SLA_DMAT - Solve Simultaneous Equations   

ACTION:

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

CALL:

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

GIVEN:

N number of unknowns

A D(N,N) matrix

Y D(N) vector

RETURNED:

A matrix inverse

Y D(N) solution

D D 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_DMAT 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=0D0 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_DMATRX.