*DECK CGBFA SUBROUTINE CGBFA (ABD, LDA, N, ML, MU, IPVT, INFO) C***BEGIN PROLOGUE CGBFA C***PURPOSE Factor a band matrix using Gaussian elimination. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2C2 C***TYPE COMPLEX (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 CGBFA factors a complex band matrix by elimination. C C CGBFA is usually called by CGBCO, but it can be called C directly with a saving in time if RCOND is not needed. C C On Entry C C ABD COMPLEX(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 CGBSL will divide by zero if C called. Use RCOND in CGBCO 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 CAXPY, CSCAL, ICAMAX 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 CGBFA INTEGER LDA,N,ML,MU,IPVT(*),INFO COMPLEX ABD(LDA,*) C COMPLEX T INTEGER I,ICAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1 COMPLEX ZDUM REAL CABS1 CABS1(ZDUM) = ABS(REAL(ZDUM)) + ABS(AIMAG(ZDUM)) C C***FIRST EXECUTABLE STATEMENT CGBFA 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) = (0.0E0,0.0E0) 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) = (0.0E0,0.0E0) 40 CONTINUE 50 CONTINUE C C FIND L = PIVOT INDEX C LM = MIN(ML,N-K) L = ICAMAX(LM+1,ABD(M,K),1) + M - 1 IPVT(K) = L + K - M C C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED C IF (CABS1(ABD(L,K)) .EQ. 0.0E0) 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 = -(1.0E0,0.0E0)/ABD(M,K) CALL CSCAL(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 CAXPY(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 (CABS1(ABD(M,N)) .EQ. 0.0E0) INFO = N RETURN END