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 10.
None.
If on entry
${\mathbf{ifail}}=0$ or
$-1$, 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