LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
dpbequ.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine DPBEQU ( CHARACTER  UPLO,
INTEGER  N,
INTEGER  KD,
DOUBLE PRECISION, dimension( ldab, * )  AB,
INTEGER  LDAB,
DOUBLE PRECISION, dimension( * )  S,
DOUBLE PRECISION  SCOND,
DOUBLE PRECISION  AMAX,
INTEGER  INFO 
)

DPBEQU

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Purpose: 

 DPBEQU 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:
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangular of A is stored;
          = 'L':  Lower triangular of A is stored.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]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.
[in]AB
          AB is DOUBLE PRECISION 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).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array A.  LDAB >= KD+1.
[out]S
          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
[out]SCOND
          SCOND is DOUBLE PRECISION
          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.
[out]AMAX
          AMAX is DOUBLE PRECISION
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.
[out]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 dpbequ.f.

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