Eigen: fold remaining OpenNL code into intern/eigen.

Differential Revision: https://developer.blender.org/D1662

intern/eigen/CMakeLists.txt

@@ -35,9 +35,11 @@ set(SRC
 	eigen_capi.h
 
 	intern/eigenvalues.cc
+	intern/linear_solver.cc
 	intern/svd.cc
 
 	intern/eigenvalues.h
+	intern/linear_solver.h
 	intern/svd.h
 )
 

intern/eigen/eigen_capi.h

@@ -28,6 +28,7 @@
 #define __EIGEN_C_API_H__
 
 #include "intern/eigenvalues.h"
+#include "intern/linear_solver.h"
 #include "intern/svd.h"
 
 #endif  /* __EIGEN_C_API_H__ */

intern/eigen/intern/eigenvalues.cc

@@ -45,7 +45,7 @@ using Eigen::Map;
 
 using Eigen::Success;
 
-bool EG3_self_adjoint_eigen_solve(const int size, const float *matrix, float *r_eigen_values, float *r_eigen_vectors)
+bool EIG_self_adjoint_eigen_solve(const int size, const float *matrix, float *r_eigen_values, float *r_eigen_vectors)
 {
 	SelfAdjointEigenSolver<MatrixXf> eigen_solver;
 

intern/eigen/intern/eigenvalues.h

@@ -31,7 +31,7 @@
 extern "C" {
 #endif
 
-bool EG3_self_adjoint_eigen_solve(const int size, const float *matrix, float *r_eigen_values, float *r_eigen_vectors);
+bool EIG_self_adjoint_eigen_solve(const int size, const float *matrix, float *r_eigen_values, float *r_eigen_vectors);
 
