spbequ.f(3)

NAME
spbequ.f -

SYNOPSIS

  Functions/Subroutines
subroutine spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
SPBEQU

Function/Subroutine Documentation

  subroutine spbequ (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND, realAMAX, integerINFO)

Purpose:

     SPBEQU computes row and column scalings intended to equilibrate a
     symmetric positive definite band matrix A and reduce its condition
     number (with respect to the two-norm).  S contains the scale factors,
     S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
     elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
     choice of S puts the condition number of B within a factor N of the
     smallest possible condition number over all possible diagonal
     scalings.

Parameters:
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangular of A is stored;
              = 'L':  Lower triangular of A is stored.

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is REAL array, dimension (LDAB,N)
              The upper or lower triangle of the symmetric band matrix A,
              stored in the first KD+1 rows of the array.  The j-th column
              of A is stored in the j-th column of the array AB as follows:
              if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

    LDAB

              LDAB is INTEGER
              The leading dimension of the array A.  LDAB >= KD+1.

    S

              S is REAL array, dimension (N)
              If INFO = 0, S contains the scale factors for A.

    SCOND

              SCOND is REAL
              If INFO = 0, S contains the ratio of the smallest S(i) to
              the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
              large nor too small, it is not worth scaling by S.

    AMAX

              AMAX is REAL
              Absolute value of largest matrix element.  If AMAX is very
              close to overflow or very close to underflow, the matrix
              should be scaled.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              > 0:  if INFO = i, the i-th diagonal element is nonpositive.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 130 of file spbequ.f.

Author

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