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

.in +1c
.ti -1c
.RI "subroutine \fBzgrqts\fP (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)"
.br
.RI "\fBZGRQTS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgrqts (integer m, integer p, integer n, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) taua, complex*16, dimension( ldb, * ) b, complex*16, dimension( ldb, * ) bf, complex*16, dimension( ldb, * ) z, complex*16, dimension( ldb, * ) t, complex*16, dimension( ldb, * ) bwk, integer ldb, complex*16, dimension( * ) taub, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( 4 ) result)"

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

.PP
.nf
!>
!> ZGRQTS tests ZGGRQF, 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*16 array, dimension (LDA,N)
!>          The M-by-N matrix A\&.
!> 
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
!>          AF is COMPLEX*16 array, dimension (LDA,N)
!>          Details of the GRQ factorization of A and B, as returned
!>          by ZGGRQF, see CGGRQF for further details\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is COMPLEX*16 array, dimension (LDA,N)
!>          The N-by-N unitary matrix Q\&.
!> 
.fi
.PP
.br
\fIR\fP 
.PP
.nf
!>          R is COMPLEX*16 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*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by DGGQRC\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 array, dimension (LDB,N)
!>          On entry, the P-by-N matrix A\&.
!> 
.fi
.PP
.br
\fIBF\fP 
.PP
.nf
!>          BF is COMPLEX*16 array, dimension (LDB,N)
!>          Details of the GQR factorization of A and B, as returned
!>          by ZGGRQF, see CGGRQF for further details\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is DOUBLE PRECISION array, dimension (LDB,P)
!>          The P-by-P unitary matrix Z\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX*16 array, dimension (LDB,max(P,N))
!> 
.fi
.PP
.br
\fIBWK\fP 
.PP
.nf
!>          BWK is COMPLEX*16 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*16 array, dimension (min(P,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by DGGRQF\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 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 DOUBLE PRECISION array, dimension (M)
!> 
.fi
.PP
.br
\fIRESULT\fP 
.PP
.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
.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 \fBzgrqts\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.