.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
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.br
\fIM\fP 
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.nf
!>          M is INTEGER
!>          The number of columns 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 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
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.br
\fIR\fP 
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.nf
!>          R is REAL array, dimension (LDA,MAX(M,N))
!> 
.fi
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.br
\fILDA\fP 
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.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
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.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 
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.nf
!>          T is REAL array, dimension (LDB,max(P,N))
!> 
.fi
.PP
.br
\fIBWK\fP 
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.nf
!>          BWK is REAL array, dimension (LDB,N)
!> 
.fi
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.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 
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.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
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.br
\fIRESULT\fP 
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.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
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

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