.TH "unglq" 3 "Wed Feb 7 2024 11:30:40" "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

.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

.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

.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.