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228 lines
7.2 KiB
Fortran
228 lines
7.2 KiB
Fortran
*DECK SSIDI
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SUBROUTINE SSIDI (A, LDA, N, KPVT, DET, INERT, WORK, JOB)
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C***BEGIN PROLOGUE SSIDI
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C***PURPOSE Compute the determinant, inertia and inverse of a real
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C symmetric matrix using the factors from SSIFA.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2B1A, D3B1A
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C***TYPE SINGLE PRECISION (SSIDI-S, DSIDI-D, CHIDI-C, CSIDI-C)
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C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX,
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C SYMMETRIC
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C***AUTHOR Bunch, J., (UCSD)
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C***DESCRIPTION
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C
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C SSIDI computes the determinant, inertia and inverse
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C of a real symmetric matrix using the factors from SSIFA.
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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 SSIFA.
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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 KPVT INTEGER(N)
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C the pivot vector from SSIFA.
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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 JOB has the decimal expansion ABC where
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C If C .NE. 0, the inverse is computed,
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C If B .NE. 0, the determinant is computed,
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C If A .NE. 0, the inertia is computed.
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C
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C For example, JOB = 111 gives all three.
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C
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C On Return
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C
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C Variables not requested by JOB are not used.
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C
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C A contains the upper triangle of the inverse of
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C the original matrix. The strict lower triangle
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C is never referenced.
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C
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C DET REAL(2)
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C determinant of original matrix.
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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) = 0.0.
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C
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C INERT INTEGER(3)
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C the inertia of the original matrix.
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C INERT(1) = number of positive eigenvalues.
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C INERT(2) = number of negative eigenvalues.
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C INERT(3) = number of zero eigenvalues.
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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 may occur if the inverse is requested
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C and SSICO has set RCOND .EQ. 0.0
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C or SSIFA has set INFO .NE. 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, SCOPY, SDOT, SSWAP
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C***REVISION HISTORY (YYMMDD)
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C 780814 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890831 Modified array declarations. (WRB)
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C 891107 Modified routine equivalence list. (WRB)
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C 891107 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 SSIDI
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INTEGER LDA,N,JOB
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REAL A(LDA,*),WORK(*)
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REAL DET(2)
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INTEGER KPVT(*),INERT(3)
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C
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REAL AKKP1,SDOT,TEMP
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REAL TEN,D,T,AK,AKP1
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INTEGER J,JB,K,KM1,KS,KSTEP
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LOGICAL NOINV,NODET,NOERT
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C***FIRST EXECUTABLE STATEMENT SSIDI
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NOINV = MOD(JOB,10) .EQ. 0
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NODET = MOD(JOB,100)/10 .EQ. 0
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NOERT = MOD(JOB,1000)/100 .EQ. 0
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C
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IF (NODET .AND. NOERT) GO TO 140
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IF (NOERT) GO TO 10
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INERT(1) = 0
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INERT(2) = 0
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INERT(3) = 0
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10 CONTINUE
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IF (NODET) GO TO 20
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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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20 CONTINUE
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T = 0.0E0
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DO 130 K = 1, N
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D = A(K,K)
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C
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C CHECK IF 1 BY 1
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C
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IF (KPVT(K) .GT. 0) GO TO 50
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C
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C 2 BY 2 BLOCK
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C USE DET (D S) = (D/T * C - T) * T , T = ABS(S)
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C (S C)
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C TO AVOID UNDERFLOW/OVERFLOW TROUBLES.
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C TAKE TWO PASSES THROUGH SCALING. USE T FOR FLAG.
