ZGEMQR overwrites the general real 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 tall skinny


 QR factorization (ZGEQR)

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 COMPLEX*16 array, dimension (LDA,K)


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

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 COMPLEX*16 array, dimension (MAX(5,TSIZE)).


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

TSIZE

          TSIZE is INTEGER


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

C

          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**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) COMPLEX*16 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


                           ZLATSQR or ZGEQRT


  Depending on the matrix dimensions M and N, and row and column


  block sizes MB and NB returned by ILAENV, ZGEQR will use either


  ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute


  the QR factorization.


  This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to


  multiply matrix Q by another matrix.


  Further Details in ZLAMTSQR or ZGEMQRT.