Add files to solve linear equations for sparse matrices.
Change-Id: I3b539aa5adaee8c3a82e41ff4ed9f9da647b826f
diff --git a/av1/av1.cmake b/av1/av1.cmake
index 3687459..3eb4a1f 100644
--- a/av1/av1.cmake
+++ b/av1/av1.cmake
@@ -276,7 +276,10 @@
endif()
if(CONFIG_OPTICAL_FLOW_API)
- list(APPEND AOM_AV1_ENCODER_SOURCES "${AOM_ROOT}/av1/encoder/optical_flow.c"
+ list(APPEND AOM_AV1_ENCODER_SOURCES
+ "${AOM_ROOT}/av1/encoder/sparse_linear_solver.c"
+ "${AOM_ROOT}/av1/encoder/sparse_linear_solver.h"
+ "${AOM_ROOT}/av1/encoder/optical_flow.c"
"${AOM_ROOT}/av1/encoder/optical_flow.h")
endif()
diff --git a/av1/encoder/sparse_linear_solver.c b/av1/encoder/sparse_linear_solver.c
new file mode 100644
index 0000000..1c556c2
--- /dev/null
+++ b/av1/encoder/sparse_linear_solver.c
@@ -0,0 +1,411 @@
+/*
+ * Copyright (c) 2021, 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.
+ */
+#include <float.h>
+#include "av1/common/av1_common_int.h"
+#include "av1/encoder/sparse_linear_solver.h"
+#include "config/aom_config.h"
+#include "aom_mem/aom_mem.h"
+#include "av1/common/alloccommon.h"
+
+#if CONFIG_OPTICAL_FLOW_API
+
+/*
+ * Input:
+ * rows: array of row positions
+ * cols: array of column positions
+ * values: array of element values
+ * num_elem: total number of elements in the matrix
+ * num_rows: number of rows in the matrix
+ * num_cols: number of columns in the matrix
+ *
+ * Output:
+ * sm: pointer to the sparse matrix to be initialized
+ */
+void av1_init_sparse_mtx(const int *rows, const int *cols, const double *values,
+ int num_elem, int num_rows, int num_cols,
+ SPARSE_MTX *sm) {
+ sm->n_elem = num_elem;
+ sm->n_rows = num_rows;
+ sm->n_cols = num_cols;
+ if (num_elem == 0) {
+ sm->row_pos = NULL;
+ sm->col_pos = NULL;
+ sm->value = NULL;
+ return;
+ }
+ sm->row_pos = aom_calloc(num_elem, sizeof(*sm->row_pos));
+ sm->col_pos = aom_calloc(num_elem, sizeof(*sm->col_pos));
+ sm->value = aom_calloc(num_elem, sizeof(*sm->value));
+
+ memcpy(sm->row_pos, rows, num_elem * sizeof(*sm->row_pos));
+ memcpy(sm->col_pos, cols, num_elem * sizeof(*sm->col_pos));
+ memcpy(sm->value, values, num_elem * sizeof(*sm->value));
+}
+
+/*
+ * Combines two sparse matrices (allocating new space).
