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SUBROUTINE SPOCO(A,LDA,N,RCOND,Z,INFO)
INTEGER LDA,N,INFO
REAL A(LDA,1),Z(1)
REAL RCOND
C
C SPOCO FACTORS A REAL SYMMETRIC POSITIVE DEFINITE MATRIX
C AND ESTIMATES THE CONDITION OF THE MATRIX.
C
C IF RCOND IS NOT NEEDED, SPOFA IS SLIGHTLY FASTER.
C TO SOLVE A*X = B , FOLLOW SPOCO BY SPOSL.
C TO COMPUTE INVERSE(A)*C , FOLLOW SPOCO BY SPOSL.
C TO COMPUTE DETERMINANT(A) , FOLLOW SPOCO BY SPODI.
C TO COMPUTE INVERSE(A) , FOLLOW SPOCO BY SPODI.
C
C ON ENTRY
C
C A REAL(LDA, N)
C THE SYMMETRIC MATRIX TO BE FACTORED. ONLY THE
C 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 ON RETURN
C
C A AN UPPER TRIANGULAR MATRIX R SO THAT A = TRANS(R)
C WHERE TRANS(R) IS THE TRANSPOSE.
C THE STRICT LOWER TRIANGLE IS UNALTERED.
C IF INFO .NE. 0 , THE FACTORIZATION IS NOT COMPLETE.
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. IF INFO .NE. 0 , RCOND IS UNCHANGED.
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 IF INFO .NE. 0 , Z IS UNCHANGED.
C
C INFO INTEGER
C = 0 FOR NORMAL RETURN.
C = K SIGNALS AN ERROR CONDITION. THE LEADING MINOR
C OF ORDER K IS NOT POSITIVE DEFINITE.
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 SPOFA
C BLAS SAXPY,SDOT,SSCAL,SASUM
C FORTRAN ABS,AMAX1,REAL,SIGN
C