DORMRZ 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 k


 elementary reflectors


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


 as returned by DTZRZF. 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':  No transpose, apply Q;


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

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 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


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


          DTZRZF 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 DOUBLE PRECISION array, dimension (K)


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


          reflector H(i), as returned by DTZRZF.

C

          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**H*C or C*Q**H or C*Q.

LDC

          LDC is INTEGER


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

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.


          If SIDE = 'L', LWORK >= max(1,N);


          if SIDE = 'R', LWORK >= max(1,M).


          For good performance, LWORK should generally be larger.


          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.

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.

December 2016

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