.TH "SRC/zlaunhr_col_getrfnp.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
SRC/zlaunhr_col_getrfnp.f
.SH SYNOPSIS
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.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlaunhr_col_getrfnp\fP (m, n, a, lda, d, info)"
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.RI "\fBZLAUNHR_COL_GETRFNP\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlaunhr_col_getrfnp (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) d, integer info)"

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\fBZLAUNHR_COL_GETRFNP\fP  
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\fBPurpose:\fP
.RS 4

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!>
!> ZLAUNHR_COL_GETRFNP computes the modified LU factorization without
!> pivoting of a complex general M-by-N matrix A\&. The factorization has
!> the form:
!>
!>     A - S = L * U,
!>
!> where:
!>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
!>    D(i) = S(i,i), 1 <= i <= min(M,N)\&. The diagonal D is constructed
!>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
!>    i-1 steps of Gaussian elimination\&. This means that the diagonal
!>    element at each step of  Gaussian elimination is
!>    at least one in absolute value (so that division-by-zero not
!>    not possible during the division by the diagonal element);
!>
!>    L is a M-by-N lower triangular matrix with unit diagonal elements
!>    (lower trapezoidal if M > N);
!>
!>    and U is a M-by-N upper triangular matrix
!>    (upper trapezoidal if M < N)\&.
!>
!> This routine is an auxiliary routine used in the Householder
!> reconstruction routine ZUNHR_COL\&. In ZUNHR_COL, this routine is
!> applied to an M-by-N matrix A with orthonormal columns, where each
!> element is bounded by one in absolute value\&. With the choice of
!> the matrix S above, one can show that the diagonal element at each
!> step of Gaussian elimination is the largest (in absolute value) in
!> the column on or below the diagonal, so that no pivoting is required
!> for numerical stability [1]\&.
!>
!> For more details on the Householder reconstruction algorithm,
!> including the modified LU factorization, see [1]\&.
!>
!> This is the blocked right-looking version of the algorithm,
!> calling Level 3 BLAS to update the submatrix\&. To factorize a block,
!> this routine calls the recursive routine ZLAUNHR_COL_GETRFNP2\&.
!>
!> [1] ,
!>     G\&. Ballard, J\&. Demmel, L\&. Grigori, M\&. Jacquelin, H\&.D\&. Nguyen,
!>     E\&. Solomonik, J\&. Parallel Distrib\&. Comput\&.,
!>     vol\&. 85, pp\&. 3-31, 2015\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIM\fP 
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!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
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\fIN\fP 
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!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
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\fIA\fP 
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!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix to be factored\&.
!>          On exit, the factors L and U from the factorization
!>          A-S=L*U; the unit diagonal elements of L are not stored\&.
!> 
.fi
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\fILDA\fP 
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!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
!> 
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\fID\fP 
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!>          D is COMPLEX*16 array, dimension min(M,N)
!>          The diagonal elements of the diagonal M-by-N sign matrix S,
!>          D(i) = S(i,i), where 1 <= i <= min(M,N)\&. The elements can be
!>          only ( +1\&.0, 0\&.0 ) or (-1\&.0, 0\&.0 )\&.
!> 
.fi
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\fIINFO\fP 
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!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBContributors:\fP
.RS 4

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.nf
!>
!> November 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!> 
.fi
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Definition at line \fB145\fP of file \fBzlaunhr_col_getrfnp\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.