+ *
+ * Input:
+ * sm1, sm2: matrices to be combined
+ * row_offset1, row_offset2: row offset of each matrix in the new matrix
+ * col_offset1, col_offset2: column offset of each matrix in the new matrix
+ * new_n_rows, new_n_cols: number of rows and columns in the new matrix
+ *
+ * Output:
+ * sm: the combined matrix
+ */
+void av1_init_combine_sparse_mtx(const SPARSE_MTX *sm1, const SPARSE_MTX *sm2,
+ SPARSE_MTX *sm, int row_offset1,
+ int col_offset1, int row_offset2,
+ int col_offset2, int new_n_rows,
+ int new_n_cols) {
+ sm->n_elem = sm1->n_elem + sm2->n_elem;
+ sm->n_cols = new_n_cols;
+ sm->n_rows = new_n_rows;
+
+ if (sm->n_elem == 0) {
+ sm->row_pos = NULL;
+ sm->col_pos = NULL;
+ sm->value = NULL;
+ return;
+ }
+ sm->row_pos = aom_calloc(sm->n_elem, sizeof(*sm->row_pos));
+ sm->col_pos = aom_calloc(sm->n_elem, sizeof(*sm->col_pos));
+ sm->value = aom_calloc(sm->n_elem, sizeof(*sm->value));
+
+ for (int i = 0; i < sm1->n_elem; i++) {
+ sm->row_pos[i] = sm1->row_pos[i] + row_offset1;
+ sm->col_pos[i] = sm1->col_pos[i] + col_offset1;
+ }
+ memcpy(sm->value, sm1->value, sm1->n_elem * sizeof(*sm1->value));
+ int n_elem1 = sm1->n_elem;
+ for (int i = 0; i < sm2->n_elem; i++) {
+ sm->row_pos[n_elem1 + i] = sm2->row_pos[i] + row_offset2;
+ sm->col_pos[n_elem1 + i] = sm2->col_pos[i] + col_offset2;
+ }
+ memcpy(sm->value + n_elem1, sm2->value, sm2->n_elem * sizeof(*sm2->value));
+}
+
+void av1_free_sparse_mtx_elems(SPARSE_MTX *sm) {
+ sm->n_cols = 0;
+ sm->n_rows = 0;
+ if (sm->n_elem != 0) {
+ aom_free(sm->row_pos);
+ aom_free(sm->col_pos);
+ aom_free(sm->value);
+ }
+ sm->n_elem = 0;
+}
+
+/*
+ * Calculate matrix and vector multiplication: A*b
+ *
+ * Input:
+ * sm: matrix A
+ * srcv: the vector b to be multiplied to
+ * dstl: the length of vectors
+ *
+ * Output:
+ * dstv: pointer to the resulting vector
+ */
+void av1_mtx_vect_multi_right(const SPARSE_MTX *sm, const double *srcv,
+ double *dstv, int dstl) {
+ memset(dstv, 0, sizeof(*dstv) * dstl);
+ for (int i = 0; i < sm->n_elem; i++) {
+ dstv[sm->row_pos[i]] += srcv[sm->col_pos[i]] * sm->value[i];
+ }
+}
+/*
+ * Calculate matrix and vector multiplication: b*A
+ *
+ * Input:
+ * sm: matrix A
+ * srcv: the vector b to be multiplied to
+ * dstl: the length of vectors
+ *
+ * Output:
+ * dstv: pointer to the resulting vector
+ */
+void av1_mtx_vect_multi_left(const SPARSE_MTX *sm, const double *srcv,
+ double *dstv, int dstl) {
+ memset(dstv, 0, sizeof(*dstv) * dstl);
+ for (int i = 0; i < sm->n_elem; i++) {
+ dstv[sm->col_pos[i]] += srcv[sm->row_pos[i]] * sm->value[i];
+ }
+}
+
+/*
+ * Calculate inner product of two vectors
+ *
+ * Input:
+ * src1, scr2: the vectors to be multiplied
