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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine dlatdf | ( | integer | ijob, |
| integer | n, | ||
| double precision, dimension( ldz, * ) | z, | ||
| integer | ldz, | ||
| double precision, dimension( * ) | rhs, | ||
| double precision | rdsum, | ||
| double precision | rdscal, | ||
| integer, dimension( * ) | ipiv, | ||
| integer, dimension( * ) | jpiv | ||
| ) |
DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
Download DLATDF + dependencies [TGZ] [ZIP] [TXT]
DLATDF uses the LU factorization of the n-by-n matrix Z computed by DGETC2 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 DGETC2 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.
| [in] | IJOB | IJOB is INTEGER
IJOB = 2: First compute an approximative null-vector e
of Z using DGECON, 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). |
| [in] | N | N is INTEGER
The number of columns of the matrix Z. |
| [in] | Z | Z is DOUBLE PRECISION array, dimension (LDZ, N)
On entry, the LU part of the factorization of the n-by-n
matrix Z computed by DGETC2: Z = P * L * U * Q |
| [in] | LDZ | LDZ is INTEGER
The leading dimension of the array Z. LDA >= max(1, N). |
| [in,out] | RHS | RHS is DOUBLE PRECISION 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). |
| [in,out] | RDSUM | RDSUM is DOUBLE PRECISION
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by DTGSYL, 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 DTGSY2 is called by STGSYL. |
| [in,out] | RDSCAL | RDSCAL is DOUBLE PRECISION
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 DTGSY2 is called by
DTGSYL. |
| [in] | IPIV | 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). |
| [in] | JPIV | 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). |
[1] Bo Kagstrom and Lars Westin,
Generalized Schur Methods with Condition Estimators for
Solving the Generalized Sylvester Equation, IEEE Transactions
on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
[2] Peter Poromaa,
On Efficient and Robust Estimators for the Separation
between two Regular Matrix Pairs with Applications in
Condition Estimation. Report IMINF-95.05, Departement of
Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. Definition at line 169 of file dlatdf.f.
1.9.7