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

.in +1c
.ti -1c
.RI "subroutine \fBsgemqr\fP (SIDE, TRANS, M, \fBN\fP, K, A, \fBLDA\fP, T, TSIZE, C, LDC, WORK, LWORK, INFO)"
.br
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgemqr (character SIDE, character TRANS, integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) T, integer TSIZE, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer LWORK, integer INFO)"

.PP
\fBPurpose:\fP
.RS 4

.RE
.PP
SGEMQR overwrites the general real M-by-N matrix C with
.PP
SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T
.PP
where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (SGEQR)
.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 A.  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.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,K)
          Part of the data structure to represent Q as returned by SGEQR.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is REAL array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by SGEQR.
.fi
.PP
.br
\fITSIZE\fP 
.PP
.nf
          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.
.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 LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK 
          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

.RE
.PP
These details are particular for this LAPACK implementation\&. Users should not take them for granted\&. These details may change in the future, and are unlikely not true for another LAPACK implementation\&. These details are relevant if one wants to try to understand the code\&. They are not part of the interface\&.
.PP
In this version,
.PP
T(2): row block size (MB) T(3): column block size (NB) T(6:TSIZE): data structure needed for Q, computed by SLATSQR or SGEQRT
.PP
Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGEQR will use either SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute the QR factorization\&. This version of SGEMQR will use either SLAMTSQR or SGEMQRT to multiply matrix Q by another matrix\&. Further Details in SLAMTSQR or SGEMQRT\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.