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SUBROUTINE SGBFA(ABD,LDA,N,ML,MU,IPVT,INFO)
INTEGER LDA,N,ML,MU,IPVT(1),INFO
REAL ABD(LDA,1)
C
C SGBFA FACTORS A REAL BAND MATRIX BY ELIMINATION.
C
C SGBFA IS USUALLY CALLED BY SGBCO, BUT IT CAN BE CALLED
C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED.
C
C ON ENTRY
C
C ABD REAL(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 SGBSL WILL DIVIDE BY ZERO IF
C CALLED. USE RCOND IN SGBCO 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 = MAX0(1, J-MU)
C I2 = MIN0(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 LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C SUBROUTINES AND FUNCTIONS
C
C BLAS SAXPY,SSCAL,ISAMAX
C FORTRAN MAX0,MIN0
C