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Diffstat (limited to 'media/libaom/src/av1/encoder/mathutils.h')
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1 files changed, 359 insertions, 0 deletions
diff --git a/media/libaom/src/av1/encoder/mathutils.h b/media/libaom/src/av1/encoder/mathutils.h new file mode 100644 index 000000000..64f936176 --- /dev/null +++ b/media/libaom/src/av1/encoder/mathutils.h @@ -0,0 +1,359 @@ +/* + * 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_ |