*DECK DPBFA SUBROUTINE DPBFA (ABD, LDA, N, M, INFO) C***BEGIN PROLOGUE DPBFA C***PURPOSE Factor a real symmetric positive definite matrix stored in C in band form. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B2 C***TYPE DOUBLE PRECISION (SPBFA-S, DPBFA-D, CPBFA-C) C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, C POSITIVE DEFINITE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C DPBFA factors a double precision symmetric positive definite C matrix stored in band form. C C DPBFA is usually called by DPBCO, but it can be called C directly with a saving in time if RCOND is not needed. C C On Entry C C ABD DOUBLE PRECISION(LDA, N) C the matrix to be factored. The columns of the upper C triangle are stored in the columns of ABD and the C diagonals of the upper triangle are stored in the C rows of ABD . See the comments below for details. C C LDA INTEGER C the leading dimension of the array ABD . C LDA must be .GE. M + 1 . 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 0 .LE. M .LT. N . C C On Return C C ABD an upper triangular matrix R , stored in band C form, so that A = TRANS(R)*R . C C INFO INTEGER C = 0 for normal return. C = K if the leading minor of order K is not C positive definite. C C Band Storage C C If A is a symmetric positive definite band matrix, C the following program segment will set up the input. C C M = (band width above diagonal) C DO 20 J = 1, N C I1 = MAX(1, J-M) C DO 10 I = I1, J C K = I-J+M+1 C ABD(K,J) = 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 DDOT 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 DPBFA INTEGER LDA,N,M,INFO DOUBLE PRECISION ABD(LDA,*) C DOUBLE PRECISION DDOT,T DOUBLE PRECISION S INTEGER IK,J,JK,K,MU C***FIRST EXECUTABLE STATEMENT DPBFA DO 30 J = 1, N INFO = J S = 0.0D0 IK = M + 1 JK = MAX(J-M,1) MU = MAX(M+2-J,1) IF (M .LT. MU) GO TO 20 DO 10 K = MU, M T = ABD(K,J) - DDOT(K-MU,ABD(IK,JK),1,ABD(MU,J),1) T = T/ABD(M+1,JK) ABD(K,J) = T S = S + T*T IK = IK - 1 JK = JK + 1 10 CONTINUE 20 CONTINUE S = ABD(M+1,J) - S IF (S .LE. 0.0D0) GO TO 40 ABD(M+1,J) = SQRT(S) 30 CONTINUE INFO = 0 40 CONTINUE RETURN END