 #ifdef __cplusplus
 }

intern/eigen/intern/linear_solver.cc

@@ -0,0 +1,354 @@
+/*
+ *  Sparse linear solver.
+ *  Copyright (C) 2004 Bruno Levy
+ *  Copyright (C) 2005-2015 Blender Foundation
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program; if not, write to the Free Software
+ *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ *  If you modify this software, you should include a notice giving the
+ *  name of the person performing the modification, the date of modification,
+ *  and the reason for such modification.
+ */
+
+#include "linear_solver.h"
+
+#include <Eigen/Sparse>
+
+#include <algorithm>
+#include <cassert>
+#include <cstdlib>
+#include <iostream>
+#include <vector>
+
+/* Eigen data structures */
+
+typedef Eigen::SparseMatrix<double, Eigen::ColMajor> EigenSparseMatrix;
+typedef Eigen::SparseLU<EigenSparseMatrix> EigenSparseLU;
+typedef Eigen::VectorXd EigenVectorX;
+typedef Eigen::Triplet<double> EigenTriplet;
+
+/* Linear Solver data structure */
+
+struct LinearSolver
+{
+	struct Coeff
+	{
+		Coeff()
+		{
+			index = 0;
+			value = 0.0;
+		}
+
+		int index;
+		double value;
+	};
+
+	struct Variable
+	{
+		Variable()
+		{
+			memset(value, 0, sizeof(value));
+			locked = false;
+			index = 0;
+		}
+
+		double value[4];
+		bool locked;
+		int index;
+		std::vector<Coeff> a;
+	};
+
+	enum State
+	{
+		STATE_VARIABLES_CONSTRUCT,
+		STATE_MATRIX_CONSTRUCT,
+		STATE_MATRIX_SOLVED
+	};
+
+	LinearSolver(int num_rows_, int num_variables_, int num_rhs_, bool lsq_)
+	{
+		assert(num_variables_ > 0);
+		assert(num_rhs_ <= 4);
+
+		state = STATE_VARIABLES_CONSTRUCT;
+		m = 0;
+		n = 0;
+		sparseLU = NULL;
+		num_variables = num_variables_;
+		num_rhs = num_rhs_;
+		num_rows = num_rows_;
+		least_squares = lsq_;
+
+		variable.resize(num_variables);
+	}
+
+	~LinearSolver()
+	{
+		delete sparseLU;
+	}
+
+	State state;
+
+	int n;
+	int m;
+
+	std::vector<EigenTriplet> Mtriplets;
+	EigenSparseMatrix M;
+	EigenSparseMatrix MtM;
+	std::vector<EigenVectorX> b;
+	std::vector<EigenVectorX> x;
+
+	EigenSparseLU *sparseLU;
+
+	int num_variables;
+	std::vector<Variable> variable;
+
+	int num_rows;
+	int num_rhs;
+
+	bool least_squares;
+};
+
+LinearSolver *EIG_linear_solver_new(int num_rows, int num_columns, int num_rhs)
+{
+	return new LinearSolver(num_rows, num_columns, num_rhs, false);
+}
+
+LinearSolver *EIG_linear_least_squares_solver_new(int num_rows, int num_columns, int num_rhs)
+{
+	return new LinearSolver(num_rows, num_columns, num_rhs, true);
+}
+
+void EIG_linear_solver_delete(LinearSolver *solver)
+{
+	delete solver;
+}
+
+/* Variables */
+
+void EIG_linear_solver_variable_set(LinearSolver *solver, int rhs, int index, double value)
+{
+	solver->variable[index].value[rhs] = value;
+}
+
+double EIG_linear_solver_variable_get(LinearSolver *solver, int rhs, int index)
+{
+	return solver->variable[index].value[rhs];
+}
+
+void EIG_linear_solver_variable_lock(LinearSolver *solver, int index)
+{
+	if (!solver->variable[index].locked) {
+		assert(solver->state == LinearSolver::STATE_VARIABLES_CONSTRUCT);
+		solver->variable[index].locked = true;
+	}
+}
+
+static void linear_solver_variables_to_vector(LinearSolver *solver)
+{
+	int num_rhs = solver->num_rhs;
+
+	for (int i = 0; i < solver->num_variables; i++) {
+		LinearSolver::Variable* v = &solver->variable[i];
+		if (!v->locked) {
+			for (int j = 0; j < num_rhs; j++)
+				solver->x[j][v->index] = v->value[j];
+		}
+	}
+}
+
+static void linear_solver_vector_to_variables(LinearSolver *solver)
+{
+	int num_rhs = solver->num_rhs;
+
+	for (int i = 0; i < solver->num_variables; i++) {
+		LinearSolver::Variable* v = &solver->variable[i];
+		if (!v->locked) {
+			for (int j = 0; j < num_rhs; j++)
+				v->value[j] = solver->x[j][v->index];
+		}
+	}
+}
+
+/* Matrix */
+
+static void linear_solver_ensure_matrix_construct(LinearSolver *solver)
+{
+	/* transition to matrix construction if necessary */
+	if (solver->state == LinearSolver::STATE_VARIABLES_CONSTRUCT) {
+		int n = 0;
+
+		for (int i = 0; i < solver->num_variables; i++) {
+			if (solver->variable[i].locked)
+				solver->variable[i].index = ~0;
+			else
+				solver->variable[i].index = n++;
+		}
+
+		int m = (solver->num_rows == 0)? n: solver->num_rows;
+
+		solver->m = m;
+		solver->n = n;
+
+		assert(solver->least_squares || m == n);
+
+		/* reserve reasonable estimate */
+		solver->Mtriplets.clear();
+		solver->Mtriplets.reserve(std::max(m, n)*3);
+
+		solver->b.resize(solver->num_rhs);
+		solver->x.resize(solver->num_rhs);
+
+		for (int i = 0; i < solver->num_rhs; i++) {
+			solver->b[i].setZero(m);
+			solver->x[i].setZero(n);
+		}
+
+		linear_solver_variables_to_vector(solver);
+
+		solver->state = LinearSolver::STATE_MATRIX_CONSTRUCT;
+	}
+}
+
+void EIG_linear_solver_matrix_add(LinearSolver *solver, int row, int col, double value)
+{
+	if (solver->state == LinearSolver::STATE_MATRIX_SOLVED)
+		return;
+
+	linear_solver_ensure_matrix_construct(solver);
+
+	if (!solver->least_squares && solver->variable[row].locked);
+	else if (solver->variable[col].locked) {
+		if (!solver->least_squares)
+			row = solver->variable[row].index;
+
+		LinearSolver::Coeff coeff;
+		coeff.index = row;
+		coeff.value = value;
+		solver->variable[col].a.push_back(coeff);
+	}
+	else {
+		if (!solver->least_squares)
+			row = solver->variable[row].index;
+		col = solver->variable[col].index;
+
+		/* direct insert into matrix is too slow, so use triplets */
+		EigenTriplet triplet(row, col, value);
+		solver->Mtriplets.push_back(triplet);
+	}
+}
+
+/* Right hand side */
+
+void EIG_linear_solver_right_hand_side_add(LinearSolver *solver, int rhs, int index, double value)
+{
+	linear_solver_ensure_matrix_construct(solver);
+
+	if (solver->least_squares) {
+		solver->b[rhs][index] += value;
+	}
+	else if (!solver->variable[index].locked) {
+		index = solver->variable[index].index;
+		solver->b[rhs][index] += value;
+	}
+}
+
+/* Solve */
+
+bool EIG_linear_solver_solve(LinearSolver *solver)
+{
+	bool result = true;
+
+	assert(solver->state != LinearSolver::STATE_VARIABLES_CONSTRUCT);
+
+	if (solver->state == LinearSolver::STATE_MATRIX_CONSTRUCT) {
+		/* create matrix from triplets */
+		solver->M.resize(solver->m, solver->n);
+		solver->M.setFromTriplets(solver->Mtriplets.begin(), solver->Mtriplets.end());
+		solver->Mtriplets.clear();
+
+		/* create least squares matrix */
+		if (solver->least_squares)
+			solver->MtM = solver->M.transpose() * solver->M;
+
+		/* convert M to compressed column format */
+		EigenSparseMatrix& M = (solver->least_squares)? solver->MtM: solver->M;
+		M.makeCompressed();
+
+		/* perform sparse LU factorization */
+		EigenSparseLU *sparseLU = new EigenSparseLU();
+		solver->sparseLU = sparseLU;
+
+		sparseLU->compute(M);
+		result = (sparseLU->info() == Eigen::Success);
+
+		solver->state = LinearSolver::STATE_MATRIX_SOLVED;
+	}
+
+	if (result) {
+		/* solve for each right hand side */
+		for (int rhs = 0; rhs < solver->num_rhs; rhs++) {
+			/* modify for locked variables */
+			EigenVectorX& b = solver->b[rhs];
+
+			for (int i = 0; i < solver->num_variables; i++) {
+				LinearSolver::Variable *variable = &solver->variable[i];
+
+				if (variable->locked) {
+					std::vector<LinearSolver::Coeff>& a = variable->a;
+
+					for (int j = 0; j < a.size(); j++)
+						b[a[j].index] -= a[j].value*variable->value[rhs];
+				}
+			}
+
+			/* solve */
+			if (solver->least_squares) {
+				EigenVectorX Mtb = solver->M.transpose() * b;
+				solver->x[rhs] = solver->sparseLU->solve(Mtb);
+			}
+			else {
+				EigenVectorX& b = solver->b[rhs];
+				solver->x[rhs] = solver->sparseLU->solve(b);
+			}
+
+			if (solver->sparseLU->info() != Eigen::Success)
+				result = false;
+		}
+
+		if (result)
+			linear_solver_vector_to_variables(solver);
+	}
+
+	/* clear for next solve */
+	for (int rhs = 0; rhs < solver->num_rhs; rhs++)
+		solver->b[rhs].setZero(solver->m);
+
+	return result;
+}
+
+/* Debugging */
+
+void EIG_linear_solver_print_matrix(LinearSolver *solver)
+{
+	std::cout << "A:" << solver->M << std::endl;
+
+	for (int rhs = 0; rhs < solver->num_rhs; rhs++)
+		std::cout << "b " << rhs << ":" << solver->b[rhs] << std::endl;
+
+	if (solver->MtM.rows() && solver->MtM.cols())
+		std::cout << "AtA:" << solver->MtM << std::endl;
+}
+