+ * src1l: length of the vectors
+ *
+ * Output:
+ * the inner product
+ */
+double av1_vect_vect_multi(const double *src1, int src1l, const double *src2) {
+ double result = 0;
+ for (int i = 0; i < src1l; i++) {
+ result += src1[i] * src2[i];
+ }
+ return result;
+}
+
+/*
+ * Multiply each element in the matrix sm with a constant c
+ */
+void av1_constant_multiply_sparse_matrix(SPARSE_MTX *sm, double c) {
+ for (int i = 0; i < sm->n_elem; i++) {
+ sm->value[i] *= c;
+ }
+}
+
+/*
+ * Solve for Ax = b
+ * no requirement on A
+ *
+ * Input:
+ * A: the sparse matrix
+ * b: the vector b
+ * bl: length of b
+ *
+ * Output:
+ * x: pointer to the solution vector
+ */
+void av1_bi_conjugate_gradient_sparse(const SPARSE_MTX *A, const double *b,
+ int bl, double *x) {
+ double *r, *r_hat, *p, *p_hat, *Ap, *p_hatA, *x_hat;
+ double alpha, beta, rtr, r_norm_2;
+ double denormtemp;
+
+ // initialize
+ r = aom_calloc(bl, sizeof(*r));
+ r_hat = aom_calloc(bl, sizeof(*r_hat));
+ p = aom_calloc(bl, sizeof(*p));
+ p_hat = aom_calloc(bl, sizeof(*p_hat));
+ Ap = aom_calloc(bl, sizeof(*Ap));
+ p_hatA = aom_calloc(bl, sizeof(*p_hatA));
+ x_hat = aom_calloc(bl, sizeof(*x_hat));
+
+ int i;
+ for (i = 0; i < bl; i++) {
+ r[i] = b[i];
+ r_hat[i] = b[i];
+ p[i] = r[i];
+ p_hat[i] = r_hat[i];
+ x[i] = 0;
+ x_hat[i] = 0;
+ }
+ r_norm_2 = av1_vect_vect_multi(r_hat, bl, r);
+ for (int k = 0; k < MAX_CG_SP_ITER; k++) {
+ rtr = r_norm_2;
+ av1_mtx_vect_multi_right(A, p, Ap, bl);
+ av1_mtx_vect_multi_left(A, p_hat, p_hatA, bl);
+
+ denormtemp = av1_vect_vect_multi(p_hat, bl, Ap);
+ if (denormtemp < 1e-10) break;
+ alpha = rtr / denormtemp;
+ r_norm_2 = 0;
+ for (i = 0; i < bl; i++) {
+ x[i] += alpha * p[i];
+ x_hat[i] += alpha * p_hat[i];
+ r[i] -= alpha * Ap[i];
+ r_hat[i] -= alpha * p_hatA[i];
+ r_norm_2 += r_hat[i] * r[i];
+ }
+ if (sqrt(r_norm_2) < 1e-2) {
+ break;
+ }
+ if (rtr < 1e-10) break;
+ beta = r_norm_2 / rtr;
+ for (i = 0; i < bl; i++) {
+ p[i] = r[i] + beta * p[i];
+ p_hat[i] = r_hat[i] + beta * p_hat[i];
+ }
+ }
+ // free
+ aom_free(r);
+ aom_free(r_hat);
+ aom_free(p);
+ aom_free(p_hat);
+ aom_free(Ap);
+ aom_free(p_hatA);
+ aom_free(x_hat);
+}
+
+/*
+ * Solve for Ax = b when A is symmetric and positive definite
+ *
+ * Input:
+ * A: the sparse matrix
+ * b: the vector b
+ * bl: length of b
+ *
+ * Output:
+ * x: pointer to the solution vector
+ */
+void av1_conjugate_gradient_sparse(const SPARSE_MTX *A, const double *b, int bl,
+ double *x) {
+ double *r, *p, *Ap;
+ double alpha, beta, rtr, r_norm_2;
+ double denormtemp;
+
+ // initialize
+ r = aom_calloc(bl, sizeof(*r));
+ p = aom_calloc(bl, sizeof(*p));
+ Ap = aom_calloc(bl, sizeof(*Ap));
+
+ int i;
