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/* Computation of Gerschgorin interval for symmetric, tridiagonal matrix */

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cfloat>

#include "util.h"
#include "gerschgorin.h"

////////////////////////////////////////////////////////////////////////////////
//! Compute Gerschgorin interval for symmetric, tridiagonal matrix
//! @param  d  diagonal elements
//! @param  s  superdiagonal elements
//! @param  n  size of matrix
//! @param  lg  lower limit of Gerschgorin interval
//! @param  ug  upper limit of Gerschgorin interval
////////////////////////////////////////////////////////////////////////////////
void computeGerschgorin(float *d, float *s, unsigned int n, float &lg,
                        float &ug) {
  lg = FLT_MAX;
  ug = -FLT_MAX;

  // compute bounds
  for (unsigned int i = 1; i < (n - 1); ++i) {
    // sum over the absolute values of all elements of row i
    float sum_abs_ni = fabsf(s[i - 1]) + fabsf(s[i]);

    lg = min(lg, d[i] - sum_abs_ni);
    ug = max(ug, d[i] + sum_abs_ni);
  }

  // first and last row, only one superdiagonal element

  // first row
  lg = min(lg, d[0] - fabsf(s[0]));
  ug = max(ug, d[0] + fabsf(s[0]));

  // last row
  lg = min(lg, d[n - 1] - fabsf(s[n - 2]));
  ug = max(ug, d[n - 1] + fabsf(s[n - 2]));

  // increase interval to avoid side effects of fp arithmetic
  float bnorm = max(fabsf(ug), fabsf(lg));

  // these values depend on the implementation of floating count that is
  // employed in the following
  float psi_0 = 11 * FLT_EPSILON * bnorm;
  float psi_n = 11 * FLT_EPSILON * bnorm;

  lg = lg - bnorm * 2 * n * FLT_EPSILON - psi_0;
  ug = ug + bnorm * 2 * n * FLT_EPSILON + psi_n;

  ug = max(lg, ug);
}