.TH "unglq" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
unglq \- {un,or}glq: generate explicit Q from gelqf
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcunglq\fP (m, n, k, a, lda, tau, work, lwork, info)"
.br
.RI "\fBCUNGLQ\fP "
.ti -1c
.RI "subroutine \fBdorglq\fP (m, n, k, a, lda, tau, work, lwork, info)"
.br
.RI "\fBDORGLQ\fP "
.ti -1c
.RI "subroutine \fBsorglq\fP (m, n, k, a, lda, tau, work, lwork, info)"
.br
.RI "\fBSORGLQ\fP "
.ti -1c
.RI "subroutine \fBzunglq\fP (m, n, k, a, lda, tau, work, lwork, info)"
.br
.RI "\fBZUNGLQ\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cunglq (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
!> which is defined as the first M rows of a product of K elementary
!> reflectors of order N
!>
!>       Q  =  H(k)**H \&. \&. \&. H(2)**H H(1)**H
!>
!> as returned by CGELQF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix Q\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Q\&. N >= M\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q\&. M >= K >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the i-th row must contain the vector which defines
!>          the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned
!>          by CGELQF in the first k rows of its array argument A\&.
!>          On exit, the M-by-N matrix Q\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The first dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by CGELQF\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&. LWORK >= max(1,M)\&.
!>          For optimum performance LWORK >= M*NB, where NB is
!>          the optimal blocksize\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit;
!>          < 0:  if INFO = -i, the i-th argument has an illegal value
!> 
.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 \fB126\fP of file \fBcunglq\&.f\fP\&.
.SS "subroutine dorglq (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> DORGLQ generates an M-by-N real matrix Q with orthonormal rows,
!> which is defined as the first M rows of a product of K elementary
!> reflectors of order N
!>
!>       Q  =  H(k) \&. \&. \&. H(2) H(1)
!>
!> as returned by DGELQF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix Q\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Q\&. N >= M\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q\&. M >= K >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the i-th row must contain the vector which defines
!>          the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned
!>          by DGELQF in the first k rows of its array argument A\&.
!>          On exit, the M-by-N matrix Q\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The first dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is DOUBLE PRECISION array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by DGELQF\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&. LWORK >= max(1,M)\&.
!>          For optimum performance LWORK >= M*NB, where NB is
!>          the optimal blocksize\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument has an illegal value
!> 
.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 \fB126\fP of file \fBdorglq\&.f\fP\&.
.SS "subroutine sorglq (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> SORGLQ generates an M-by-N real matrix Q with orthonormal rows,
!> which is defined as the first M rows of a product of K elementary
!> reflectors of order N
!>
!>       Q  =  H(k) \&. \&. \&. H(2) H(1)
!>
!> as returned by SGELQF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix Q\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Q\&. N >= M\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q\&. M >= K >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the i-th row must contain the vector which defines
!>          the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned
!>          by SGELQF in the first k rows of its array argument A\&.
!>          On exit, the M-by-N matrix Q\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The first dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is REAL array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by SGELQF\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&. LWORK >= max(1,M)\&.
!>          For optimum performance LWORK >= M*NB, where NB is
!>          the optimal blocksize\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument has an illegal value
!> 
.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 \fB126\fP of file \fBsorglq\&.f\fP\&.
.SS "subroutine zunglq (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
!> which is defined as the first M rows of a product of K elementary
!> reflectors of order N
!>
!>       Q  =  H(k)**H \&. \&. \&. H(2)**H H(1)**H
!>
!> as returned by ZGELQF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix Q\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Q\&. N >= M\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q\&. M >= K >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the i-th row must contain the vector which defines
!>          the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned
!>          by ZGELQF in the first k rows of its array argument A\&.
!>          On exit, the M-by-N matrix Q\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The first dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX*16 array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by ZGELQF\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&. LWORK >= max(1,M)\&.
!>          For optimum performance LWORK >= M*NB, where NB is
!>          the optimal blocksize\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit;
!>          < 0:  if INFO = -i, the i-th argument has an illegal value
!> 
.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 \fB126\fP of file \fBzunglq\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.