*DECK SPOSL SUBROUTINE SPOSL (A, LDA, N, B) C***BEGIN PROLOGUE SPOSL C***PURPOSE Solve the real symmetric positive definite linear system C using the factors computed by SPOCO or SPOFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B1B C***TYPE SINGLE PRECISION (SPOSL-S, DPOSL-D, CPOSL-C) C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, POSITIVE DEFINITE, SOLVE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C SPOSL solves the real symmetric positive definite system C A * X = B C using the factors computed by SPOCO or SPOFA. C C On Entry C C A REAL(LDA, N) C the output from SPOCO or SPOFA. 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 B REAL(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 SPOCO(A,LDA,N,RCOND,Z,INFO) C IF (RCOND is too small .OR. INFO .NE. 0) GO TO ... C DO 10 J = 1, P C CALL SPOSL(A,LDA,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 SAXPY, SDOT 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 SPOSL INTEGER LDA,N REAL A(LDA,*),B(*) C REAL SDOT,T INTEGER K,KB C C SOLVE TRANS(R)*Y = B C C***FIRST EXECUTABLE STATEMENT SPOSL DO 10 K = 1, N T = SDOT(K-1,A(1,K),1,B(1),1) B(K) = (B(K) - T)/A(K,K) 10 CONTINUE C C SOLVE R*X = Y C DO 20 KB = 1, N K = N + 1 - KB B(K) = B(K)/A(K,K) T = -B(K) CALL SAXPY(K-1,T,A(1,K),1,B(1),1) 20 CONTINUE RETURN END