.TH "ungl2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ungl2 \- {un,or}gl2: generate explicit Q, level 2, step in unglq
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcungl2\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBCUNGL2\fP generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBdorgl2\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBDORGL2\fP "
.ti -1c
.RI "subroutine \fBsorgl2\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBSORGL2\fP "
.ti -1c
.RI "subroutine \fBzungl2\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBZUNGL2\fP generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm)\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cungl2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)"

.PP
\fBCUNGL2\fP generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CUNGL2 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 (M)
.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 dorgl2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)"

.PP
\fBDORGL2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DORGL2 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 (M)
.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 sorgl2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)"

.PP
\fBSORGL2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SORGL2 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 (M)
.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 zungl2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)"

.PP
\fBZUNGL2\fP generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZUNGL2 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 (M)
.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 
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