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-/*
- * 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_AV1_ENCODER_MATHUTILS_H_
-#define AOM_AV1_ENCODER_MATHUTILS_H_
-
-#include <memory.h>
-#include <math.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <assert.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
-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);
- if (scratch_) aom_free(scratch_);
- return ret;
-}
-
-// 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;
- }
- }
-}
-
-//
-// 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 sign(double a, double b) {
- return ((b) >= 0 ? fabs(a) : -fabs(a));
-}
-
-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);
- }
-}
-
-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 = -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 = -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 + 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;
-}
-
-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;
-}
-
-#endif // AOM_AV1_ENCODER_MATHUTILS_H_
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