TESTING/EIG/sgrqts.f(3)    Library Functions Manual    TESTING/EIG/sgrqts.f(3)

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

                     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.

LAPACK                          Version 3.12.0         TESTING/EIG/sgrqts.f(3)