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# SPBFA

```       SUBROUTINE SPBFA(ABD,LDA,N,M,INFO)
INTEGER LDA,N,M,INFO
REAL ABD(LDA,1)
C
C     SPBFA FACTORS A REAL SYMMETRIC POSITIVE DEFINITE MATRIX
C     STORED IN BAND FORM.
C
C     SPBFA IS USUALLY CALLED BY SPBCO, 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                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
C        INFO    INTEGER
C                = 0  FOR NORMAL RETURN.
C                = K  IF THE LEADING MINOR OF ORDER  K  IS NOT
C                     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     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 SDOT
C     FORTRAN MAX0,SQRT
C

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