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149 lines
4.3 KiB
Fortran
149 lines
4.3 KiB
Fortran
*DECK CNBSL
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SUBROUTINE CNBSL (ABE, LDA, N, ML, MU, IPVT, B, JOB)
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C***BEGIN PROLOGUE CNBSL
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C***PURPOSE Solve a complex band system using the factors computed by
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C CNBCO or CNBFA.
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C***LIBRARY SLATEC
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C***CATEGORY D2C2
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C***TYPE COMPLEX (SNBSL-S, DNBSL-D, CNBSL-C)
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C***KEYWORDS BANDED, LINEAR EQUATIONS, NONSYMMETRIC, SOLVE
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C***AUTHOR Voorhees, E. A., (LANL)
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C***DESCRIPTION
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C
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C CNBSL solves the complex band system
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C A * X = B or CTRANS(A) * X = B
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C using the factors computed by CNBCO or CNBFA.
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C
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C On Entry
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C
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C ABE COMPLEX(LDA, NC)
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C the output from CNBCO or CNBFA.
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C NC must be .GE. 2*ML+MU+1 .
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C
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C LDA INTEGER
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C the leading dimension of the array ABE .
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C
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C N INTEGER
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C the order of the original matrix.
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C
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C ML INTEGER
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C number of diagonals below the main diagonal.
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C
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C MU INTEGER
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C number of diagonals above the main diagonal.
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C
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C IPVT INTEGER(N)
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C the pivot vector from CNBCO or CNBFA.
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C
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C B COMPLEX(N)
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C the right hand side vector.
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C
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C JOB INTEGER
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C = 0 to solve A*X = B .
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C = nonzero to solve CTRANS(A)*X = B , where
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C CTRANS(A) is the conjugate transpose.
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C
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C On Return
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C
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C B the solution vector X .
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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 a
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C zero on the diagonal. Technically this indicates singularity
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C but it is often caused by improper arguments or improper
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C setting of LDA. It will not occur if the subroutines are
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C called correctly and if CNBCO has set RCOND .GT. 0.0
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C or CNBFA has set INFO .EQ. 0 .
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C
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C To compute INVERSE(A) * C where C is a matrix
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C with P columns
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C CALL CNBCO(ABE,LDA,N,ML,MU,IPVT,RCOND,Z)
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C IF (RCOND is too small) GO TO ...
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C DO 10 J = 1, P
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C CALL CNBSL(ABE,LDA,N,ML,MU,IPVT,C(1,J),0)
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C 10 CONTINUE
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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 CAXPY, CDOTC
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C***REVISION HISTORY (YYMMDD)
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C 800730 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 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 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE CNBSL
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INTEGER LDA,N,ML,MU,IPVT(*),JOB
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COMPLEX ABE(LDA,*),B(*)
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C
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COMPLEX CDOTC,T
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INTEGER K,KB,L,LB,LDB,LM,M,MLM,NM1
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C***FIRST EXECUTABLE STATEMENT CNBSL
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M=MU+ML+1
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NM1=N-1
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LDB=1-LDA
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IF(JOB.NE.0)GO TO 50
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C
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C JOB = 0 , SOLVE A * X = B
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C FIRST SOLVE L*Y = B
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C
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IF(ML.EQ.0)GO TO 30
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IF(NM1.LT.1)GO TO 30
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DO 20 K=1,NM1
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LM=MIN(ML,N-K)
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L=IPVT(K)
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T=B(L)
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IF(L.EQ.K)GO TO 10
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B(L)=B(K)
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B(K)=T
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10 CONTINUE
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MLM=ML-(LM-1)
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CALL CAXPY(LM,T,ABE(K+LM,MLM),LDB,B(K+1),1)
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20 CONTINUE
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30 CONTINUE
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C
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C NOW SOLVE U*X = Y
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C
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DO 40 KB=1,N
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K=N+1-KB
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B(K)=B(K)/ABE(K,ML+1)
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LM=MIN(K,M)-1
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LB=K-LM
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T=-B(K)
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CALL CAXPY(LM,T,ABE(K-1,ML+2),LDB,B(LB),1)
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40 CONTINUE
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GO TO 100
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50 CONTINUE
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C
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C JOB = NONZERO, SOLVE CTRANS(A) * X = B
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C FIRST SOLVE CTRANS(U)*Y = B
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C
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DO 60 K = 1, N
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LM = MIN(K,M) - 1
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LB = K - LM
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T = CDOTC(LM,ABE(K-1,ML+2),LDB,B(LB),1)
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B(K) = (B(K) - T)/CONJG(ABE(K,ML+1))
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60 CONTINUE
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C
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C NOW SOLVE CTRANS(L)*X = Y
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C
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IF (ML .EQ. 0) GO TO 90
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IF (NM1 .LT. 1) GO TO 90
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DO 80 KB = 1, NM1
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K = N - KB
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LM = MIN(ML,N-K)
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MLM = ML - (LM - 1)
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B(K) = B(K) + CDOTC(LM,ABE(K+LM,MLM),LDB,B(K+1),1)
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L = IPVT(K)
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IF (L .EQ. K) GO TO 70
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T = B(L)
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B(L) = B(K)
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B(K) = T
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70 CONTINUE
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80 CONTINUE
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90 CONTINUE
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100 CONTINUE
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RETURN
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END
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