LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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spbequ.f File Reference

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subroutine spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)

Function/Subroutine Documentation

subroutine spbequ ( character  UPLO,
integer  N,
integer  KD,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( * )  S,
real  SCOND,
real  AMAX,
integer  INFO 


Download SPBEQU + dependencies [TGZ] [ZIP] [TXT]
 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
          UPLO is CHARACTER*1
          = 'U':  Upper triangular of A is stored;
          = 'L':  Lower triangular of A is stored.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          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 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 is INTEGER
          The leading dimension of the array A.  LDAB >= KD+1.
          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
          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 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 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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011

Definition at line 130 of file spbequ.f.

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