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SUBROUTINE sla_SMAT (N, A, Y, D, JF, IW)
*+
* - - - - -
* S M A T
* - - - - -
*
* Matrix inversion & solution of simultaneous equations
* (single precision)
*
* For the set of n simultaneous equations in n unknowns:
* A.Y = X
*
* where:
* A is a non-singular N x N matrix
* Y is the vector of N unknowns
* X is the known vector
*
* SMATRX computes:
* the inverse of matrix A
* the determinant of matrix A
* the vector of N unknowns
*
* Arguments:
*
* symbol type dimension before after
*
* N int no. of unknowns unchanged
* A real (N,N) matrix inverse
* Y real (N) vector solution
* D real - determinant
* * JF int - singularity flag
* IW int (N) - workspace
*
* * JF is the singularity flag. If the matrix is non-singular,
* JF=0 is returned. If the matrix is singular, JF=-1 & D=0.0 are
* returned. In the latter case, the contents of array A on return
* are undefined.
*
* Algorithm:
* Gaussian elimination with partial pivoting.
*
* Speed:
* Very fast.
*
* Accuracy:
* Fairly accurate - errors 1 to 4 times those of routines optimised
* for accuracy.
*
* Note: replaces the obsolete sla_SMATRX routine.
*
* P.T.Wallace Starlink 10 September 1990
*
* Copyright (C) 1995 Rutherford Appleton Laboratory
*-
IMPLICIT NONE
INTEGER N
REAL A(N,N),Y(N),D
INTEGER JF
INTEGER IW(N)
REAL SFA
PARAMETER (SFA=1E-20)
INTEGER K,IMX,I,J,NP1MK,KI
REAL AMX,T,AKK,YK,AIK
JF=0
D=1.0
DO K=1,N
AMX=ABS(A(K,K))
IMX=K
IF (K.NE.N) THEN
DO I=K+1,N
T=ABS(A(I,K))
IF (T.GT.AMX) THEN
AMX=T
IMX=I
END IF
END DO
END IF
IF (AMX.LT.SFA) THEN
JF=-1
ELSE
IF (IMX.NE.K) THEN
DO J=1,N
T=A(K,J)
A(K,J)=A(IMX,J)
A(IMX,J)=T
END DO
T=Y(K)
Y(K)=Y(IMX)
Y(IMX)=T
D=-D
END IF
IW(K)=IMX
AKK=A(K,K)
D=D*AKK
IF (ABS(D).LT.SFA) THEN
JF=-1
ELSE
AKK=1.0/AKK
A(K,K)=AKK
DO J=1,N
IF (J.NE.K) A(K,J)=A(K,J)*AKK
END DO
YK=Y(K)*AKK
Y(K)=YK
DO I=1,N
AIK=A(I,K)
IF (I.NE.K) THEN
DO J=1,N
IF (J.NE.K) A(I,J)=A(I,J)-AIK*A(K,J)
END DO
Y(I)=Y(I)-AIK*YK
END IF
END DO
DO I=1,N
IF (I.NE.K) A(I,K)=-A(I,K)*AKK
END DO
END IF
END IF
END DO
IF (JF.NE.0) THEN
D=0.0
ELSE
DO K=1,N
NP1MK=N+1-K
KI=IW(NP1MK)
IF (NP1MK.NE.KI) THEN
DO I=1,N
T=A(I,NP1MK)
A(I,NP1MK)=A(I,KI)
A(I,KI)=T
END DO
END IF
END DO
END IF
END
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