.TH "lamswlq" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lamswlq \- lamswlq: multiply by Q from laswlq
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclamswlq\fP (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)"
.br
.RI "\fBCLAMSWLQ\fP "
.ti -1c
.RI "subroutine \fBdlamswlq\fP (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)"
.br
.RI "\fBDLAMSWLQ\fP "
.ti -1c
.RI "subroutine \fBslamswlq\fP (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)"
.br
.RI "\fBSLAMSWLQ\fP "
.ti -1c
.RI "subroutine \fBzlamswlq\fP (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)"
.br
.RI "\fBZLAMSWLQ\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension(ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
    CLAMSWLQ overwrites the general complex M-by-N matrix C with


                    SIDE = 'L'     SIDE = 'R'
    TRANS = 'N':      Q * C          C * Q
    TRANS = 'T':      Q**H * C       C * Q**H
    where Q is a complex unitary matrix defined as the product of blocked
    elementary reflectors computed by short wide LQ
    factorization (CLASWLQ)
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.  M >=0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&. N >= 0\&.
.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
\fIMB\fP 
.PP
.nf
          MB is INTEGER
          The row block size to be used in the blocked LQ\&.
          M >= MB >= 1
.fi
.PP
.br
\fINB\fP 
.PP
.nf
          NB is INTEGER
          The column block size to be used in the blocked LQ\&.
          NB > M\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the blocked
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          CLASWLQ in the first k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA => max(1,K)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX array, dimension
          ( M * Number of blocks(CEIL(N-K/NB-K)),
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.  See below
          for further details\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= MB\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C\&.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If SIDE = 'L', LWORK >= max(1,NB) * MB;
          if SIDE = 'R', LWORK >= max(1,M) * MB\&.
          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 
.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
 Short-Wide LQ (SWLQ) performs LQ by a sequence of unitary transformations,
 representing Q as a product of other unitary 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
   \&. \&. \&.

 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\&.

 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 TPLQT\&.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2\&.2 of [1]\&.

 [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
.fi
.PP
 
.RE
.PP

.SS "subroutine dlamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension(ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
    DLAMSWLQ overwrites the general real M-by-N matrix C with


                    SIDE = 'L'     SIDE = 'R'
    TRANS = 'N':      Q * C          C * Q
    TRANS = 'T':      Q**T * C       C * Q**T
    where Q is a real orthogonal matrix defined as the product of blocked
    elementary reflectors computed by short wide LQ
    factorization (DLASWLQ)
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.  M >=0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&. N >= 0\&.
.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
\fIMB\fP 
.PP
.nf
          MB is INTEGER
          The row block size to be used in the blocked LQ\&.
          M >= MB >= 1
.fi
.PP
.br
\fINB\fP 
.PP
.nf
          NB is INTEGER
          The column block size to be used in the blocked LQ\&.
          NB > M\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the blocked
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          DLASWLQ in the first k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,K)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is DOUBLE PRECISION array, dimension
          ( M * Number of blocks(CEIL(N-K/NB-K)),
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.  See below
          for further details\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= MB\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C\&.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
         (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If SIDE = 'L', LWORK >= max(1,NB) * MB;
          if SIDE = 'R', LWORK >= max(1,M) * MB\&.
          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 
.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
 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
   \&. \&. \&.

 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\&.

 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 TPLQT\&.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2\&.2 of [1]\&.

 [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
.fi
.PP
 
.RE
.PP

.SS "subroutine slamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension(ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
    SLAMSWLQ overwrites the general real M-by-N matrix C with


                    SIDE = 'L'     SIDE = 'R'
    TRANS = 'N':      Q * C          C * Q
    TRANS = 'T':      Q**T * C       C * Q**T
    where Q is a real orthogonal matrix defined as the product of blocked
    elementary reflectors computed by short wide LQ
    factorization (SLASWLQ)
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.  M >=0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&. N >= 0\&.
.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
\fIMB\fP 
.PP
.nf
          MB is INTEGER
          The row block size to be used in the blocked LQ\&.
          M >= MB >= 1
.fi
.PP
.br
\fINB\fP 
.PP
.nf
          NB is INTEGER
          The column block size to be used in the blocked LQ\&.
          NB > M\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the blocked
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          SLASWLQ in the first k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,K)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is REAL array, dimension
          ( M * Number of blocks(CEIL(N-K/NB-K)),
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.  See below
          for further details\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= MB\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (LDC,N)
          On entry, the M-by-N matrix C\&.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
         (workspace) REAL array, dimension (MAX(1,LWORK))
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If SIDE = 'L', LWORK >= max(1,NB) * MB;
          if SIDE = 'R', LWORK >= max(1,M) * MB\&.
          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 
.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
 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
   \&. \&. \&.

 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\&.

 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 TPLQT\&.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2\&.2 of [1]\&.

 [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
.fi
.PP
 
.RE
.PP

.SS "subroutine zlamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
    ZLAMSWLQ overwrites the general complex M-by-N matrix C with


                    SIDE = 'L'     SIDE = 'R'
    TRANS = 'N':      Q * C          C * Q
    TRANS = 'C':      Q**H * C       C * Q**H
    where Q is a complex unitary matrix defined as the product of blocked
    elementary reflectors computed by short wide LQ
    factorization (ZLASWLQ)
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate Transpose, apply Q**H\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix C\&.  M >=0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix C\&. N >= 0\&.
.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
\fIMB\fP 
.PP
.nf
          MB is INTEGER
          The row block size to be used in the blocked LQ\&.
          M >= MB >= 1
.fi
.PP
.br
\fINB\fP 
.PP
.nf
          NB is INTEGER
          The column block size to be used in the blocked LQ\&.
          NB > M\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the blocked
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          ZLASWLQ in the first k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= MAX(1,K)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX*16 array, dimension
          ( M * Number of blocks(CEIL(N-K/NB-K)),
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.  See below
          for further details\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= MB\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX*16 array, dimension (LDC,N)
          On entry, the M-by-N matrix C\&.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If SIDE = 'L', LWORK >= max(1,NB) * MB;
          if SIDE = 'R', LWORK >= max(1,M) * MB\&.
          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\&.
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\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 
.PP
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

.PP
.nf
 Short-Wide LQ (SWLQ) performs LQ by a sequence of unitary transformations,
 representing Q as a product of other unitary 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
   \&. \&. \&.

 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\&.

 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 TPLQT\&.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2\&.2 of [1]\&.

 [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
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.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.