SORMR3 overwrites the general real m by n matrix C with


       Q * C  if SIDE = 'L' and TRANS = 'N', or


       Q**T* C  if SIDE = 'L' and TRANS = 'C', or


       C * Q  if SIDE = 'R' and TRANS = 'N', or


       C * Q**T if SIDE = 'R' and TRANS = 'C',


 where Q is a real orthogonal matrix defined as the product of k


 elementary reflectors


       Q = H(1) H(2) . . . H(k)


 as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n


 if SIDE = 'R'.

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': apply Q  (No transpose)


          = 'T': apply Q**T (Transpose)

M

          M is INTEGER


          The number of rows of the matrix C. 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.

L

          L is INTEGER


          The number of columns of the matrix A containing


          the meaningful part of the Householder reflectors.


          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.

A

          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


          elementary reflector H(i), for i = 1,2,...,k, as returned by


          STZRZF in the last k rows of its array argument A.


          A is modified by the routine but restored on exit.

LDA

          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,K).

TAU

          TAU is REAL array, dimension (K)


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i), as returned by STZRZF.

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

          WORK is REAL array, dimension


                                   (N) if SIDE = 'L',


                                   (M) if SIDE = 'R'

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.

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA