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140 lines
4.1 KiB
Fortran
140 lines
4.1 KiB
Fortran
*DECK SGEDI
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SUBROUTINE SGEDI (A, LDA, N, IPVT, DET, WORK, JOB)
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C***BEGIN PROLOGUE SGEDI
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C***PURPOSE Compute the determinant and inverse of a matrix using the
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C factors computed by SGECO or SGEFA.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2A1, D3A1
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C***TYPE SINGLE PRECISION (SGEDI-S, DGEDI-D, CGEDI-C)
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C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX
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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 SGEDI computes the determinant and inverse of a matrix
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C using the factors computed by SGECO or SGEFA.
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C
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C On Entry
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C
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C A REAL(LDA, N)
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C the output from SGECO or SGEFA.
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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 IPVT INTEGER(N)
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C the pivot vector from SGECO or SGEFA.
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C
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C WORK REAL(N)
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C work vector. Contents destroyed.
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C
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C JOB INTEGER
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C = 11 both determinant and inverse.
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C = 01 inverse only.
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C = 10 determinant only.
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C
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C On Return
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C
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C A inverse of original matrix if requested.
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C Otherwise unchanged.
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C
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C DET REAL(2)
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C determinant of original matrix if requested.
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C Otherwise not referenced.
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C Determinant = DET(1) * 10.0**DET(2)
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C with 1.0 .LE. ABS(DET(1)) .LT. 10.0
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C or DET(1) .EQ. 0.0 .
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C
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C Error Condition
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C
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C A division by zero will occur if the input factor contains
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C a zero on the diagonal and the inverse is requested.
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C It will not occur if the subroutines are called correctly
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C and if SGECO has set RCOND .GT. 0.0 or SGEFA has set
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C INFO .EQ. 0 .
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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 SAXPY, SSCAL, SSWAP
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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 SGEDI
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INTEGER LDA,N,IPVT(*),JOB
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REAL A(LDA,*),DET(2),WORK(*)
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C
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REAL T
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REAL TEN
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INTEGER I,J,K,KB,KP1,L,NM1
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C***FIRST EXECUTABLE STATEMENT SGEDI
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C
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C COMPUTE DETERMINANT
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C
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IF (JOB/10 .EQ. 0) GO TO 70
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DET(1) = 1.0E0
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DET(2) = 0.0E0
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TEN = 10.0E0
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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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IF (DET(1) .EQ. 0.0E0) GO TO 60
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10 IF (ABS(DET(1)) .GE. 1.0E0) GO TO 20
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DET(1) = TEN*DET(1)
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DET(2) = DET(2) - 1.0E0
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GO TO 10
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20 CONTINUE
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30 IF (ABS(DET(1)) .LT. TEN) GO TO 40
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DET(1) = DET(1)/TEN
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DET(2) = DET(2) + 1.0E0
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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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C
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C COMPUTE INVERSE(U)
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C
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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) = 1.0E0/A(K,K)
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T = -A(K,K)
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CALL SSCAL(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) = 0.0E0
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CALL SAXPY(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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C
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C FORM INVERSE(U)*INVERSE(L)
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C
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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) = 0.0E0
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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 SAXPY(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 SSWAP(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
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