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slalib/smat.f

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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
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330, 
+*    Boston, MA  02111-1307  USA
+*
+*-
+
+      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