+ for (i = 0; i < bl; i++) {
+ r[i] = b[i];
+ p[i] = r[i];
+ x[i] = 0;
+ }
+ r_norm_2 = av1_vect_vect_multi(r, bl, r);
+ int k;
+ for (k = 0; k < MAX_CG_SP_ITER; k++) {
+ rtr = r_norm_2;
+ av1_mtx_vect_multi_right(A, p, Ap, bl);
+ denormtemp = av1_vect_vect_multi(p, bl, Ap);
+ if (denormtemp < 1e-10) break;
+ alpha = rtr / denormtemp;
+ r_norm_2 = 0;
+ for (i = 0; i < bl; i++) {
+ x[i] += alpha * p[i];
+ r[i] -= alpha * Ap[i];
+ r_norm_2 += r[i] * r[i];
+ }
+ if (r_norm_2 < 1e-8 * bl) break;
+ if (rtr < 1e-10) break;
+ beta = r_norm_2 / rtr;
+ for (i = 0; i < bl; i++) {
+ p[i] = r[i] + beta * p[i];
+ }
+ }
+ // free
+ aom_free(r);
+ aom_free(p);
+ aom_free(Ap);
+}
+
+/*
+ * Solve for Ax = b using Jacobi method
+ *
+ * Input:
+ * A: the sparse matrix
+ * b: the vector b
+ * bl: length of b
+ *
+ * Output:
+ * x: pointer to the solution vector
+ */
+void av1_jacobi_sparse(const SPARSE_MTX *A, const double *b, int bl,
+ double *x) {
+ double *diags, *Rx, *x_last, *x_cur, *tempx;
+ double resi2;
+ diags = aom_calloc(bl, sizeof((*diags)));
+ Rx = aom_calloc(bl, sizeof(*Rx));
+ x_last = aom_calloc(bl, sizeof(*x_last));
+ x_cur = aom_calloc(bl, sizeof(*x_cur));
+ int i;
+ memset(x_last, 0, sizeof(*x_last) * bl);
+ // get the diagonals of A
+ memset(diags, 0, sizeof(*diags) * bl);
+ for (int c = 0; c < A->n_elem; c++) {
+ if (A->row_pos[c] != A->col_pos[c]) continue;
+ diags[A->row_pos[c]] = A->value[c];
+ }
+ int k;
+ for (k = 0; k < MAX_CG_SP_ITER; k++) {
+ // R = A - diag(diags)
+ // get R*x_last
+ memset(Rx, 0, sizeof(*Rx) * bl);
+ for (int c = 0; c < A->n_elem; c++) {
+ if (A->row_pos[c] == A->col_pos[c]) continue;
+ Rx[A->row_pos[c]] += x_last[A->col_pos[c]] * A->value[c];
+ }
+ resi2 = 0;
+ for (i = 0; i < bl; i++) {
+ x_cur[i] = (b[i] - Rx[i]) / diags[i];
+ resi2 += (x_last[i] - x_cur[i]) * (x_last[i] - x_cur[i]);
+ }
+ if (resi2 <= 1e-10 * bl) break;
+ // swap last & cur buffer ptrs
+ tempx = x_last;
+ x_last = x_cur;
+ x_cur = tempx;
+ }
+ printf("\n numiter: %d\n", k);
+ for (i = 0; i < bl; i++) {
+ x[i] = x_cur[i];
+ }
+ aom_free(diags);
+ aom_free(Rx);
+ aom_free(x_last);
+ aom_free(x_cur);
+}
+
+/*
+ * Solve for Ax = b using Steepest descent method
+ *
+ * Input:
+ * A: the sparse matrix
+ * b: the vector b
+ * bl: length of b
+ *
+ * Output:
+ * x: pointer to the solution vector
+ */
+void av1_steepest_descent_sparse(const SPARSE_MTX *A, const double *b, int bl,
+ double *x) {
+ double *d, *Ad, *Ax;
+ double resi2, resi2_last, dAd, diff, temp;
+ d = aom_calloc(bl, sizeof(*d));
+ Ax = aom_calloc(bl, sizeof(*Ax));
+ Ad = aom_calloc(bl, sizeof(*Ad));
+ int i;
+ // initialize with 0s
+ resi2 = 0;
+ for (i = 0; i < bl; i++) {
+ x[i] = 0;
