.TH "ung2l" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ung2l \- {un,or}g2l: step in ungql
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcung2l\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBCUNG2L\fP generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBdorg2l\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBDORG2L\fP generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBsorg2l\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBSORG2L\fP generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBzung2l\fP (m, n, k, a, lda, tau, work, info)"
.br
.RI "\fBZUNG2L\fP generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm)\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)"

.PP
\fBCUNG2L\fP generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CUNG2L generates an m by n complex matrix Q with orthonormal columns,
 which is defined as the last n columns of a product of k elementary
 reflectors of order m

       Q  =  H(k) \&. \&. \&. H(2) H(1)

 as returned by CGEQLF\&.
.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\&. M >= N >= 0\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q\&. N >= K >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          On entry, the (n-k+i)-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as
          returned by CGEQLF in the last k columns 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 CGEQLF\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (N)
.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 dorg2l (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)"

.PP
\fBDORG2L\fP generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DORG2L generates an m by n real matrix Q with orthonormal columns,
 which is defined as the last n columns of a product of k elementary
 reflectors of order m

       Q  =  H(k) \&. \&. \&. H(2) H(1)

 as returned by DGEQLF\&.
.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\&. M >= N >= 0\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q\&. N >= K >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the (n-k+i)-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as
          returned by DGEQLF in the last k columns 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 DGEQLF\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (N)
.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 sorg2l (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)"

.PP
\fBSORG2L\fP generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SORG2L generates an m by n real matrix Q with orthonormal columns,
 which is defined as the last n columns of a product of k elementary
 reflectors of order m

       Q  =  H(k) \&. \&. \&. H(2) H(1)

 as returned by SGEQLF\&.
.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\&. M >= N >= 0\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q\&. N >= K >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          On entry, the (n-k+i)-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as
          returned by SGEQLF in the last k columns 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 SGEQLF\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N)
.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 zung2l (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)"

.PP
\fBZUNG2L\fP generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
 which is defined as the last n columns of a product of k elementary
 reflectors of order m

       Q  =  H(k) \&. \&. \&. H(2) H(1)

 as returned by ZGEQLF\&.
.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\&. M >= N >= 0\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q\&. N >= K >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the (n-k+i)-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as
          returned by ZGEQLF in the last k columns 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 ZGEQLF\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (N)
.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\&.