145 lines
4.5 KiB
C
145 lines
4.5 KiB
C
/*
|
|
* 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;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////////////////
|
|
// 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));
|
|
}
|
|
|
|
// 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);
|
|
}
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
static inline int least_squares_solve(double *mat, double *y, double *x,
|
|
int n) {
|
|
return linsolve(n, mat, n, y, x);
|
|
}
|
|
|
|
// 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;
|
|
}
|
|
}
|
|
}
|
|
|
|
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
|
|
}
|
|
#endif // AOM_AOM_DSP_MATHUTILS_H_
|