/*
 * Copyright (c) 2005-2017 National Technology & Engineering Solutions
 * of Sandia, LLC (NTESS).  Under the terms of Contract DE-NA0003525 with
 * NTESS, the U.S. Government retains certain rights in this software.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *
 *     * Redistributions of source code must retain the above copyright
 *       notice, this list of conditions and the following disclaimer.
 *
 *     * Redistributions in binary form must reproduce the above
 *       copyright notice, this list of conditions and the following
 *       disclaimer in the documentation and/or other materials provided
 *       with the distribution.
 *
 *     * Neither the name of NTESS nor the names of its
 *       contributors may be used to endorse or promote products derived
 *       from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 */

#include "defs.h"
#include <math.h>

/* Find eigenvalues of 2x2 symmetric system by solving quadratic. */
void evals2(double  H[2][2], /* symmetric matrix for eigenvalues */
            double *eval1,   /* smallest eigenvalue */
            double *eval2    /* middle eigenvalue */
)
{
  double M[2][2];      /* normalized version of matrix */
  double b, c;         /* coefficients of cubic equation */
  double root1, root2; /* roots of quadratic */
  double xmax;         /* largest matrix element */
  int    i, j;         /* loop counters */

  M[0][0] = M[1][0] = M[0][1] = M[1][1] = 0.0;

  xmax = 0.0;
  for (i = 0; i < 2; i++) {
    for (j = i; j < 2; j++) {
      if (fabs(H[i][j]) > xmax) {
        xmax = fabs(H[i][j]);
      }
    }
  }
  if (xmax != 0) {
    for (i = 0; i < 2; i++) {
      for (j = 0; j < 2; j++) {
        M[i][j] = H[i][j] / xmax;
      }
    }
  }

  b     = -M[0][0] - M[1][1];
  c     = M[0][0] * M[1][1] - M[1][0] * M[1][0];
  root1 = -.5 * (b + sign(b) * sqrt(b * b - 4 * c));
  root2 = c / root1;

  root1 *= xmax;
  root2 *= xmax;
  *eval1 = min(root1, root2);
  *eval2 = max(root1, root2);
}

/* Solve for eigenvector of SPD 2x2 matrix, with given eigenvalue. */
void eigenvec2(double  A[2][2], /* matrix */
               double  eval,    /* eigenvalue */
               double  evec[2], /* eigenvector returned */
               double *res      /* normalized residual */
)
{
  double norm;       /* norm of eigenvector */
  double res1, res2; /* components of residual vector */
  int    i;          /* loop counter */

  if (fabs(A[0][0] - eval) > fabs(A[1][1] - eval)) {
    evec[0] = -A[1][0];
    evec[1] = A[0][0] - eval;
  }
  else {
    evec[0] = A[1][1] - eval;
    evec[1] = -A[1][0];
  }

  /* Normalize eigenvector and calculate a normalized eigen-residual. */
  norm = sqrt(evec[0] * evec[0] + evec[1] * evec[1]);
  if (norm == 0) {
    evec[0] = 1;
    evec[1] = 0;
    norm    = 1;
  }
  for (i = 0; i < 2; i++) {
    evec[i] /= norm;
  }
  res1 = (A[0][0] - eval) * evec[0] + A[1][0] * evec[1];
  res2 = A[1][0] * evec[0] + (A[1][1] - eval) * evec[1];
  *res = sqrt(res1 * res1 + res2 * res2);

  res1 = fabs(A[0][0]) + fabs(A[1][0]);
  res2 = fabs(A[1][1]) + fabs(A[1][0]);
  *res /= max(res1, res2);
}
