LSLSF

Solves a real symmetric system of linear equations without iterative refinement .

Required Arguments

A — N by N matrix containing the coefficient matrix of the symmetric linear system. (Input)

Only the upper triangle of A is referenced.

Only the upper triangle of A is referenced.

B — Vector of length N containing the right-hand side of the linear system. (Input)

X — Vector of length N containing the solution to the linear system. (Output)

Optional Arguments

N — Number of equations. (Input)

Default: N = size (A,2).

Default: N = size (A,2).

LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program. (Input)

Default: LDA = size (A,1).

Default: LDA = size (A,1).

FORTRAN 90 Interface

Generic: CALL LSLSF (A, B, X [, …])

Specific: The specific interface names are S_LSLSF and D_LSLSF.

FORTRAN 77 Interface

Single: CALL LSLSF (N, A, LDA, B, X)

Double: The double precision name is DLSLSF.

Description

Routine LSLSF solves systems of linear algebraic equations having a real symmetric indefinite coefficient matrix. It first uses the routine LFCSF to compute a U DUT factorization of the coefficient matrix. D is a block diagonal matrix with blocks of order 1 or 2, and U is a matrix composed of the product of a permutation matrix and a unit upper triangular matrix.

The solution of the linear system is then found using the routine LFSSF.

LSLSF fails if a block in D is singular. This occurs only if A either is singular or is very close to a singular matrix.

Comments

1. Workspace may be explicitly provided, if desired, by use of L2LSF/DL2LSF. The reference is:

CALL L2LSF (N, A, LDA, B, X, FACT, IPVT, WK)

The additional arguments are as follows:

FACT — N × N work array containing information about the U DUT factorization of A on output. If A is not needed, A and FACT can share the same storage locations.

IPVT — Integer work vector of length N containing the pivoting information for the factorization of A on output.

WK — Work vector of length N.

2. Informational errors

Type | Code | Description |
---|---|---|

3 | 1 | The input matrix is too ill-conditioned. The solution might not be accurate. |

4 | 2 | The input matrix is singular. |

3. Integer Options with Chapter 11 Options Manager

16 This option uses four values to solve memory bank conflict (access inefficiency) problems. In routine LSLSF the leading dimension of FACT is increased by IVAL(3) when N is a multiple of IVAL(4). The values IVAL(3) and IVAL(4) are temporarily replaced by IVAL(1) and IVAL(2), respectively, in LSLSF. Additional memory allocation for FACT and option value restoration are done automatically in LSLSF. Users directly calling LSLSF can allocate additional space for FACT and set IVAL(3) and IVAL(4) so that memory bank conflicts no longer cause inefficiencies. There is no requirement that users change existing applications that use LSLSF or LSLSF. Default values for the option are IVAL(*) = 1, 16, 0, 1.

17 This option has two values that determine if the L1 condition number is to be computed. Routine LSLSF temporarily replaces IVAL(2) by IVAL(1). The routine L2CSF computes the condition number if IVAL(2) = 2. Otherwise L2CSF skips this computation. LSLSF restores the option. Default values for the option are IVAL(*) = 1, 2.

Example

A system of three linear equations is solved. The coefficient matrix has real symmetric form and the right-hand-side vector b has three elements.

USE LSLSF_INT

USE WRRRN_INT

! Declare variables

PARAMETER (LDA=3, N=3)

REAL A(LDA,LDA), B(N), X(N)

!

! Set values for A and B

!

! A = ( 1.0 -2.0 1.0)

! ( -2.0 3.0 -2.0)

! ( 1.0 -2.0 3.0)

!

! B = ( 4.1 -4.7 6.5)

!

DATA A/1.0, -2.0, 1.0, -2.0, 3.0, -2.0, 1.0, -2.0, 3.0/

DATA B/4.1, -4.7, 6.5/

!

CALL LSLSF (A, B, X)

! Print results

CALL WRRRN (’X’, X, 1, N, 1)

END

Output

X

1 2 3

-4.100 -3.500 1.200