/*

 * Copyright (c) 2017, Alliance for Open Media. All rights reserved

 *

 * This source code is subject to the terms of the BSD 2 Clause License and

 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License

 * was not distributed with this source code in the LICENSE file, you can

 * obtain it at www.aomedia.org/license/software. If the Alliance for Open

 * Media Patent License 1.0 was not distributed with this source code in the

 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.

 */

#ifndef AOM_AOM_DSP_MATHUTILS_H_

#define AOM_AOM_DSP_MATHUTILS_H_

#include <assert.h>

#include <math.h>

#include <string.h>

#include "aom_dsp/aom_dsp_common.h"

#include "aom_mem/aom_mem.h"

static const double TINY_NEAR_ZERO = 1.0E-16;

// Solves Ax = b, where x and b are column vectors of size nx1 and A is nxn

static INLINE int linsolve(int n, double *A, int stride, double *b, double *x) {

  int i, j, k;

  double c;

  // Forward elimination

  for (k = 0; k < n - 1; k++) {

    // Bring the largest magnitude to the diagonal position

    for (i = n - 1; i > k; i--) {

      if (fabs(A[(i - 1) * stride + k]) < fabs(A[i * stride + k])) {

        for (j = 0; j < n; j++) {

          c = A[i * stride + j];

          A[i * stride + j] = A[(i - 1) * stride + j];

          A[(i - 1) * stride + j] = c;

        }

        c = b[i];

        b[i] = b[i - 1];

        b[i - 1] = c;

      }

    }

    for (i = k; i < n - 1; i++) {

      if (fabs(A[k * stride + k]) < TINY_NEAR_ZERO) return 0;

      c = A[(i + 1) * stride + k] / A[k * stride + k];

      for (j = 0; j < n; j++) A[(i + 1) * stride + j] -= c * A[k * stride + j];

      b[i + 1] -= c * b[k];

    }

  }

  // Backward substitution

  for (i = n - 1; i >= 0; i--) {

    if (fabs(A[i * stride + i]) < TINY_NEAR_ZERO) return 0;

    c = 0;

    for (j = i + 1; j <= n - 1; j++) c += A[i * stride + j] * x[j];

    x[i] = (b[i] - c) / A[i * stride + i];

  }

  return 1;

}

Unexecuted instantiation: pickrst.c:linsolve

Unexecuted instantiation: noise_model.c:linsolve

Unexecuted instantiation: ransac.c:linsolve

////////////////////////////////////////////////////////////////////////////////

// Least-squares

// Solves for n-dim x in a least squares sense to minimize |Ax - b|^2

// The solution is simply x = (A'A)^-1 A'b or simply the solution for

// the system: A'A x = A'b

static INLINE int least_squares(int n, double *A, int rows, int stride,

                                double *b, double *scratch, double *x) {

  int i, j, k;

  double *scratch_ = NULL;

  double *AtA, *Atb;

  if (!scratch) {

    scratch_ = (double *)aom_malloc(sizeof(*scratch) * n * (n + 1));

    scratch = scratch_;

  }

  AtA = scratch;

  Atb = scratch + n * n;

  for (i = 0; i < n; ++i) {

    for (j = i; j < n; ++j) {

      AtA[i * n + j] = 0.0;

      for (k = 0; k < rows; ++k)

        AtA[i * n + j] += A[k * stride + i] * A[k * stride + j];

      AtA[j * n + i] = AtA[i * n + j];

    }

    Atb[i] = 0;

    for (k = 0; k < rows; ++k) Atb[i] += A[k * stride + i] * b[k];

  }

  int ret = linsolve(n, AtA, n, Atb, x);

  aom_free(scratch_);

  return ret;

}

Unexecuted instantiation: pickrst.c:least_squares

Unexecuted instantiation: noise_model.c:least_squares

Unexecuted instantiation: ransac.c:least_squares

// Matrix multiply

static INLINE void multiply_mat(const double *m1, const double *m2, double *res,

                                const int m1_rows, const int inner_dim,

                                const int m2_cols) {

  double sum;

  int row, col, inner;

  for (row = 0; row < m1_rows; ++row) {

    for (col = 0; col < m2_cols; ++col) {

      sum = 0;

      for (inner = 0; inner < inner_dim; ++inner)

        sum += m1[row * inner_dim + inner] * m2[inner * m2_cols + col];

      *(res++) = sum;

    }

  }

}

Unexecuted instantiation: pickrst.c:multiply_mat

Unexecuted instantiation: noise_model.c:multiply_mat

Unexecuted instantiation: ransac.c:multiply_mat

//

// The functions below are needed only for homography computation

// Remove if the homography models are not used.

//

///////////////////////////////////////////////////////////////////////////////

// svdcmp

// Adopted from Numerical Recipes in C

static INLINE double apply_sign(double a, double b) {

  return ((b) >= 0 ? fabs(a) : -fabs(a));

}

Unexecuted instantiation: pickrst.c:apply_sign

Unexecuted instantiation: noise_model.c:apply_sign

Unexecuted instantiation: ransac.c:apply_sign

static INLINE double pythag(double a, double b) {

  double ct;

  const double absa = fabs(a);

  const double absb = fabs(b);

  if (absa > absb) {

    ct = absb / absa;

    return absa * sqrt(1.0 + ct * ct);

  } else {

    ct = absa / absb;

    return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct);

  }

}

Unexecuted instantiation: pickrst.c:pythag

Unexecuted instantiation: noise_model.c:pythag

Unexecuted instantiation: ransac.c:pythag

static INLINE int svdcmp(double **u, int m, int n, double w[], double **v) {

  const int max_its = 30;

  int flag, i, its, j, jj, k, l, nm;

  double anorm, c, f, g, h, s, scale, x, y, z;

  double *rv1 = (double *)aom_malloc(sizeof(*rv1) * (n + 1));

  g = scale = anorm = 0.0;

  for (i = 0; i < n; i++) {

    l = i + 1;

    rv1[i] = scale * g;

    g = s = scale = 0.0;

    if (i < m) {

      for (k = i; k < m; k++) scale += fabs(u[k][i]);

      if (scale != 0.) {

        for (k = i; k < m; k++) {

          u[k][i] /= scale;

          s += u[k][i] * u[k][i];

        }

        f = u[i][i];

        g = -apply_sign(sqrt(s), f);

        h = f * g - s;

        u[i][i] = f - g;

        for (j = l; j < n; j++) {

          for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j];

          f = s / h;

          for (k = i; k < m; k++) u[k][j] += f * u[k][i];

        }

        for (k = i; k < m; k++) u[k][i] *= scale;

      }

    }

    w[i] = scale * g;

    g = s = scale = 0.0;

    if (i < m && i != n - 1) {

      for (k = l; k < n; k++) scale += fabs(u[i][k]);

      if (scale != 0.) {

        for (k = l; k < n; k++) {

          u[i][k] /= scale;

          s += u[i][k] * u[i][k];

        }

        f = u[i][l];

        g = -apply_sign(sqrt(s), f);

        h = f * g - s;

        u[i][l] = f - g;

        for (k = l; k < n; k++) rv1[k] = u[i][k] / h;

        for (j = l; j < m; j++) {

          for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k];

          for (k = l; k < n; k++) u[j][k] += s * rv1[k];

        }

        for (k = l; k < n; k++) u[i][k] *= scale;

      }

    }

    anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i])));

  }

  for (i = n - 1; i >= 0; i--) {

    if (i < n - 1) {

      if (g != 0.) {

        for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g;

        for (j = l; j < n; j++) {

          for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j];

          for (k = l; k < n; k++) v[k][j] += s * v[k][i];

        }

      }

      for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;

    }

    v[i][i] = 1.0;

    g = rv1[i];

    l = i;

  }

  for (i = AOMMIN(m, n) - 1; i >= 0; i--) {

    l = i + 1;

    g = w[i];

    for (j = l; j < n; j++) u[i][j] = 0.0;

    if (g != 0.) {

      g = 1.0 / g;

      for (j = l; j < n; j++) {

        for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j];

        f = (s / u[i][i]) * g;

        for (k = i; k < m; k++) u[k][j] += f * u[k][i];

      }

      for (j = i; j < m; j++) u[j][i] *= g;

    } else {

      for (j = i; j < m; j++) u[j][i] = 0.0;

    }

    ++u[i][i];

  }

  for (k = n - 1; k >= 0; k--) {

    for (its = 0; its < max_its; its++) {

      flag = 1;

      for (l = k; l >= 0; l--) {

        nm = l - 1;

        if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) {

          flag = 0;

          break;

        }

        if ((double)(fabs(w[nm]) + anorm) == anorm) break;

      }

      if (flag) {

        c = 0.0;

        s = 1.0;

        for (i = l; i <= k; i++) {

          f = s * rv1[i];

          rv1[i] = c * rv1[i];

          if ((double)(fabs(f) + anorm) == anorm) break;

          g = w[i];

          h = pythag(f, g);

          w[i] = h;

          h = 1.0 / h;

          c = g * h;

          s = -f * h;

          for (j = 0; j < m; j++) {

            y = u[j][nm];

            z = u[j][i];

            u[j][nm] = y * c + z * s;

            u[j][i] = z * c - y * s;

          }

        }

      }

      z = w[k];

      if (l == k) {

        if (z < 0.0) {

          w[k] = -z;

          for (j = 0; j < n; j++) v[j][k] = -v[j][k];

        }

        break;

      }

      if (its == max_its - 1) {

        aom_free(rv1);

        return 1;

      }

      assert(k > 0);

      x = w[l];

      nm = k - 1;

      y = w[nm];

      g = rv1[nm];

      h = rv1[k];

      f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);

      g = pythag(f, 1.0);

      f = ((x - z) * (x + z) + h * ((y / (f + apply_sign(g, f))) - h)) / x;

      c = s = 1.0;

      for (j = l; j <= nm; j++) {

        i = j + 1;

        g = rv1[i];

        y = w[i];

        h = s * g;

        g = c * g;

        z = pythag(f, h);

        rv1[j] = z;

        c = f / z;

        s = h / z;

        f = x * c + g * s;

        g = g * c - x * s;

        h = y * s;

        y *= c;

        for (jj = 0; jj < n; jj++) {

          x = v[jj][j];

          z = v[jj][i];

          v[jj][j] = x * c + z * s;

          v[jj][i] = z * c - x * s;

        }

        z = pythag(f, h);

        w[j] = z;

        if (z != 0.) {

          z = 1.0 / z;

          c = f * z;

          s = h * z;

        }

        f = c * g + s * y;

        x = c * y - s * g;

        for (jj = 0; jj < m; jj++) {

          y = u[jj][j];

          z = u[jj][i];

          u[jj][j] = y * c + z * s;

          u[jj][i] = z * c - y * s;

        }

      }

      rv1[l] = 0.0;

      rv1[k] = f;

      w[k] = x;

    }

  }

  aom_free(rv1);

  return 0;

}

Unexecuted instantiation: pickrst.c:svdcmp

Unexecuted instantiation: noise_model.c:svdcmp

Unexecuted instantiation: ransac.c:svdcmp

static INLINE int SVD(double *U, double *W, double *V, double *matx, int M,

                      int N) {

  // Assumes allocation for U is MxN

  double **nrU = (double **)aom_malloc((M) * sizeof(*nrU));

  double **nrV = (double **)aom_malloc((N) * sizeof(*nrV));

  int problem, i;

  problem = !(nrU && nrV);

  if (!problem) {

    for (i = 0; i < M; i++) {

      nrU[i] = &U[i * N];

    }

    for (i = 0; i < N; i++) {

      nrV[i] = &V[i * N];

    }

  } else {

    if (nrU) aom_free(nrU);

    if (nrV) aom_free(nrV);

    return 1;

  }

  /* copy from given matx into nrU */

  for (i = 0; i < M; i++) {

    memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx));

  }

  /* HERE IT IS: do SVD */

  if (svdcmp(nrU, M, N, W, nrV)) {

    aom_free(nrU);

    aom_free(nrV);

    return 1;

  }

  /* aom_free Numerical Recipes arrays */

  aom_free(nrU);

  aom_free(nrV);

  return 0;

}

Unexecuted instantiation: pickrst.c:SVD

Unexecuted instantiation: noise_model.c:SVD

Unexecuted instantiation: ransac.c:SVD

#endif  // AOM_AOM_DSP_MATHUTILS_H_