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

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

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

.PP
.nf
 SGQRTS tests SGGQRF, which computes the GQR factorization of an
 N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of rows of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of columns of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIP\fP 
.PP
.nf
          P is INTEGER
          The number of columns of the matrix B\&.  P >= 0\&.
.fi
.PP
.br
\fIA\fP 
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.nf
          A is REAL array, dimension (LDA,M)
          The N-by-M matrix A\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          AF is REAL array, dimension (LDA,N)
          Details of the GQR factorization of A and B, as returned
          by SGGQRF, see SGGQRF for further details\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is REAL array, dimension (LDA,N)
          The M-by-M orthogonal matrix Q\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is REAL 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 REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGQRF\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,P)
          On entry, the N-by-P matrix A\&.
.fi
.PP
.br
\fIBF\fP 
.PP
.nf
          BF is REAL array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by SGGQRF, see SGGQRF for further details\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL array, dimension (LDB,P)
          The P-by-P orthogonal matrix Z\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is REAL array, dimension (LDB,max(P,N))
.fi
.PP
.br
\fIBWK\fP 
.PP
.nf
          BWK is REAL 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 REAL 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 REAL array, dimension (LWORK)
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(N,M,P)**2\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (max(N,M,P))
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
          RESULT is REAL array, dimension (4)
          The test ratios:
            RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
            RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
            RESULT(3) = norm( I - Q'*Q ) / ( M*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 \fBsgqrts\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.