mirror of https://gitlab.com/QEF/q-e.git
252 lines
7.0 KiB
Fortran
252 lines
7.0 KiB
Fortran
! Slightly modified version of LINPACK routines zgefa and zgedi
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SUBROUTINE ZGEFA(A,LDA,N,IPVT,INFO)
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USE kinds, ONLY : DP
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INTEGER LDA,N,IPVT(*),INFO
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COMPLEX(DP) A(LDA,*)
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!
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! ZGEFA FACTORS A COMPLEX(DP) MATRIX BY GAUSSIAN ELIMINATION.
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!
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! ZGEFA IS USUALLY CALLED BY ZGECO, BUT IT CAN BE CALLED
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! DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED.
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! (TIME FOR ZGECO) = (1 + 9/N)*(TIME FOR ZGEFA) .
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!
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! ON ENTRY
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!
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! A COMPLEX(DP)(LDA, N)
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! THE MATRIX TO BE FACTORED.
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!
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! LDA INTEGER
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! THE LEADING DIMENSION OF THE ARRAY A .
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!
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! N INTEGER
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! THE ORDER OF THE MATRIX A .
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!
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! ON RETURN
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!
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! A AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS
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! WHICH WERE USED TO OBTAIN IT.
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! THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE
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! L IS A PRODUCT OF PERMUTATION AND UNIT LOWER
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! TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR.
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!
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! IPVT INTEGER(N)
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! AN INTEGER VECTOR OF PIVOT INDICES.
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!
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! INFO INTEGER
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! = 0 NORMAL VALUE.
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! = K IF U(K,K) .EQ. 0.0 . THIS IS NOT AN ERROR
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! CONDITION FOR THIS SUBROUTINE, BUT IT DOES
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! INDICATE THAT ZGESL OR ZGEDI WILL DIVIDE BY ZERO
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! IF CALLED. USE RCOND IN ZGECO FOR A RELIABLE
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! INDICATION OF SINGULARITY.
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!
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! LINPACK. THIS VERSION DATED 08/14/78 .
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! CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
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!
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! SUBROUTINES AND FUNCTIONS
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!
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! BLAS ZAXPY,ZSCAL,IZAMAX
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! FORTRAN DABS
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!
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! INTERNAL VARIABLES
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!
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COMPLEX(DP) T
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INTEGER IZAMAX,J,K,KP1,L,NM1
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!
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COMPLEX(DP) ZDUM
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REAL(DP) CABS1
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REAL(DP) REAL,AIMAG
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COMPLEX(DP) ZDUMR,ZDUMI
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REAL(ZDUMR) = ZDUMR
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AIMAG(ZDUMI) = (0.0D0,-1.0D0)*ZDUMI
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CABS1(ZDUM) = DABS(REAL(ZDUM)) + DABS(AIMAG(ZDUM))
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!
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! GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
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!
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INFO = 0
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NM1 = N - 1
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IF (NM1 .LT. 1) GO TO 70
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DO 60 K = 1, NM1
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KP1 = K + 1
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!
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! FIND L = PIVOT INDEX
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!
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L = IZAMAX(N-K+1,A(K,K),1) + K - 1
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IPVT(K) = L
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!
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! ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
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!
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IF (CABS1(A(L,K)) .EQ. 0.0D0) GO TO 40
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!
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! INTERCHANGE IF NECESSARY
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!
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IF (L .EQ. K) GO TO 10
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T = A(L,K)
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A(L,K) = A(K,K)
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A(K,K) = T
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10 CONTINUE
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!
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! COMPUTE MULTIPLIERS
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!
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T = -(1.0D0,0.0D0)/A(K,K)
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CALL ZSCAL(N-K,T,A(K+1,K),1)
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!
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! ROW ELIMINATION WITH COLUMN INDEXING
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!
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DO 30 J = KP1, N
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T = A(L,J)
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IF (L .EQ. K) GO TO 20
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A(L,J) = A(K,J)
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A(K,J) = T
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20 CONTINUE
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CALL ZAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1)
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30 CONTINUE
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GO TO 50
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40 CONTINUE
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INFO = K
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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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IPVT(N) = N
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IF (CABS1(A(N,N)) .EQ. 0.0D0) INFO = N
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RETURN
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END SUBROUTINE ZGEFA
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SUBROUTINE ZGEDI(A,LDA,N,IPVT,DET,WORK,JOB)
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USE kinds, ONLY : DP
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INTEGER LDA,N,IPVT(*),JOB
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COMPLEX(DP) A(LDA,*),DET(2),WORK(*)
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!
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! ZGEDI COMPUTES THE DETERMINANT AND INVERSE OF A MATRIX
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! USING THE FACTORS COMPUTED BY ZGECO OR ZGEFA.
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!
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! ON ENTRY
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!
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! A COMPLEX(DP)(LDA, N)
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! THE OUTPUT FROM ZGECO OR ZGEFA.
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!
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! LDA INTEGER
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! THE LEADING DIMENSION OF THE ARRAY A .
