mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2025-01-01 06:23:39 +01:00
187 lines
5.8 KiB
Fortran
187 lines
5.8 KiB
Fortran
*DECK DGBFA
|
|
SUBROUTINE DGBFA (ABD, LDA, N, ML, MU, IPVT, INFO)
|
|
C***BEGIN PROLOGUE DGBFA
|
|
C***PURPOSE Factor a band matrix using Gaussian elimination.
|
|
C***LIBRARY SLATEC (LINPACK)
|
|
C***CATEGORY D2A2
|
|
C***TYPE DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C)
|
|
C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION
|
|
C***AUTHOR Moler, C. B., (U. of New Mexico)
|
|
C***DESCRIPTION
|
|
C
|
|
C DGBFA factors a double precision band matrix by elimination.
|
|
C
|
|
C DGBFA is usually called by DGBCO, but it can be called
|
|
C directly with a saving in time if RCOND is not needed.
|
|
C
|
|
C On Entry
|
|
C
|
|
C ABD DOUBLE PRECISION(LDA, N)
|
|
C contains the matrix in band storage. The columns
|
|
C of the matrix are stored in the columns of ABD and
|
|
C the diagonals of the matrix are stored in rows
|
|
C ML+1 through 2*ML+MU+1 of ABD .
|
|
C See the comments below for details.
|
|
C
|
|
C LDA INTEGER
|
|
C the leading dimension of the array ABD .
|
|
C LDA must be .GE. 2*ML + MU + 1 .
|
|
C
|
|
C N INTEGER
|
|
C the order of the original matrix.
|
|
C
|
|
C ML INTEGER
|
|
C number of diagonals below the main diagonal.
|
|
C 0 .LE. ML .LT. N .
|
|
C
|
|
C MU INTEGER
|
|
C number of diagonals above the main diagonal.
|
|
C 0 .LE. MU .LT. N .
|
|
C More efficient if ML .LE. MU .
|
|
C On Return
|
|
C
|
|
C ABD an upper triangular matrix in band storage and
|
|
C the multipliers which were used to obtain it.
|
|
C The factorization can be written A = L*U where
|
|
C L is a product of permutation and unit lower
|
|
C triangular matrices and U is upper triangular.
|
|
C
|
|
C IPVT INTEGER(N)
|
|
C an integer vector of pivot indices.
|
|
C
|
|
C INFO INTEGER
|
|
C = 0 normal value.
|
|
C = K if U(K,K) .EQ. 0.0 . This is not an error
|
|
C condition for this subroutine, but it does
|
|
C indicate that DGBSL will divide by zero if
|
|
C called. Use RCOND in DGBCO for a reliable
|
|
C indication of singularity.
|
|
C
|
|
C Band Storage
|
|
C
|
|
C If A is a band matrix, the following program segment
|
|
C will set up the input.
|
|
C
|
|
C ML = (band width below the diagonal)
|
|
C MU = (band width above the diagonal)
|
|
C M = ML + MU + 1
|
|
C DO 20 J = 1, N
|
|
C I1 = MAX(1, J-MU)
|
|
C I2 = MIN(N, J+ML)
|
|
C DO 10 I = I1, I2
|
|
C K = I - J + M
|
|
C ABD(K,J) = A(I,J)
|
|
C 10 CONTINUE
|
|
C 20 CONTINUE
|
|
C
|
|
C This uses rows ML+1 through 2*ML+MU+1 of ABD .
|
|
C In addition, the first ML rows in ABD are used for
|
|
C elements generated during the triangularization.
|
|
C The total number of rows needed in ABD is 2*ML+MU+1 .
|
|
C The ML+MU by ML+MU upper left triangle and the
|
|
C ML by ML lower right triangle are not referenced.
|
|
C
|
|
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
|
|
C Stewart, LINPACK Users' Guide, SIAM, 1979.
