.TH "claswlq.f" 3 "Wed May 24 2017" "Version 3.7.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
claswlq.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBclaswlq\fP (M, \fBN\fP, MB, NB, A, \fBLDA\fP, T, LDT, WORK, LWORK, INFO)"
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.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine claswlq (integer M, integer N, integer MB, integer NB, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldt, *) T, integer LDT, complex, dimension( * ) WORK, integer LWORK, integer INFO)"

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\fBPurpose:\fP
.RS 4

.RE
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CLASWLQ computes a blocked Short-Wide LQ factorization of a M-by-N matrix A, where N >= M: A = L * Q  
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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.
.fi
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\fIN\fP 
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          N is INTEGER
          The number of columns of the matrix A.  N >= M >= 0.
.fi
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\fIMB\fP 
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          MB is INTEGER
          The row block size to be used in the blocked QR.
          M >= MB >= 1
.fi
.PP
 
.br
\fINB\fP 
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.nf
          NB is INTEGER
          The column block size to be used in the blocked QR.
          NB > M.
.fi
.PP
.br
\fIA\fP 
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          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and bleow the diagonal
          of the array contain the N-by-N lower triangular matrix L;
          the elements above the diagonal represent Q by the rows
          of blocked V (see Further Details).
.fi
.PP
.br
\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
.fi
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\fIT\fP 
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          T is COMPLEX array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((N-M)/(NB-M))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.
.fi
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\fILDT\fP 
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          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.
.fi
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\fIWORK\fP 
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         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
.fi
.PP
 
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\fILWORK\fP 
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          The dimension of the array WORK.  LWORK >= MB*M.
          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 
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.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
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.RE
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\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4
Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations, representing Q as a product of other orthogonal matrices Q = Q(1) * Q(2) * \&. \&. \&. * Q(k) where each Q(i) zeros out upper diagonal entries of a block of NB rows of A: Q(1) zeros out the upper diagonal entries of rows 1:NB of A Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A \&. \&. \&.
.RE
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Q(1) is computed by GELQT, which represents Q(1) by Householder vectors stored under the diagonal of rows 1:MB of A, and by upper triangular block reflectors, stored in array T(1:LDT,1:N)\&. For more information see Further Details in GELQT\&.
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Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M)\&. The last Q(k) may use fewer rows\&. For more information see Further Details in TPQRT\&.
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For more details of the overall algorithm, see the description of Sequential TSQR in Section 2\&.2 of [1]\&.
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[1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,” J\&. Demmel, L\&. Grigori, M\&. Hoemmen, J\&. Langou, SIAM J\&. Sci\&. Comput, vol\&. 34, no\&. 1, 2012  
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.