LATDF - 5.2 English - 68552

LATDF uses the LU factorization of the n-by-n matrix computed by sgetc2

and computes a contribution to the reciprocal Dif-estimate.

Purpose:

 LATDF uses the LU factorization of the n-by-n matrix Z computed by
 SGETC2 and computes a contribution to the reciprocal Dif-estimate
 by solving Z * x = b for x, and choosing the r.h.s. b such that
 the norm of x is as large as possible. On entry RHS = b holds the
 contribution from earlier solved sub-systems, and on   return RHS = x.

 The factorization of Z   returned by SGETC2 has the form Z = P*L*U*Q,
 where P and Q are permutation matrices. L is lower triangular with
 unit diagonal elements and U is upper triangular.

Parameters:

• IJOB – [in]

  IJOB is INTEGER

  IJOB = 2: First compute an approximative null-vector e of Z using SGECON, e is normalized and solve for Zx = +-e - f with the sign giving the greater value of 2-norm(x). About 5 times as expensive as Default.

  IJOB .ne. 2: Local look ahead strategy where all entries of the r.h.s. b is chosen as either +1 or -1 (Default).

• N – [in]

  N is INTEGER

  The number of columns of the matrix Z.

• Z – [in]

  Z is REAL array, dimension (LDZ, N)

  On entry, the LU part of the factorization of the n-by-n matrix Z computed by SGETC2: Z = P * L * U * Q

• LDZ – [in]

  LDZ is INTEGER

  The leading dimension of the array Z. LDA >= fla_max(1, N).

• RHS – [inout]

  RHS is REAL array, dimension N.

  On entry, RHS contains contributions from other subsystems. On exit, RHS contains the solution of the subsystem with entries according to the value of IJOB (see above).

• RDSUM – [inout]

  RDSUM is REAL

  On entry, the sum of squares of computed contributions to the Dif-estimate under computation by STGSYL, where the scaling factor RDSCAL (see below) has been factored out.

  On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = ‘T’ RDSUM is not touched. NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.

• RDSCAL – [inout]

  RDSCAL is REAL

  On entry, scaling factor used to prevent overflow in RDSUM.

  On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM.

  If TRANS = ‘T’, RDSCAL is not touched.

  NOTE: RDSCAL only makes sense when STGSY2 is called by STGSYL.

• IPIV – [in]

  IPIV is INTEGER array, dimension (N).

  The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).

• JPIV – [in]

  JPIV is INTEGER array, dimension (N).

  The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).