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187 lines
5.8 KiB
Fortran
187 lines
5.8 KiB
Fortran
*DECK SGBFA
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SUBROUTINE SGBFA (ABD, LDA, N, ML, MU, IPVT, INFO)
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C***BEGIN PROLOGUE SGBFA
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C***PURPOSE Factor a band matrix using Gaussian elimination.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2A2
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C***TYPE SINGLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C)
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C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION
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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 SGBFA factors a real band matrix by elimination.
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C
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C SGBFA is usually called by SBGCO, but it can be called
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C directly with a saving in time if RCOND is not needed.
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C
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C On Entry
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C
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C ABD REAL(LDA, N)
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C contains the matrix in band storage. The columns
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C of the matrix are stored in the columns of ABD and
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C the diagonals of the matrix are stored in rows
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C ML+1 through 2*ML+MU+1 of ABD .
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C See the comments below for details.
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C
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C LDA INTEGER
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C the leading dimension of the array ABD .
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C LDA must be .GE. 2*ML + MU + 1 .
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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 0 .LE. ML .LT. N .
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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 0 .LE. MU .LT. N .
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C More efficient if ML .LE. MU .
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C On Return
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C
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C ABD an upper triangular matrix in band storage and
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C the multipliers which were used to obtain it.
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C The factorization can be written A = L*U , where
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C L is a product of permutation and unit lower
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C triangular matrices and U is upper triangular.
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C
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C IPVT INTEGER(N)
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C an integer vector of pivot indices.
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C
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C INFO INTEGER
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C = 0 normal value.
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C = K if U(K,K) .EQ. 0.0 . This is not an error
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C condition for this subroutine, but it does
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C indicate that SGBSL will divide by zero if
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C called. Use RCOND in SBGCO for a reliable
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C indication of singularity.
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C
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C Band Storage
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C
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C If A is a band matrix, the following program segment
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C will set up the input.
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C
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C ML = (band width below the diagonal)
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C MU = (band width above the diagonal)
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C M = ML + MU + 1
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C DO 20 J = 1, N
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C I1 = MAX(1, J-MU)
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C I2 = MIN(N, J+ML)
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C DO 10 I = I1, I2
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C K = I - J + M
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C ABD(K,J) = A(I,J)
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C 10 CONTINUE
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C 20 CONTINUE
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C
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C This uses rows ML+1 through 2*ML+MU+1 of ABD .
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C In addition, the first ML rows in ABD are used for
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C elements generated during the triangularization.
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C The total number of rows needed in ABD is 2*ML+MU+1 .
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C The ML+MU by ML+MU upper left triangle and the
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C ML by ML lower right triangle are not referenced.
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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 ISAMAX, SAXPY, SSCAL
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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 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 SGBFA
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INTEGER LDA,N,ML,MU,IPVT(*),INFO
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REAL ABD(LDA,*)
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C
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REAL T
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INTEGER I,ISAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1
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C
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C***FIRST EXECUTABLE STATEMENT SGBFA
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M = ML + MU + 1
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INFO = 0
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C
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C ZERO INITIAL FILL-IN COLUMNS
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C
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J0 = MU + 2
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J1 = MIN(N,M) - 1
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IF (J1 .LT. J0) GO TO 30
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DO 20 JZ = J0, J1
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I0 = M + 1 - JZ
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DO 10 I = I0, ML
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ABD(I,JZ) = 0.0E0
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10 CONTINUE
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20 CONTINUE
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30 CONTINUE
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JZ = J1
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JU = 0
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C
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C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
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C
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NM1 = N - 1
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IF (NM1 .LT. 1) GO TO 130
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DO 120 K = 1, NM1
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KP1 = K + 1
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C
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C ZERO NEXT FILL-IN COLUMN
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C
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JZ = JZ + 1
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IF (JZ .GT. N) GO TO 50
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IF (ML .LT. 1) GO TO 50
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DO 40 I = 1, ML
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ABD(I,JZ) = 0.0E0
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40 CONTINUE
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50 CONTINUE
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C
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C FIND L = PIVOT INDEX
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C
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LM = MIN(ML,N-K)
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L = ISAMAX(LM+1,ABD(M,K),1) + M - 1
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IPVT(K) = L + K - M
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C
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C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
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C
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IF (ABD(L,K) .EQ. 0.0E0) GO TO 100
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C
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C INTERCHANGE IF NECESSARY
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C
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IF (L .EQ. M) GO TO 60
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T = ABD(L,K)
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ABD(L,K) = ABD(M,K)
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ABD(M,K) = T
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60 CONTINUE
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C
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C COMPUTE MULTIPLIERS
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C
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T = -1.0E0/ABD(M,K)
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CALL SSCAL(LM,T,ABD(M+1,K),1)
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C
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C ROW ELIMINATION WITH COLUMN INDEXING
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C
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JU = MIN(MAX(JU,MU+IPVT(K)),N)
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MM = M
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IF (JU .LT. KP1) GO TO 90
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DO 80 J = KP1, JU
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L = L - 1
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MM = MM - 1
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T = ABD(L,J)
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IF (L .EQ. MM) GO TO 70
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ABD(L,J) = ABD(MM,J)
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ABD(MM,J) = T
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70 CONTINUE
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CALL SAXPY(LM,T,ABD(M+1,K),1,ABD(MM+1,J),1)
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80 CONTINUE
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90 CONTINUE
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GO TO 110
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100 CONTINUE
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INFO = K
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110 CONTINUE
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120 CONTINUE
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130 CONTINUE
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IPVT(N) = N
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IF (ABD(M,N) .EQ. 0.0E0) INFO = N
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RETURN
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END
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