PSLDLT(3F)PSLDLT(3F)NAME
PSLDLT_Preprocess, PSLDLT_Factor, PSLDLT_Solve, PSLDLT_Destroy,
PSLDLT_Ordering - parallel sparse symmetric linear system solver
DESCRIPTION
PSLDLT solves sparse symmetric linear systems of the form
Ax = b
where A is an n x n symmetric input matrix, b is an input vector of
length n, and x is an unknown vector of length n. PSLDLT uses a direct
method: A is factored into the form
A = L D L-transpose
where L is a lower triangular matrix with unit diagonal and D is a
diagonal matrix.
The PSLDLT library contains four main routines. PSLDLT_Preprocess()
performs preprocessing operations on the structure of A (heuristic
reordering to reduce fill in L, symbolic factorization, etc.).
PSLDLT_Factor() factors the matrix A into L and D, using the previously
computed preprocessing data. PSLDLT_Solve() solves for a vector x, given
an input vector b. PSLDLT_Destroy() frees all storage associated with
the matrix A (including L, D, and various data structures computed during
preprocessing). Note that the user can call PSLDLT_Factor() several
times after a single call to PSLDLT_Preprocess() to factor multiple
matrices with identical non-zero structures but different values.
Similarly, the user can call PSLDLT_Solve() several times after a single
call to PSLDLT_Factor() to solve for multiple right-hand-sides.
Sparse matrix A must be input to PSLDLT in Harwell-Boeing format (also
known as Compressed Column Storage format). The matrix is held in three
arrays: pointers[], indices[], and values[]. The indices[] array
contains the row indices of the non-zeros in A. The values[] array holds
the corresponding non-zero values. The pointers[] array contains the
index in indices[] for the first non-zero in each column of A. Thus, the
row indices for the non-zeros in column i can be found in locations
indices[pointers[i]] through indices[pointers[i+1]-1]. The corresponding
values can be found in location values[pointers[i]] through
values[pointers[i+1]-1].
For a symmetric matrix A, the user must input either the lower or upper
triangle of A, but not both. Non-zeroes within a column of A can be
stored in any order.
To give an example, the following symmetric matrix...
1.0 symmetric
0.0 3.0
2.0 0.0 5.0
0.0 4.0 0.0 6.0
would be represented in FORTRAN as follows:
pointers[] = {1, 3, 5, 6, 7}
indices[] = {1, 3, 2, 4, 3, 4}
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PSLDLT(3F)PSLDLT(3F)
values[] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0}
Zero-based indexing is used in C, so the pointers[] and indices[] arrays
would instead contain:
pointers[] = {0, 2, 4, 5, 6}
indices[] = {0, 2, 1, 3, 2, 3}
The routine PSLDLT_Ordering allows the user to change the ordering method
used to pre-order the matrix before factorization. This routine must be
called before calling PSLDLT_Preprocess. Three options are currently
available: method 0 performs no pre-ordering, method 1 (the default)
performs Approximate Minimum Degree ordering, and method 2 performs
multi-level nested dissection ordering. Method 2 is significantly more
expensive than method 1, but it often produces significantly better
orderings.
The environment variable MPC_NUM_THREADS determines the number of
processors that are used for the numerical factorization. Setting the
environment variable PSLDLT_VERBOSE causes PSLDLT to output information
about the factorization.
FORTRAN SYNOPSIS
SUBROUTINE PSLDLT_PREPROCESS (TOKEN, N, POINTERS, INDICES, NONZ, OPS)
INTEGER TOKEN, N
INTEGER POINTERS( * ), INDICES( *)
INTEGER NONZ,
DOUBLE PRECISION OPS
SUBROUTINE PSLDLT_FACTOR (TOKEN, N, POINTERS, INDICES, VALUES)
INTEGER TOKEN, N
INTEGER POINTERS( * ), INDICES( * )
DOUBLE PRECISION VALUES( * )
SUBROUTINE PSLDLT_SOLVE (TOKEN, X, B)
INTEGER TOKEN
DOUBLE PRECISION X( * ), B( * )
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PSLDLT(3F)PSLDLT(3F)
SUBROUTINE PSLDLT_DESTROY (TOKEN)
INTEGER TOKEN
SUBROUTINE PSLDLT_DESTROY (TOKEN, METHOD)
INTEGER TOKEN
INTEGER METHOD
C SYNOPSIS
void PSLDLT_Preprocess (
int token,
int n,
int pointers[],
int indices[],
int *nonz,
double *ops
);
void PSLDLT_Factor (
int token,
int n,
int pointers[],
int indices[],
double values[]
);
void PSLDLT_Solve (
int token,
double x[],
double b[]
);
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PSLDLT(3F)PSLDLT(3F)
void PSLDLT_Destroy (
int token
);
void PSLDLT_Ordering (
int token,
int method
);
ARGUMENTS
token (input)
PSLDLT can handle multiple matrices simultaneously. The token
distinguishes between active matrices. The token passed to
PSLDLT_Factor() must match the token used in some previous call
to PSLDLT_Preprocess(). Similarly, the token passed to
PSLDLT_Solve() must match the token used in some previous call to
PSLDLT_Factor().
n (input)
The number of rows and columns in the matrix A. n >= 0.
pointers, indices, values (input)
The pointers and indices arrays store the non-zero structure of
sparse input matrix A in Harwell-Boeing or Compressed Sparse
Column (CSC) format. The pointers array stores n+1 integers,
where pointers[i] gives the index in indices of the first non-
zero in column i of A. The indices array stores the row indices
of the non-zeros in A. The nz array stores the non-zero values
in the matrix A.
nonz, ops (output)
The number of non-zero values in L, and the number of floating-
point operations required to factor A.
b (input)
The right-hand-side vector in a PSLDLT_Solve call.
x (output)
The solution vector in a PSLDLT_Solve call.
TUNING
Optimized and parallelized for the SGI R8000 platform.
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