPLEX array, dimension (LDB,N)


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



          BF is COMPLEX array, dimension (LDB,N)


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


          by CGGRQF, see CGGRQF for further details.



          Z is REAL array, dimension (LDB,P)


          The P-by-P unitary matrix Z.



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

BWK



          BWK is COMPLEX 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 array, dimension (min(P,N))


          The scalar factors of the elementary reflectors, as returned


          by SGGRQF.

WORK



          WORK is COMPLEX 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 174 of file cgrqts.f.

Author

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