*DECK DPPSL SUBROUTINE DPPSL (AP, N, B) C***BEGIN PROLOGUE DPPSL C***PURPOSE Solve the real symmetric positive definite system using C the factors computed by DPPCO or DPPFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B1B C***TYPE DOUBLE PRECISION (SPPSL-S, DPPSL-D, CPPSL-C) C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, PACKED, C POSITIVE DEFINITE, SOLVE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C DPPSL solves the double precision symmetric positive definite C system A * X = B C using the factors computed by DPPCO or DPPFA. C C On Entry C C AP DOUBLE PRECISION (N*(N+1)/2) C the output from DPPCO or DPPFA. C C N INTEGER C the order of the matrix A . C C B DOUBLE PRECISION(N) C the right hand side vector. C C On Return C C B the solution vector X . C C Error Condition C C A division by zero will occur if the input factor contains C a zero on the diagonal. Technically this indicates C singularity, but it is usually caused by improper subroutine C arguments. It will not occur if the subroutines are called C correctly and INFO .EQ. 0 . C C To compute INVERSE(A) * C where C is a matrix C with P columns C CALL DPPCO(AP,N,RCOND,Z,INFO) C IF (RCOND is too small .OR. INFO .NE. 0) GO TO ... C DO 10 J = 1, P C CALL DPPSL(AP,N,C(1,J)) C 10 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 DAXPY, DDOT C***REVISION HISTORY (YYMMDD) C 780814 DATE WRITTEN 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 DPPSL INTEGER N DOUBLE PRECISION AP(*),B(*) C DOUBLE PRECISION DDOT,T INTEGER K,KB,KK C***FIRST EXECUTABLE STATEMENT DPPSL KK = 0 DO 10 K = 1, N T = DDOT(K-1,AP(KK+1),1,B(1),1) KK = KK + K B(K) = (B(K) - T)/AP(KK) 10 CONTINUE DO 20 KB = 1, N K = N + 1 - KB B(K) = B(K)/AP(KK) KK = KK - K T = -B(K) CALL DAXPY(K-1,T,AP(KK+1),1,B(1),1) 20 CONTINUE RETURN END