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SUBROUTINE SGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z)
INTEGER LDA,N,ML,MU,IPVT(1)
REAL ABD(LDA,1),Z(1)
REAL RCOND
C
C SGBCO FACTORS A REAL BAND MATRIX BY GAUSSIAN
C ELIMINATION AND ESTIMATES THE CONDITION OF THE MATRIX.
C
C IF RCOND IS NOT NEEDED, SGBFA IS SLIGHTLY FASTER.
C TO SOLVE A*X = B , FOLLOW SGBCO BY SGBSL.
C TO COMPUTE INVERSE(A)*C , FOLLOW SGBCO BY SGBSL.
C TO COMPUTE DETERMINANT(A) , FOLLOW SGBCO BY SGBDI.
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
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 RCOND REAL
C AN ESTIMATE OF THE RECIPROCAL CONDITION OF A .
C FOR THE SYSTEM A*X = B , RELATIVE PERTURBATIONS
C IN A AND B OF SIZE EPSILON MAY CAUSE
C RELATIVE PERTURBATIONS IN X OF SIZE EPSILON/RCOND .
C IF RCOND IS SO SMALL THAT THE LOGICAL EXPRESSION
C 1.0 + RCOND .EQ. 1.0
C IS TRUE, THEN A MAY BE SINGULAR TO WORKING
C PRECISION. IN PARTICULAR, RCOND IS ZERO IF
C EXACT SINGULARITY IS DETECTED OR THE ESTIMATE
C UNDERFLOWS.
C
C Z REAL(N)
C A WORK VECTOR WHOSE CONTENTS ARE USUALLY UNIMPORTANT.
C IF A IS CLOSE TO A SINGULAR MATRIX, THEN Z IS
C AN APPROXIMATE NULL VECTOR IN THE SENSE THAT
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
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 EXAMPLE.. IF THE ORIGINAL MATRIX IS
C
C 11 12 13 0 0 0
C 21 22 23 24 0 0
C 0 32 33 34 35 0
C 0 0 43 44 45 46
C 0 0 0 54 55 56
C 0 0 0 0 65 66
C
C THEN N = 6, ML = 1, MU = 2, LDA .GE. 5 AND ABD SHOULD CONTAIN
C
C * * * + + + , * = NOT USED
C * * 13 24 35 46 , + = USED FOR PIVOTING
C * 12 23 34 45 56
C 11 22 33 44 55 66
C 21 32 43 54 65 *
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 LINPACK SGBFA
C BLAS SAXPY,SDOT,SSCAL,SASUM
C FORTRAN ABS,AMAX1,MAX0,MIN0,SIGN