zpoctrf.f

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C     ====================================================================
C                            N U L A P A C K
C                            U U L A P A C K
C                            L L L A P A C K
C                            A A A A P A C K
C                            P P P P P A C K
C                            A A A A A A C K
C                            C C C C C C C K
C                            K K K K K K K K
C
C     This file is part of NULAPACK - NUmerical Linear Algebra PACKage
C
C     Copyright (C) 2025  Saud Zahir
C
C     NULAPACK is free software: you can redistribute it and/or modify
C     it under the terms of the GNU General Public License as published by
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C
C     You should have received a copy of the GNU General Public License
C     along with NULAPACK.  If not, see <https://www.gnu.org/licenses/>.
C
C     ====================================================================
C       ZPOCTRF  -  Cholesky Factorization for A = L * L^T
C     ====================================================================
C       Description:
C       ------------------------------------------------------------------
C         Computes the Cholesky factorization of a complex Hermitian
C         positive-definite matrix A stored in a flat row-major array.
C         The lower-triangular matrix L overwrites the lower triangle of A.
C
C         On output: A contains L in the lower triangle, upper triangle is
C         not referenced.
C
C     ====================================================================
C       Arguments:
C       ------------------------------------------------------------------
C         N    : INTEGER       -> order of the matrix
C         A(*) : COMPLEX*16    -> flat row-major matrix, size (LDA*N)
C         L(*) : COMPLEX*16    -> flat row-major matrix, size (LDA*N)
C         LDA  : INTEGER       -> leading dimension of A (usually N)
C         INFO : INTEGER       -> return code:
C                                0 = success
C                               <0 = illegal argument
C                               >0 = matrix not positive definite
C     ====================================================================
      SUBROUTINE zpoctrf(N, A, L, LDA, INFO)
 
C   I m p l i c i t   t y p e s
C   ------------------------------------------------------------------
      IMPLICIT NONE
 
C   D u m m y   a r g u m e n t s
C   ------------------------------------------------------------------
      INTEGER       :: N, LDA, INFO
      COMPLEX*16    :: A(*), L(*)
 
C   L o c a l   v a r i a b l e s
C   ------------------------------------------------------------------
      INTEGER       :: I, J, K, INDEX
      COMPLEX*16    :: SUM
 
C   I n i t i a l i z e
C   ------------------------------------------------------------------
      info = 0
 
C   M a i n   l o o p   o v e r   r o w s
C   ------------------------------------------------------------------
      DO i = 1, n
 
C       Compute diagonal element L(I,I)
         sum = (0.0d0, 0.0d0)
         DO k = 1, i-1
            index = (i-1)*lda + k
            sum = sum + l(index)*dconjg(l(index))
         END DO
 
         index = (i-1)*lda + i
         IF (dble(a(index)) - dble(sum) .LE. 0.0d0) THEN
            info = i
            RETURN
         END IF
         l(index) = zsqrt(a(index) - sum)
 
C       Compute off-diagonal elements L(J,I), J = I+1:N
         DO j = i+1, n
            sum = (0.0d0, 0.0d0)
            DO k = 1, i-1
               sum = sum + l((j-1)*lda + k) * dconjg(l((i-1)*lda + k))
            END DO
            index = (j-1)*lda + i
            l(index) = (a(index) - sum)/l((i-1)*lda + i)
         END DO
 
      END DO
 
C   S u c c e s s f u l   e x i t
C   ------------------------------------------------------------------
      RETURN
      END