F11JPF solves a system of complex linear equations involving the incomplete Cholesky preconditioning matrix generated by
F11JNF.
F11JPF solves a system of linear equations
involving the preconditioning matrix
$M=PLD{L}^{\mathrm{H}}{P}^{\mathrm{T}}$, corresponding to an incomplete Cholesky decomposition of a complex sparse Hermitian matrix stored in symmetric coordinate storage (SCS) format (see
Section 2.1.2 in the F11 Chapter Introduction), as generated by
F11JNF.
In the above decomposition
$L$ is a complex lower triangular sparse matrix with unit diagonal,
$D$ is a real diagonal matrix and
$P$ is a permutation matrix.
$L$ and
$D$ are supplied to F11JPF through the matrix
which is a lower triangular
$n$ by
$n$ complex sparse matrix, stored in SCS format, as returned by
F11JNF. The permutation matrix
$P$ is returned from
F11JNF via the array
IPIV.
F11JPF may also be used in combination with
F11JNF to solve a sparse complex Hermitian positive definite system of linear equations directly (see
F11JNF). This is illustrated in
Section 9.
None.
If on entry
${\mathbf{IFAIL}}={\mathbf{0}}$ or
${-{\mathbf{1}}}$, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The computed solution
$x$ is the exact solution of a perturbed system of equations
$\left(M+\delta M\right)x=y$, where
$c\left(n\right)$ is a modest linear function of
$n$, and
$\epsilon $ is the
machine precision.
The time taken for a call to F11JPF is proportional to the value of
NNZC returned from
F11JNF.
This example reads in a complex sparse Hermitian positive definite matrix
$A$ and a vector
$y$. It then calls
F11JNF, with
${\mathbf{LFILL}}=-1$ and
${\mathbf{DTOL}}=0.0$, to compute the
complete Cholesky decomposition of
$A$:
Finally it calls F11JPF to solve the system