SUBROUTINE DPPCO (AP, N, RCOND, Z, INFO) C***BEGIN PROLOGUE DPPCO C***PURPOSE Factor a symmetric positive definite matrix stored in C packed form and estimate the condition number of the C matrix. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B1B C***TYPE DOUBLE PRECISION (SPPCO-S, DPPCO-D, CPPCO-C) C***KEYWORDS CONDITION NUMBER, LINEAR ALGEBRA, LINPACK, C MATRIX FACTORIZATION, PACKED, POSITIVE DEFINITE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C DPPCO factors a double precision symmetric positive definite C matrix stored in packed form C and estimates the condition of the matrix. C C If RCOND is not needed, DPPFA is slightly faster. C To solve A*X = B , follow DPPCO by DPPSL. C To compute INVERSE(A)*C , follow DPPCO by DPPSL. C To compute DETERMINANT(A) , follow DPPCO by DPPDI. C To compute INVERSE(A) , follow DPPCO by DPPDI. C C On Entry C C AP DOUBLE PRECISION (N*(N+1)/2) C the packed form of a symmetric matrix A . The C columns of the upper triangle are stored sequentially C in a one-dimensional array of length N*(N+1)/2 . C See comments below for details. C C N INTEGER C the order of the matrix A . C C On Return C C AP an upper triangular matrix R , stored in packed C form, so that A = TRANS(R)*R . C If INFO .NE. 0 , the factorization is not complete. C C RCOND DOUBLE PRECISION 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 DOUBLE PRECISION(N) C a work vector whose contents are usually unimportant. C If A is singular to working precision, 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 Packed Storage C C The following program segment will pack the upper C triangle of a symmetric matrix. C C K = 0 C DO 20 J = 1, N C DO 10 I = 1, J C K = K + 1 C AP(K) = A(I,J) C 10 CONTINUE C 20 CONTINUE C C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. C Stewart, LINPACK Users' Guide, SIAM, 1979. C***ROUTINES CALLED DASUM, DAXPY, DDOT, DPPFA, DSCAL C***REVISION HISTORY (YYMMDD) C 780814 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 890831 Modified array declarations. (WRB) C 890831 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 900326 Removed duplicate information from DESCRIPTION section. C (WRB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE DPPCO