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81 lines
2.6 KiB
Fortran
81 lines
2.6 KiB
Fortran
*DECK CPOFA
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SUBROUTINE CPOFA (A, LDA, N, INFO)
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C***BEGIN PROLOGUE CPOFA
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C***PURPOSE Factor a complex Hermitian positive definite matrix.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2D1B
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C***TYPE COMPLEX (SPOFA-S, DPOFA-D, CPOFA-C)
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C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION,
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C POSITIVE DEFINITE
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C***AUTHOR Moler, C. B., (U. of New Mexico)
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C***DESCRIPTION
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C
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C CPOFA factors a complex Hermitian positive definite matrix.
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C
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C CPOFA is usually called by CPOCO, but it can be called
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C directly with a saving in time if RCOND is not needed.
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C (Time for CPOCO) = (1 + 18/N)*(Time for CPOFA) .
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C
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C On Entry
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C
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C A COMPLEX(LDA, N)
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C the Hermitian matrix to be factored. Only the
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C diagonal and upper triangle are used.
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C
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C LDA INTEGER
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C the leading dimension of the array A .
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C
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C N INTEGER
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C the order of the matrix A .
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C
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C On Return
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C
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C A an upper triangular matrix R so that A =
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C CTRANS(R)*R where CTRANS(R) is the conjugate
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C transpose. The strict lower triangle is unaltered.
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C If INFO .NE. 0 , the factorization is not complete.
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C
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C INFO INTEGER
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C = 0 for normal return.
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C = K signals an error condition. The leading minor
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C of order K is not positive definite.
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C
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C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
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C Stewart, LINPACK Users' Guide, SIAM, 1979.
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C***ROUTINES CALLED CDOTC
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C***REVISION HISTORY (YYMMDD)
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C 780814 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE CPOFA
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INTEGER LDA,N,INFO
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COMPLEX A(LDA,*)
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C
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COMPLEX CDOTC,T
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REAL S
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INTEGER J,JM1,K
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C***FIRST EXECUTABLE STATEMENT CPOFA
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DO 30 J = 1, N
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INFO = J
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S = 0.0E0
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JM1 = J - 1
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IF (JM1 .LT. 1) GO TO 20
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DO 10 K = 1, JM1
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T = A(K,J) - CDOTC(K-1,A(1,K),1,A(1,J),1)
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T = T/A(K,K)
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A(K,J) = T
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S = S + REAL(T*CONJG(T))
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10 CONTINUE
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20 CONTINUE
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S = REAL(A(J,J)) - S
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IF (S .LE. 0.0E0 .OR. AIMAG(A(J,J)) .NE. 0.0E0) GO TO 40
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A(J,J) = CMPLX(SQRT(S),0.0E0)
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30 CONTINUE
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INFO = 0
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40 CONTINUE
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RETURN
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END
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