ORM2L - 5.2 English - 68552

ORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf.

Purpose:

   ORM2L 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 = 'T', or

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

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

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

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

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

Parameters:

• SIDE – [in]

  SIDE is CHARACTER*1

  = ‘L’: apply Q or Q**T from the Left

  = ‘R’: apply Q or Q**T from the Right

• TRANS – [in]

  TRANS is CHARACTER*1

  = ‘N’: apply Q (No transpose)

  = ‘T’: apply Q**T (Transpose)

• M – [in]

  M is INTEGER

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

• N – [in]

  N is INTEGER

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

• K – [in]

  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 – [in]

  A is REAL array, dimension (LDA,K)

  The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,…,k, as returned by SGEQLF in the last k columns of its array argument A. A is modified by the routine but restored on exit.

• LDA – [in]

  LDA is INTEGER

  The leading dimension of the array A.

  If SIDE = ‘L’, LDA >= fla_max(1,M);

  if SIDE = ‘R’, LDA >= fla_max(1,N).

• TAU – [in]

  TAU is REAL array, dimension (K)

  TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQLF.

• C – [inout]

  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 – [in]

  LDC is INTEGER

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

• WORK – [out]

  WORK is REAL array, dimension

  (N) if SIDE = ‘L’,

  (M) if SIDE = ‘R’

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

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