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SUBROUTINE SPBCO(ABD,LDA,N,M,RCOND,Z,INFO)
INTEGER LDA,N,M,INFO
REAL ABD(LDA,1),Z(1)
REAL RCOND
C
C SPBCO FACTORS A REAL SYMMETRIC POSITIVE DEFINITE MATRIX
C STORED IN BAND FORM AND ESTIMATES THE CONDITION OF THE MATRIX.
C
C IF RCOND IS NOT NEEDED, SPBFA IS SLIGHTLY FASTER.
C TO SOLVE A*X = B , FOLLOW SPBCO BY SPBSL.
C TO COMPUTE INVERSE(A)*C , FOLLOW SPBCO BY SPBSL.
C TO COMPUTE DETERMINANT(A) , FOLLOW SPBCO BY SPBDI.
C
C ON ENTRY
C
C ABD REAL(LDA, N)
C THE MATRIX TO BE FACTORED. THE COLUMNS OF THE UPPER
C TRIANGLE ARE STORED IN THE COLUMNS OF ABD AND THE
C DIAGONALS OF THE UPPER TRIANGLE ARE STORED IN THE
C ROWS OF ABD . SEE THE COMMENTS BELOW FOR DETAILS.
C
C LDA INTEGER
C THE LEADING DIMENSION OF THE ARRAY ABD .
C LDA MUST BE .GE. M + 1 .
C
C N INTEGER
C THE ORDER OF THE MATRIX A .
C
C M INTEGER
C THE NUMBER OF DIAGONALS ABOVE THE MAIN DIAGONAL.
C 0 .LE. M .LT. N .
C
C ON RETURN
C
C ABD AN UPPER TRIANGULAR MATRIX R , STORED IN BAND
C FORM, SO THAT A = TRANS(R)*R .
C IF INFO .NE. 0 , THE FACTORIZATION IS NOT COMPLETE.
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. IF INFO .NE. 0 , RCOND IS UNCHANGED.
C
C Z REAL(N)
C A WORK VECTOR WHOSE CONTENTS ARE USUALLY UNIMPORTANT
C IF A IS SINGULAR TO WORKING PRECISION, THEN Z IS
C AN APPROXIMATE NULL VECTOR IN THE SENSE THAT
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C IF INFO .NE. 0 , Z IS UNCHANGED.
C
C INFO INTEGER
C = 0 FOR NORMAL RETURN.
C = K SIGNALS AN ERROR CONDITION. THE LEADING MINOR
C OF ORDER K IS NOT POSITIVE DEFINITE.
C
C BAND STORAGE
C
C IF A IS A SYMMETRIC POSITIVE DEFINITE BAND MATRIX,
C THE FOLLOWING PROGRAM SEGMENT WILL SET UP THE INPUT.
C
C M = (BAND WIDTH ABOVE DIAGONAL)
C DO 20 J = 1, N
C I1 = MAX0(1, J-M)
C DO 10 I = I1, J
C K = I-J+M+1
C ABD(K,J) = A(I,J)
C 10 CONTINUE
C 20 CONTINUE
C
C THIS USES M + 1 ROWS OF A , EXCEPT FOR THE M BY M
C UPPER LEFT TRIANGLE, WHICH IS IGNORED.
C
C EXAMPLE.. IF THE ORIGINAL MATRIX IS
C
C 11 12 13 0 0 0
C 12 22 23 24 0 0
C 13 23 33 34 35 0
C 0 24 34 44 45 46
C 0 0 35 45 55 56
C 0 0 0 46 56 66
C
C THEN N = 6 , M = 2 AND ABD SHOULD CONTAIN
C
C * * 13 24 35 46
C * 12 23 34 45 56
C 11 22 33 44 55 66
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 SPBFA
C BLAS SAXPY,SDOT,SSCAL,SASUM
C FORTRAN ABS,AMAX1,MAX0,MIN0,REAL,SIGN
C