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---
:name: dlatdf
:md5sum: 69cfce3953f1837f451afd56bf000e43
:category: :subroutine
:arguments:
- ijob:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- z:
:type: doublereal
:intent: input
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- rhs:
:type: doublereal
:intent: input/output
:dims:
- n
- rdsum:
:type: doublereal
:intent: input/output
- rdscal:
:type: doublereal
:intent: input/output
- ipiv:
:type: integer
:intent: input
:dims:
- n
- jpiv:
:type: integer
:intent: input
:dims:
- n
:substitutions: {}
:fortran_help: " SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLATDF uses the LU factorization of the n-by-n matrix Z computed by\n\
* DGETC2 and computes a contribution to the reciprocal Dif-estimate\n\
* by solving Z * x = b for x, and choosing the r.h.s. b such that\n\
* the norm of x is as large as possible. On entry RHS = b holds the\n\
* contribution from earlier solved sub-systems, and on return RHS = x.\n\
*\n\
* The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,\n\
* where P and Q are permutation matrices. L is lower triangular with\n\
* unit diagonal elements and U is upper triangular.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* IJOB (input) INTEGER\n\
* IJOB = 2: First compute an approximative null-vector e\n\
* of Z using DGECON, e is normalized and solve for\n\
* Zx = +-e - f with the sign giving the greater value\n\
* of 2-norm(x). About 5 times as expensive as Default.\n\
* IJOB .ne. 2: Local look ahead strategy where all entries of\n\
* the r.h.s. b is chosen as either +1 or -1 (Default).\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix Z.\n\
*\n\
* Z (input) DOUBLE PRECISION array, dimension (LDZ, N)\n\
* On entry, the LU part of the factorization of the n-by-n\n\
* matrix Z computed by DGETC2: Z = P * L * U * Q\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDA >= max(1, N).\n\
*\n\
* RHS (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, RHS contains contributions from other subsystems.\n\
* On exit, RHS contains the solution of the subsystem with\n\
* entries acoording to the value of IJOB (see above).\n\
*\n\
* RDSUM (input/output) DOUBLE PRECISION\n\
* On entry, the sum of squares of computed contributions to\n\
* the Dif-estimate under computation by DTGSYL, where the\n\
* scaling factor RDSCAL (see below) has been factored out.\n\
* On exit, the corresponding sum of squares updated with the\n\
* contributions from the current sub-system.\n\
* If TRANS = 'T' RDSUM is not touched.\n\
* NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.\n\
*\n\
* RDSCAL (input/output) DOUBLE PRECISION\n\
* On entry, scaling factor used to prevent overflow in RDSUM.\n\
* On exit, RDSCAL is updated w.r.t. the current contributions\n\
* in RDSUM.\n\
* If TRANS = 'T', RDSCAL is not touched.\n\
* NOTE: RDSCAL only makes sense when DTGSY2 is called by\n\
* DTGSYL.\n\
*\n\
* IPIV (input) INTEGER array, dimension (N).\n\
* The pivot indices; for 1 <= i <= N, row i of the\n\
* matrix has been interchanged with row IPIV(i).\n\
*\n\
* JPIV (input) INTEGER array, dimension (N).\n\
* The pivot indices; for 1 <= j <= N, column j of the\n\
* matrix has been interchanged with column JPIV(j).\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,\n\
* Umea University, S-901 87 Umea, Sweden.\n\
*\n\
* This routine is a further developed implementation of algorithm\n\
* BSOLVE in [1] using complete pivoting in the LU factorization.\n\
*\n\
* [1] Bo Kagstrom and Lars Westin,\n\
* Generalized Schur Methods with Condition Estimators for\n\
* Solving the Generalized Sylvester Equation, IEEE Transactions\n\
* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.\n\
*\n\
* [2] Peter Poromaa,\n\
* On Efficient and Robust Estimators for the Separation\n\
* between two Regular Matrix Pairs with Applications in\n\
* Condition Estimation. Report IMINF-95.05, Departement of\n\
* Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.\n\
*\n\
* =====================================================================\n\
*\n"
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