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SUBROUTINE SSICO(A,LDA,N,KPVT,RCOND,Z) INTEGER LDA,N,KPVT(1) REAL A(LDA,1),Z(1) REAL RCOND C C SSICO FACTORS A REAL SYMMETRIC MATRIX BY ELIMINATION WITH C SYMMETRIC PIVOTING AND ESTIMATES THE CONDITION OF THE MATRIX. C C IF RCOND IS NOT NEEDED, SSIFA IS SLIGHTLY FASTER. C TO SOLVE A*X = B , FOLLOW SSICO BY SSISL. C TO COMPUTE INVERSE(A)*C , FOLLOW SSICO BY SSISL. C TO COMPUTE INVERSE(A) , FOLLOW SSICO BY SSIDI. C TO COMPUTE DETERMINANT(A) , FOLLOW SSICO BY SSIDI. C TO COMPUTE INERTIA(A), FOLLOW SSICO BY SSIDI. C C ON ENTRY C C A REAL(LDA, N) C THE SYMMETRIC MATRIX TO BE FACTORED. C ONLY THE DIAGONAL AND UPPER TRIANGLE ARE USED. C C LDA INTEGER C THE LEADING DIMENSION OF THE ARRAY A . C C N INTEGER C THE ORDER OF THE MATRIX A . C C OUTPUT C C A A BLOCK DIAGONAL MATRIX AND THE MULTIPLIERS WHICH C WERE USED TO OBTAIN IT. C THE FACTORIZATION CAN BE WRITTEN A = U*D*TRANS(U) C WHERE U IS A PRODUCT OF PERMUTATION AND UNIT C UPPER TRIANGULAR MATRICES , TRANS(U) IS THE C TRANSPOSE OF U , AND D IS BLOCK DIAGONAL C WITH 1 BY 1 AND 2 BY 2 BLOCKS. C C KPVT INTEGER(N) C AN INTEGER VECTOR OF PIVOT INDICES. C C RCOND REAL C AN ESTIMATE OF THE RECIPROCAL CONDITION OF A . C FOR THE SYSTEM A*X = B , RELATIVE PERTURBATIONS C IN A AND B OF SIZE EPSILON MAY CAUSE C RELATIVE PERTURBATIONS IN X OF SIZE EPSILON/RCOND C IF RCOND IS SO SMALL THAT THE LOGICAL EXPRESSION C 1.0 + RCOND .EQ. 1.0 C IS TRUE, THEN A MAY BE SINGULAR TO WORKING C PRECISION. IN PARTICULAR, RCOND IS ZERO IF C EXACT SINGULARITY IS DETECTED OR THE ESTIMATE C UNDERFLOWS. C C Z REAL(N) C A WORK VECTOR WHOSE CONTENTS ARE USUALLY UNIMPORTANT C IF A IS CLOSE TO A SINGULAR MATRIX, THEN Z IS C AN APPROXIMATE NULL VECTOR IN THE SENSE THAT C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . C C LINPACK. THIS VERSION DATED 08/14/78 . C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. C C SUBROUTINES AND FUNCTIONS C C LINPACK SSIFA C BLAS SAXPY,SDOT,SSCAL,SASUM C FORTRAN ABS,AMAX1,IABS,SIGN C