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)