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C
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IF (T .NE. 0.0E0) GO TO 30
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T = ABS(A(K,K+1))
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D = (D/T)*A(K+1,K+1) - T
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GO TO 40
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30 CONTINUE
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D = T
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T = 0.0E0
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40 CONTINUE
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50 CONTINUE
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C
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IF (NOERT) GO TO 60
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IF (D .GT. 0.0E0) INERT(1) = INERT(1) + 1
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IF (D .LT. 0.0E0) INERT(2) = INERT(2) + 1
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IF (D .EQ. 0.0E0) INERT(3) = INERT(3) + 1
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60 CONTINUE
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C
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IF (NODET) GO TO 120
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DET(1) = D*DET(1)
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IF (DET(1) .EQ. 0.0E0) GO TO 110
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70 IF (ABS(DET(1)) .GE. 1.0E0) GO TO 80
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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 70
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80 CONTINUE
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90 IF (ABS(DET(1)) .LT. TEN) GO TO 100
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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 90
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100 CONTINUE
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110 CONTINUE
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120 CONTINUE
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130 CONTINUE
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140 CONTINUE
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C
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C COMPUTE INVERSE(A)
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C
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IF (NOINV) GO TO 270
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K = 1
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150 IF (K .GT. N) GO TO 260
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KM1 = K - 1
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IF (KPVT(K) .LT. 0) GO TO 180
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C
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C 1 BY 1
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C
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A(K,K) = 1.0E0/A(K,K)
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IF (KM1 .LT. 1) GO TO 170
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CALL SCOPY(KM1,A(1,K),1,WORK,1)
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DO 160 J = 1, KM1
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A(J,K) = SDOT(J,A(1,J),1,WORK,1)
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CALL SAXPY(J-1,WORK(J),A(1,J),1,A(1,K),1)
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160 CONTINUE
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A(K,K) = A(K,K) + SDOT(KM1,WORK,1,A(1,K),1)
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170 CONTINUE
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KSTEP = 1
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GO TO 220
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180 CONTINUE
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C
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C 2 BY 2
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C
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T = ABS(A(K,K+1))
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AK = A(K,K)/T
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AKP1 = A(K+1,K+1)/T
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AKKP1 = A(K,K+1)/T
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D = T*(AK*AKP1 - 1.0E0)
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A(K,K) = AKP1/D
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A(K+1,K+1) = AK/D
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A(K,K+1) = -AKKP1/D
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IF (KM1 .LT. 1) GO TO 210
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CALL SCOPY(KM1,A(1,K+1),1,WORK,1)
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DO 190 J = 1, KM1
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A(J,K+1) = SDOT(J,A(1,J),1,WORK,1)
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CALL SAXPY(J-1,WORK(J),A(1,J),1,A(1,K+1),1)
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190 CONTINUE
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A(K+1,K+1) = A(K+1,K+1) + SDOT(KM1,WORK,1,A(1,K+1),1)
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A(K,K+1) = A(K,K+1) + SDOT(KM1,A(1,K),1,A(1,K+1),1)
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CALL SCOPY(KM1,A(1,K),1,WORK,1)
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DO 200 J = 1, KM1
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A(J,K) = SDOT(J,A(1,J),1,WORK,1)
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CALL SAXPY(J-1,WORK(J),A(1,J),1,A(1,K),1)
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200 CONTINUE
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A(K,K) = A(K,K) + SDOT(KM1,WORK,1,A(1,K),1)
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210 CONTINUE
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KSTEP = 2
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220 CONTINUE
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C
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C SWAP
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C
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KS = ABS(KPVT(K))
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IF (KS .EQ. K) GO TO 250
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CALL SSWAP(KS,A(1,KS),1,A(1,K),1)
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DO 230 JB = KS, K
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J = K + KS - JB
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TEMP = A(J,K)
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A(J,K) = A(KS,J)
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A(KS,J) = TEMP
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230 CONTINUE
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IF (KSTEP .EQ. 1) GO TO 240
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TEMP = A(KS,K+1)
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A(KS,K+1) = A(K,K+1)
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A(K,K+1) = TEMP
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240 CONTINUE
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250 CONTINUE
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K = K + KSTEP
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GO TO 150
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260 CONTINUE
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270 CONTINUE
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RETURN
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END
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