|
|
C***ROUTINES CALLED DAXPY, DSCAL, IDAMAX
|
|
C***REVISION HISTORY (YYMMDD)
|
|
C 780814 DATE WRITTEN
|
|
C 890531 Changed all specific intrinsics to generic. (WRB)
|
|
C 890831 Modified array declarations. (WRB)
|
|
C 890831 REVISION DATE from Version 3.2
|
|
C 891214 Prologue converted to Version 4.0 format. (BAB)
|
|
C 900326 Removed duplicate information from DESCRIPTION section.
|
|
C (WRB)
|
|
C 920501 Reformatted the REFERENCES section. (WRB)
|
|
C***END PROLOGUE DGBFA
|
|
INTEGER LDA,N,ML,MU,IPVT(*),INFO
|
|
DOUBLE PRECISION ABD(LDA,*)
|
|
C
|
|
DOUBLE PRECISION T
|
|
INTEGER I,IDAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1
|
|
C
|
|
C***FIRST EXECUTABLE STATEMENT DGBFA
|
|
M = ML + MU + 1
|
|
INFO = 0
|
|
C
|
|
C ZERO INITIAL FILL-IN COLUMNS
|
|
C
|
|
J0 = MU + 2
|
|
J1 = MIN(N,M) - 1
|
|
IF (J1 .LT. J0) GO TO 30
|
|
DO 20 JZ = J0, J1
|
|
I0 = M + 1 - JZ
|
|
DO 10 I = I0, ML
|
|
ABD(I,JZ) = 0.0D0
|
|
10 CONTINUE
|
|
20 CONTINUE
|
|
30 CONTINUE
|
|
JZ = J1
|
|
JU = 0
|
|
C
|
|
C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
|
|
C
|
|
NM1 = N - 1
|
|
IF (NM1 .LT. 1) GO TO 130
|
|
DO 120 K = 1, NM1
|
|
KP1 = K + 1
|
|
C
|
|
C ZERO NEXT FILL-IN COLUMN
|
|
C
|
|
JZ = JZ + 1
|
|
IF (JZ .GT. N) GO TO 50
|
|
IF (ML .LT. 1) GO TO 50
|
|
DO 40 I = 1, ML
|
|
ABD(I,JZ) = 0.0D0
|
|
40 CONTINUE
|
|
50 CONTINUE
|
|
C
|
|
C FIND L = PIVOT INDEX
|
|
C
|
|
LM = MIN(ML,N-K)
|
|
L = IDAMAX(LM+1,ABD(M,K),1) + M - 1
|
|
IPVT(K) = L + K - M
|
|
C
|
|
C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
|
|
C
|
|
IF (ABD(L,K) .EQ. 0.0D0) GO TO 100
|
|
C
|
|
C INTERCHANGE IF NECESSARY
|
|
C
|
|
IF (L .EQ. M) GO TO 60
|
|
T = ABD(L,K)
|
|
ABD(L,K) = ABD(M,K)
|
|
ABD(M,K) = T
|
|
60 CONTINUE
|
|
C
|
|
C COMPUTE MULTIPLIERS
|
|
C
|
|
T = -1.0D0/ABD(M,K)
|
|
CALL DSCAL(LM,T,ABD(M+1,K),1)
|
|
C
|
|
C ROW ELIMINATION WITH COLUMN INDEXING
|
|
C
|
|
JU = MIN(MAX(JU,MU+IPVT(K)),N)
|
|
MM = M
|
|
IF (JU .LT. KP1) GO TO 90
|
|
DO 80 J = KP1, JU
|
|
L = L - 1
|
|
MM = MM - 1
|
|
T = ABD(L,J)
|
|
IF (L .EQ. MM) GO TO 70
|
|
ABD(L,J) = ABD(MM,J)
|
|
ABD(MM,J) = T
|
|
70 CONTINUE
|
|
CALL DAXPY(LM,T,ABD(M+1,K),1,ABD(MM+1,J),1)
|
|
80 CONTINUE
|
|
90 CONTINUE
|
|
GO TO 110
|
|
100 CONTINUE
|
|
INFO = K
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
IPVT(N) = N
|
|
IF (ABD(M,N) .EQ. 0.0D0) INFO = N
|
|
RETURN
|
|
END
|