Array of size 64.

Handle to internal data structure. The entries must be set to zero before the first call to

cluster_sparse_solver

.

Ignored; assumed equal to 1.

Ignored; assumed equal to 1.

Defines the matrix type, which influences the pivoting method. The Parallel Direct Sparse Solver for Clusters solver supports the following matrices:

Controls the execution of the solver. Usually it is a two- or three-digit integer. The first digit indicates the starting phase of execution and the second digit indicates the ending phase. Parallel Direct Sparse Solver for Clusters has the following phases of execution:

Phase 1: Fill-reduction analysis and symbolic factorization
Phase 2: Numerical factorization
Phase 3: Forward and Backward solve including optional iterative refinement
Memory release (
phase
= -1)

If a previous call to the routine has computed information from previous phases, execution may start at any phase. The

phase

parameter can have the following values:

Number of equations in the sparse linear systems of equations

A

*

X

=

B

. Constraint:

n

> 0

.

Array. Contains the non-zero elements of the coefficient matrix

A

corresponding to the indices in

ja

. The coefficient matrix can be either real or complex. The matrix must be stored in the three-array variant of the compressed sparse row (CSR3) or in the three-array variant of the block compressed sparse row (BSR3) format, and the matrix must be stored with increasing values of

ja

for each row.

For CSR3 format, the size of

a

is the same as that of

ja

. Refer to the

values

array description in Three Array Variation of CSR Format for more details.

For BSR3 format the size of

a

is the size of

ja

multiplied by the square of the block size. Refer to the

values

array description in Three Array Variation of BSR Format for more details.

For CSR3 format,

ia

[

i

]

(

i

<

n

) points to the first column index of row

i

in the array

ja

. That is,

ia

[

i

]

gives the index of the element in array

a

that contains the first non-zero element from row

i

of

A

. The last element

ia

[

n

]

is taken to be equal to the number of non-zero elements in

A

, plus one. Refer to

rowIndex

array description in Three Array Variation of CSR Format for more details.

For BSR3 format,

ia

[

i

]

(

i

<

n

) points to the first column index of row

i

in the array

ja

. That is,

ia

[

i

]

gives the index of the element in array

a

that contains the first non-zero block from row

i

of

A

. The last element

ia

[

n

]

is taken to be equal to the number of non-zero blcoks in

A

, plus one. Refer to

rowIndex

array description in Three Array Variation of BSR Format for more details.

The array

ia

is accessed in all phases of the solution process.

Indexing of

ia

is one-based by default, but it can be changed to zero-based by setting the appropriate value to the parameter

iparm

[34]

. For zero-based indexing, the last element

ia

[

n

]

is assumed to be equal to the number of non-zero elements in matrix

A

.

For CSR3 format, array

ja

contains column indices of the sparse matrix

A

. It is important that the indices are in increasing order per row. For symmetric matrices, the solver needs only the upper triangular part of the system as is shown for

columns

array in Three Array Variation of CSR Format.

For BSR3 format, array

ja

contains column indices of the sparse matrix

A

. It is important that the indices are in increasing order per row. For symmetric matrices, the solver needs only the upper triangular part of the system as is shown for

columns

array in Three Array Variation of BSR Format.

The array

ja

is accessed in all phases of the solution process.

Indexing of

ja

is one-based by default, but it can be changed to zero-based by setting the appropriate value to the parameter

iparm

(35)

.

Ignored.

Number of right-hand sides that need to be solved for.

Array, size

64

. This array is used to pass various parameters to Parallel Direct Sparse Solver for Clusters Interface and to return some useful information after execution of the solver.

See cluster_sparse_solver iparm Parameter for more details about the

iparm

parameters.

Message level information. If

msglvl

= 0

then

cluster_sparse_solver

generates no output, if

msglvl

= 1

the solver prints statistical information to the screen.

Statistics include information such as the number of non-zero elements in

L-factor

and the timing for each phase.

Set

msglvl

= 1

if you report a problem with the solver, since the additional information provided can facilitate a solution.

Array, size

n

*

nrhs

. On entry, contains the right-hand side vector/matrix

B

, which is placed in memory contiguously. The

b

[

i

+

k

*

n

]

must hold the

i

-th component of

k

-th right-hand side vector. Note that

b

is only accessed in the solution phase.

MPI communicator. The solver uses the Fortran MPI communicator internally.

C

onvert the MPI communicator to Fortran using the

MPI_Comm_c2f()

function. See the examples in the

<install_dir>

/examples

directory.

Handle to internal data structure.

Ignored.

On output, some

iparm

values report information such as the numbers of non-zero elements in the factors.

See cluster_sparse_solver iparm Parameter for more details about the

iparm

parameters.

On output, the array is replaced with the solution if

iparm

[5]

= 1.

Array, size (

n

*

nrhs

). If

iparm

[5]

=0 it contains solution vector/matrix

X

, which is placed contiguously in memory. The

x

[

i

+

k

*

n

]

element must hold the

i

-th component of the

k

-th solution vector. Note that

x

is only accessed in the solution phase.

The error indicator according to the below table: