/*

 * 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"

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: temporal_filter.c:linsolve

Unexecuted instantiation: noise_model.c:linsolve

Unexecuted instantiation: ml.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

//

// This process is split into three steps in order to avoid needing to

// explicitly allocate the A matrix, which may be very large if there

// are many equations to solve.

//

// The process for using this is (in pseudocode):

//

// Allocate mat (size n*n), y (size n), a (size n), x (size n)

// least_squares_init(mat, y, n)

// for each equation a . x = b {

//    least_squares_accumulate(mat, y, a, b, n)

// }

// least_squares_solve(mat, y, x, n)

//

// where:

// * mat, y are accumulators for the values A'A and A'b respectively,

// * a, b are the coefficients of each individual equation,

// * x is the result vector

// * and n is the problem size

static inline void least_squares_init(double *mat, double *y, int n) {

  memset(mat, 0, n * n * sizeof(double));

  memset(y, 0, n * sizeof(double));

}

Unexecuted instantiation: pickrst.c:least_squares_init

Unexecuted instantiation: temporal_filter.c:least_squares_init

Unexecuted instantiation: noise_model.c:least_squares_init

Unexecuted instantiation: ml.c:least_squares_init

Unexecuted instantiation: ransac.c:least_squares_init

// Round the given positive value to nearest integer

static AOM_FORCE_INLINE int iroundpf(float x) {

  assert(x >= 0.0);

  return (int)(x + 0.5f);

}

Unexecuted instantiation: pickrst.c:iroundpf

Unexecuted instantiation: temporal_filter.c:iroundpf

Unexecuted instantiation: noise_model.c:iroundpf

Unexecuted instantiation: ml.c:iroundpf

Unexecuted instantiation: ransac.c:iroundpf

static inline void least_squares_accumulate(double *mat, double *y,

                                            const double *a, double b, int n) {

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

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

      mat[i * n + j] += a[i] * a[j];

    }

  }

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

    y[i] += a[i] * b;

  }

}

Unexecuted instantiation: pickrst.c:least_squares_accumulate

Unexecuted instantiation: temporal_filter.c:least_squares_accumulate

Unexecuted instantiation: noise_model.c:least_squares_accumulate

Unexecuted instantiation: ml.c:least_squares_accumulate

Unexecuted instantiation: ransac.c:least_squares_accumulate

static inline int least_squares_solve(double *mat, double *y, double *x,

                                      int n) {

  return linsolve(n, mat, n, y, x);

}

Unexecuted instantiation: pickrst.c:least_squares_solve

Unexecuted instantiation: temporal_filter.c:least_squares_solve

Unexecuted instantiation: noise_model.c:least_squares_solve

Unexecuted instantiation: ml.c:least_squares_solve

Unexecuted instantiation: ransac.c:least_squares_solve

// 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: temporal_filter.c:multiply_mat

Unexecuted instantiation: noise_model.c:multiply_mat

Unexecuted instantiation: ml.c:multiply_mat

Unexecuted instantiation: ransac.c:multiply_mat

static inline float approx_exp(float y) {

#define A ((1 << 23) / 0.69314718056f)  // (1 << 23) / ln(2)

#define B \

  127  // Offset for the exponent according to IEEE floating point standard.

#define C 60801  // Magic number controls the accuracy of approximation

  union {

    float as_float;

    int32_t as_int32;

  } container;

  container.as_int32 = ((int32_t)(y * A)) + ((B << 23) - C);

  return container.as_float;

#undef A

#undef B

#undef C

}

Unexecuted instantiation: pickrst.c:approx_exp

Unexecuted instantiation: temporal_filter.c:approx_exp

Unexecuted instantiation: noise_model.c:approx_exp

Unexecuted instantiation: ml.c:approx_exp

Unexecuted instantiation: ransac.c:approx_exp

#endif  // AOM_AOM_DSP_MATHUTILS_H_