+ d[i] = b[i];
+ resi2 += d[i] * d[i] / bl;
+ }
+ int k;
+ for (k = 0; k < MAX_CG_SP_ITER; k++) {
+ // get A*x_last
+ av1_mtx_vect_multi_right(A, d, Ad, bl);
+ dAd = resi2 * bl / av1_vect_vect_multi(d, bl, Ad);
+ diff = 0;
+ for (i = 0; i < bl; i++) {
+ temp = dAd * d[i];
+ x[i] = x[i] + temp;
+ diff += temp * temp;
+ }
+ av1_mtx_vect_multi_right(A, x, Ax, bl);
+ resi2_last = resi2;
+ resi2 = 0;
+ for (i = 0; i < bl; i++) {
+ d[i] = b[i] - Ax[i];
+ resi2 += d[i] * d[i] / bl;
+ }
+ if (resi2 <= 1e-8) break;
+ if (resi2_last - resi2 < 1e-8) {
+ break;
+ }
+ }
+ aom_free(d);
+ aom_free(Ax);
+ aom_free(Ad);
+}
+
+#endif // CONFIG_OPFL
diff --git a/av1/encoder/sparse_linear_solver.h b/av1/encoder/sparse_linear_solver.h
new file mode 100644
index 0000000..3cacb51
--- /dev/null
+++ b/av1/encoder/sparse_linear_solver.h
@@ -0,0 +1,67 @@
+/*
+ * Copyright (c) 2021, 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 AV1_COMMON_SPARSE_LINEAR_SOLVER_H_
+#define AV1_COMMON_SPARSE_LINEAR_SOLVER_H_
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include "config/aom_config.h"
+
+#if CONFIG_OPTICAL_FLOW_API
+
+// Number of iterations for solving linear equations.
+#define MAX_CG_SP_ITER 100
+
+typedef struct {
+ int n_elem; // number of non-zero elements
+ int n_rows;
+ int n_cols;
+ // using arrays to represent non-zero elements.
+ int *col_pos;
+ int *row_pos; // starts with 0
+ double *value;
+} SPARSE_MTX;
+
+void av1_init_sparse_mtx(const int *rows, const int *cols, const double *values,
+ int num_elem, int num_rows, int num_cols,
+ SPARSE_MTX *sm);
+void av1_init_combine_sparse_mtx(const SPARSE_MTX *sm1, const SPARSE_MTX *sm2,
+ SPARSE_MTX *sm, int row_offset1,
+ int col_offset1, int row_offset2,
+ int col_offset2, int new_n_rows,
+ int new_n_cols);
+void av1_free_sparse_mtx_elems(SPARSE_MTX *sm);
+
+void av1_mtx_vect_multi_right(const SPARSE_MTX *sm, const double *srcv,
+ double *dstv, int dstl);
+void av1_mtx_vect_multi_left(const SPARSE_MTX *sm, const double *srcv,
+ double *dstv, int dstl);
+double av1_vect_vect_multi(const double *src1, int src1l, const double *src2);
+void av1_constant_multiply_sparse_matrix(SPARSE_MTX *sm, double c);
+
+void av1_conjugate_gradient_sparse(const SPARSE_MTX *A, const double *b, int bl,
+ double *x);
+void av1_bi_conjugate_gradient_sparse(const SPARSE_MTX *A, const double *b,
+ int bl, double *x);
+void av1_jacobi_sparse(const SPARSE_MTX *A, const double *b, int bl, double *x);
+void av1_steepest_descent_sparse(const SPARSE_MTX *A, const double *b, int bl,
+ double *x);
+
+#endif // CONFIG_OPTICAL_FLOW_API
+
+#ifdef __cplusplus
+} // extern "C"
+#endif
+
+#endif /* AV1_COMMON_SPARSE_LINEAR_SOLVER_H_ */
