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

.in +1c
.ti -1c
.RI "subroutine \fBcgrqts\fP (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)"
.br
.RI "\fBCGRQTS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

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

.PP
.nf
 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\&.
.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
.PP
.br
\fIP\fP 
.PP
.nf
          P is INTEGER
          The number of rows of the matrix B\&.  P >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          The M-by-N matrix A\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is COMPLEX array, dimension (LDA,N)
          The N-by-N unitary matrix Q\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is COMPLEX array, dimension (LDA,MAX(M,N))
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          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 COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGQRC\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB,N)
          On entry, the P-by-N matrix A\&.
.fi
.PP
.br
\fIBF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL array, dimension (LDB,P)
          The P-by-P unitary matrix Z\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX array, dimension (LDB,max(P,N))
.fi
.PP
.br
\fIBWK\fP 
.PP
.nf
          BWK is COMPLEX array, dimension (LDB,N)
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the arrays B, BF, Z and T\&.
          LDB >= max(P,N)\&.
.fi
.PP
.br
\fITAUB\fP 
.PP
.nf
          TAUB is COMPLEX array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGRQF\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (LWORK)
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(M,P,N)**2\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (M)
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
          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 )
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

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