*DECK SPBSL SUBROUTINE SPBSL (ABD, LDA, N, M, B) C***BEGIN PROLOGUE SPBSL C***PURPOSE Solve a real symmetric positive definite band system C using the factors computed by SPBCO or SPBFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B2 C***TYPE SINGLE PRECISION (SPBSL-S, DPBSL-D, CPBSL-C) C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX, C POSITIVE DEFINITE, SOLVE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C SPBSL solves the real symmetric positive definite band C system A*X = B C using the factors computed by SPBCO or SPBFA. C C On Entry C C ABD REAL(LDA, N) C the output from SPBCO or SPBFA. C C LDA INTEGER C the leading dimension of the array ABD . C C N INTEGER C the order of the matrix A . C C M INTEGER C the number of diagonals above the main diagonal. 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 SPBCO(ABD,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 SPBSL(ABD,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 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 SPBSL INTEGER LDA,N,M REAL ABD(LDA,*),B(*) C REAL SDOT,T INTEGER K,KB,LA,LB,LM C C SOLVE TRANS(R)*Y = B C C***FIRST EXECUTABLE STATEMENT SPBSL DO 10 K = 1, N LM = MIN(K-1,M) LA = M + 1 - LM LB = K - LM T = SDOT(LM,ABD(LA,K),1,B(LB),1) B(K) = (B(K) - T)/ABD(M+1,K) 10 CONTINUE C C SOLVE R*X = Y C DO 20 KB = 1, N K = N + 1 - KB LM = MIN(K-1,M) LA = M + 1 - LM LB = K - LM B(K) = B(K)/ABD(M+1,K) T = -B(K) CALL SAXPY(LM,T,ABD(LA,K),1,B(LB),1) 20 CONTINUE RETURN END