.TH "TESTING/EIG/dgrqts.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/dgrqts.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdgrqts\fP (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)"
.br
.RI "\fBDGRQTS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dgrqts (integer m, integer p, integer n, double precision, dimension( lda, * ) a, double precision, dimension( lda, * ) af, double precision, dimension( lda, * ) q, double precision, dimension( lda, * ) r, integer lda, double precision, dimension( * ) taua, double precision, dimension( ldb, * ) b, double precision, dimension( ldb, * ) bf, double precision, dimension( ldb, * ) z, double precision, dimension( ldb, * ) t, double precision, dimension( ldb, * ) bwk, integer ldb, double precision, dimension( * ) taub, double precision, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( 4 ) result)"

.PP
\fBDGRQTS\fP 
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\fBPurpose:\fP
.RS 4

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.nf
 DGRQTS tests DGGRQF, 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
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.br
\fIP\fP 
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.nf
          P is INTEGER
          The number of rows of the matrix B\&.  P >= 0\&.
.fi
.PP
.br
\fIN\fP 
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.nf
          N is INTEGER
          The number of columns of the matrices A and B\&.  N >= 0\&.
.fi
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\fIA\fP 
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          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A\&.
.fi
.PP
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\fIAF\fP 
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.nf
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the GRQ factorization of A and B, as returned
          by DGGRQF, see SGGRQF for further details\&.
.fi
.PP
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\fIQ\fP 
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          Q is DOUBLE PRECISION array, dimension (LDA,N)
          The N-by-N orthogonal matrix Q\&.
.fi
.PP
.br
\fIR\fP 
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          R is DOUBLE PRECISION array, dimension (LDA,MAX(M,N))
.fi
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\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the arrays A, AF, R and Q\&.
          LDA >= max(M,N)\&.
.fi
.PP
.br
\fITAUA\fP 
.PP
.nf
          TAUA is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGGQRC\&.
.fi
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\fIB\fP 
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.nf
          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the P-by-N matrix A\&.
.fi
.PP
.br
\fIBF\fP 
.PP
.nf
          BF is DOUBLE PRECISION array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by DGGRQF, see SGGRQF for further details\&.
.fi
.PP
.br
\fIZ\fP 
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.nf
          Z is DOUBLE PRECISION array, dimension (LDB,P)
          The P-by-P orthogonal matrix Z\&.
.fi
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\fIT\fP 
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          T is DOUBLE PRECISION array, dimension (LDB,max(P,N))
.fi
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\fIBWK\fP 
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          BWK is DOUBLE PRECISION array, dimension (LDB,N)
.fi
.PP
.br
\fILDB\fP 
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          LDB is INTEGER
          The leading dimension of the arrays B, BF, Z and T\&.
          LDB >= max(P,N)\&.
.fi
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\fITAUB\fP 
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.nf
          TAUB is DOUBLE PRECISION array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by DGGRQF\&.
.fi
.PP
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\fIWORK\fP 
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.nf
          WORK is DOUBLE PRECISION array, dimension (LWORK)
.fi
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\fILWORK\fP 
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          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(M,P,N)**2\&.
.fi
.PP
.br
\fIRWORK\fP 
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.nf
          RWORK is DOUBLE PRECISION array, dimension (M)
.fi
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\fIRESULT\fP 
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.nf
          RESULT is DOUBLE PRECISION 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 )
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB174\fP of file \fBdgrqts\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.