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authorJoseph Hunkeler <jhunkeler@gmail.com>2015-07-08 20:46:52 -0400
committerJoseph Hunkeler <jhunkeler@gmail.com>2015-07-08 20:46:52 -0400
commitfa080de7afc95aa1c19a6e6fc0e0708ced2eadc4 (patch)
treebdda434976bc09c864f2e4fa6f16ba1952b1e555 /math/slalib/smat.f
downloadiraf-linux-fa080de7afc95aa1c19a6e6fc0e0708ced2eadc4.tar.gz
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+ SUBROUTINE slSMAT (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 slSMATRX 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., 51 Franklin Street, Fifth Floor,
+* Boston, MA 02110-1301 USA
+*
+* Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+ 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