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!
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! N INTEGER
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! THE ORDER OF THE MATRIX A .
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!
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! IPVT INTEGER(N)
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! THE PIVOT VECTOR FROM ZGECO OR ZGEFA.
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!
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! WORK COMPLEX(DP)(N)
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! WORK VECTOR. CONTENTS DESTROYED.
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!
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! JOB INTEGER
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! = 11 BOTH DETERMINANT AND INVERSE.
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! = 01 INVERSE ONLY.
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! = 10 DETERMINANT ONLY.
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!
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! ON RETURN
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!
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! A INVERSE OF ORIGINAL MATRIX IF REQUESTED.
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! OTHERWISE UNCHANGED.
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!
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! DET COMPLEX(DP)(2)
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! DETERMINANT OF ORIGINAL MATRIX IF REQUESTED.
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! OTHERWISE NOT REFERENCED.
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! DETERMINANT = DET(1) * 10.0**DET(2)
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! WITH 1.0 .LE. CABS1(DET(1)) .LT. 10.0
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! OR DET(1) .EQ. 0.0 .
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!
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! ERROR CONDITION
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!
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! A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS
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! A ZERO ON THE DIAGONAL AND THE INVERSE IS REQUESTED.
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! IT WILL NOT OCCUR IF THE SUBROUTINES ARE CALLED CORRECTLY
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! AND IF ZGECO HAS SET RCOND .GT. 0.0 OR ZGEFA HAS SET
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! INFO .EQ. 0 .
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!
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! LINPACK. THIS VERSION DATED 08/14/78 .
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! CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
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!
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! SUBROUTINES AND FUNCTIONS
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!
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! BLAS ZAXPY,ZSCAL,ZSWAP
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! FORTRAN DABS,CMPLX,MOD
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!
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! INTERNAL VARIABLES
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!
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COMPLEX(DP) T
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REAL(DP) TEN
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INTEGER I,J,K,KB,KP1,L,NM1
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!
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COMPLEX(DP) ZDUM
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REAL(DP) CABS1
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REAL(DP) REAL,AIMAG
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COMPLEX(DP) ZDUMR,ZDUMI
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REAL(ZDUMR) = ZDUMR
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AIMAG(ZDUMI) = (0.0D0,-1.0D0)*ZDUMI
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CABS1(ZDUM) = DABS(REAL(ZDUM)) + DABS(AIMAG(ZDUM))
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!
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! COMPUTE DETERMINANT
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!
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IF (JOB/10 .EQ. 0) GO TO 70
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DET(1) = (1.0D0,0.0D0)
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DET(2) = (0.0D0,0.0D0)
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TEN = 10.0D0
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DO 50 I = 1, N
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IF (IPVT(I) .NE. I) DET(1) = -DET(1)
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DET(1) = A(I,I)*DET(1)
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! ...EXIT
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IF (CABS1(DET(1)) .EQ. 0.0D0) GO TO 60
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10 IF (CABS1(DET(1)) .GE. 1.0D0) GO TO 20
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DET(1) = CMPLX(TEN,0.0D0,KIND=dp)*DET(1)
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DET(2) = DET(2) - (1.0D0,0.0D0)
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GO TO 10
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20 CONTINUE
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30 IF (CABS1(DET(1)) .LT. TEN) GO TO 40
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DET(1) = DET(1)/CMPLX(TEN,0.0D0,KIND=dp)
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DET(2) = DET(2) + (1.0D0,0.0D0)
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GO TO 30
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40 CONTINUE
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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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!
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! COMPUTE INVERSE(U)
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!
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IF (MOD(JOB,10) .EQ. 0) GO TO 150
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DO 100 K = 1, N
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A(K,K) = (1.0D0,0.0D0)/A(K,K)
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T = -A(K,K)
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CALL ZSCAL(K-1,T,A(1,K),1)
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KP1 = K + 1
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IF (N .LT. KP1) GO TO 90
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DO 80 J = KP1, N
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T = A(K,J)
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A(K,J) = (0.0D0,0.0D0)
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CALL ZAXPY(K,T,A(1,K),1,A(1,J),1)
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80 CONTINUE
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90 CONTINUE
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100 CONTINUE
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!
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! FORM INVERSE(U)*INVERSE(L)
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!
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NM1 = N - 1
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IF (NM1 .LT. 1) GO TO 140
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DO 130 KB = 1, NM1
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K = N - KB
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KP1 = K + 1
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DO 110 I = KP1, N
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WORK(I) = A(I,K)
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A(I,K) = (0.0D0,0.0D0)
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110 CONTINUE
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DO 120 J = KP1, N
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T = WORK(J)
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CALL ZAXPY(N,T,A(1,J),1,A(1,K),1)
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120 CONTINUE
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L = IPVT(K)
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IF (L .NE. K) CALL ZSWAP(N,A(1,K),1,A(1,L),1)
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130 CONTINUE
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140 CONTINUE
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150 CONTINUE
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RETURN
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END SUBROUTINE ZGEDI
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