.TH "SRC/zgelq2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zgelq2.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgelq2\fP (m, n, a, lda, tau, work, info)"
.br
.RI "\fBZGELQ2\fP computes the LQ factorization of a general rectangular matrix using an unblocked algorithm\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgelq2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)"

.PP
\fBZGELQ2\fP computes the LQ factorization of a general rectangular matrix using an unblocked algorithm\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A:

    A = ( L 0 ) *  Q

 where:

    Q is a n-by-n orthogonal matrix;
    L is a lower-triangular m-by-m matrix;
    0 is a m-by-(n-m) zero matrix, if m < n\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the m by n matrix A\&.
          On exit, the elements on and below the diagonal of the array
          contain the m by min(m,n) lower trapezoidal matrix L (L is
          lower triangular if m <= n); the elements above the diagonal,
          with the array TAU, represent the unitary matrix Q as a
          product of elementary reflectors (see Further Details)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details)\&.
.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 had 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The matrix Q is represented as a product of elementary reflectors

     Q = H(k)**H \&. \&. \&. H(2)**H H(1)**H, where k = min(m,n)\&.

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
  A(i,i+1:n), and tau in TAU(i)\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB128\fP of file \fBzgelq2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.