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	I	number of unknowns
A	D(N,N)	matrix
Y	D(N)	vector

RETURNED:

A	D(N,N)	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.