SLA_SMAT - Solve Simultaneous Equations   

ACTION:

Matrix inversion and solution of simultaneous equations (single precision).

CALL:

CALL sla_SMAT (N, A, Y, D, JF, IW)

GIVEN:

N number of unknowns

A R(N,N) matrix

Y R(N) vector

RETURNED:

A matrix inverse

Y R(N) solution

D R determinant

JF I singularity flag: 0=OK

IW I(N) workspace

NOTES:

1.

For the set of n simultaneous linear equations in n unknowns:

A$\cdot$y = x

where:

• A is a non-singular $n \times n$ matrix,
• y is the vector of n unknowns, and
• x is the known vector,

sla_SMAT computes:

• the inverse of matrix A,
• the determinant of matrix A, and
• the vector of n unknowns y.

Argument N is the order n, A (given) is the matrix A, Y (given) is the vector x and Y (returned) is the vector y. The argument A (returned) is the inverse matrix A^-1, and D is det(A).

2.

JF is the singularity flag. If the matrix is non-singular, JF=0 is returned. If the matrix is singular, JF=-1 and D=0.0 are returned. In the latter case, the contents of array A on return are undefined.

3.

The algorithm is Gaussian elimination with partial pivoting. This method is very fast; some much slower algorithms can give better accuracy, but only by a small factor.

4.

This routine replaces the obsolete sla_SMATRX.