SGEMQR 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 tall skinny


 QR factorization (SGEQR)

SIDE

          SIDE is CHARACTER*1


          = 'L': apply Q or Q**T from the Left;


          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'T':  Transpose, apply Q**T.

M

          M is INTEGER


          The number of rows of the matrix A.  M >=0.

N

          N is INTEGER


          The number of columns of the matrix C. N >= 0.

K

          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.

A

          A is REAL array, dimension (LDA,K)


          Part of the data structure to represent Q as returned by SGEQR.

LDA

          LDA is INTEGER


          The leading dimension of the array A.


          If SIDE = 'L', LDA >= max(1,M);


          if SIDE = 'R', LDA >= max(1,N).

T

          T is REAL array, dimension (MAX(5,TSIZE)).


          Part of the data structure to represent Q as returned by SGEQR.

TSIZE

          TSIZE is INTEGER


          The dimension of the array T. TSIZE >= 5.

C

          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.

LDC

          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK

         (workspace) REAL array, dimension (MAX(1,LWORK))

LWORK

          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.

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 These details are particular for this LAPACK implementation. Users should not 


 take them for granted. These details may change in the future, and are not likely


 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.


 In this version,


          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


  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.