*DECK CPBFA
SUBROUTINE CPBFA (ABD, LDA, N, M, INFO)
C***BEGIN PROLOGUE CPBFA
C***PURPOSE Factor a complex Hermitian positive definite matrix stored
C in band form.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2D2
C***TYPE COMPLEX (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 CPBFA factors a complex Hermitian positive definite matrix
C stored in band form.
C
C CPBFA is usually called by CPBCO, but it can be called
C directly with a saving in time if RCOND is not needed.
C
C On Entry
C
C ABD COMPLEX(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 = CTRANS(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 Hermitian 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 CDOTC
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 CPBFA
INTEGER LDA,N,M,INFO
COMPLEX ABD(LDA,*)
C
COMPLEX CDOTC,T
REAL S
INTEGER IK,J,JK,K,MU
C***FIRST EXECUTABLE STATEMENT CPBFA
DO 30 J = 1, N
INFO = J
S = 0.0E0
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) - CDOTC(K-MU,ABD(IK,JK),1,ABD(MU,J),1)
T = T/ABD(M+1,JK)
ABD(K,J) = T
S = S + REAL(T*CONJG(T))
IK = IK - 1
JK = JK + 1
10 CONTINUE
20 CONTINUE
S = REAL(ABD(M+1,J)) - S
IF (S .LE. 0.0E0 .OR. AIMAG(ABD(M+1,J)) .NE. 0.0E0)
1 GO TO 40
ABD(M+1,J) = CMPLX(SQRT(S),0.0E0)
30 CONTINUE
INFO = 0
40 CONTINUE
RETURN
END