*DECK CPOFA SUBROUTINE CPOFA (A, LDA, N, INFO) C***BEGIN PROLOGUE CPOFA C***PURPOSE Factor a complex Hermitian positive definite matrix. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2D1B C***TYPE COMPLEX (SPOFA-S, DPOFA-D, CPOFA-C) C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, C POSITIVE DEFINITE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C CPOFA factors a complex Hermitian positive definite matrix. C C CPOFA is usually called by CPOCO, but it can be called C directly with a saving in time if RCOND is not needed. C (Time for CPOCO) = (1 + 18/N)*(Time for CPOFA) . C C On Entry C C A COMPLEX(LDA, N) C the Hermitian matrix to be factored. Only the C diagonal and upper triangle are used. 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 On Return C C A an upper triangular matrix R so that A = C CTRANS(R)*R where CTRANS(R) is the conjugate C transpose. The strict lower triangle is unaltered. C If INFO .NE. 0 , the factorization is not complete. C C INFO INTEGER C = 0 for normal return. C = K signals an error condition. The leading minor C of order K is not positive definite. 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 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 CPOFA INTEGER LDA,N,INFO COMPLEX A(LDA,*) C COMPLEX CDOTC,T REAL S INTEGER J,JM1,K C***FIRST EXECUTABLE STATEMENT CPOFA DO 30 J = 1, N INFO = J S = 0.0E0 JM1 = J - 1 IF (JM1 .LT. 1) GO TO 20 DO 10 K = 1, JM1 T = A(K,J) - CDOTC(K-1,A(1,K),1,A(1,J),1) T = T/A(K,K) A(K,J) = T S = S + REAL(T*CONJG(T)) 10 CONTINUE 20 CONTINUE S = REAL(A(J,J)) - S IF (S .LE. 0.0E0 .OR. AIMAG(A(J,J)) .NE. 0.0E0) GO TO 40 A(J,J) = CMPLX(SQRT(S),0.0E0) 30 CONTINUE INFO = 0 40 CONTINUE RETURN END