intern/eigen/intern/linear_solver.h

@@ -0,0 +1,71 @@
+/*
+ *  Sparse linear solver.
+ *  Copyright (C) 2004 Bruno Levy
+ *  Copyright (C) 2005-2015 Blender Foundation
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program; if not, write to the Free Software
+ *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ *  If you modify this software, you should include a notice giving the
+ *  name of the person performing the modification, the date of modification,
+ *  and the reason for such modification.
+ */
+
+#pragma once
+
+#include <stdbool.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Solvers for Ax = b and AtAx = Atb */
+
+typedef struct LinearSolver LinearSolver;
+
+LinearSolver *EIG_linear_solver_new(
+	int num_rows,
+	int num_columns,
+	int num_right_hand_sides);
+
+LinearSolver *EIG_linear_least_squares_solver_new(
+	int num_rows,
+	int num_columns,
+	int num_right_hand_sides);
+
+void EIG_linear_solver_delete(LinearSolver *solver);
+
+/* Variables (x). Any locking must be done before matrix construction. */
+
+void EIG_linear_solver_variable_set(LinearSolver *solver, int rhs, int index, double value);
+double EIG_linear_solver_variable_get(LinearSolver *solver, int rhs, int index);
+void EIG_linear_solver_variable_lock(LinearSolver *solver, int index);
+
+/* Matrix (A) and right hand side (b) */
+
+void EIG_linear_solver_matrix_add(LinearSolver *solver, int row, int col, double value);
+void EIG_linear_solver_right_hand_side_add(LinearSolver *solver, int rhs, int index, double value);
+
+/* Solve. Repeated solves are supported, by changing b between solves. */
+
+bool EIG_linear_solver_solve(LinearSolver *solver);
+
+/* Debugging */
+
+void EIG_linear_solver_print_matrix(LinearSolver *solver);
+
+#ifdef __cplusplus
+}
+#endif
+

intern/eigen/intern/svd.cc

@@ -48,7 +48,7 @@ using Eigen::MatrixXf;
 using Eigen::VectorXf;
 using Eigen::Map;
 
-void EG3_svd_square_matrix(const int size, const float *matrix, float *r_U, float *r_S, float *r_V)
+void EIG_svd_square_matrix(const int size, const float *matrix, float *r_U, float *r_S, float *r_V)
 {
 	/* Since our matrix is squared, we can use thinU/V. */
 	unsigned int flags = (r_U ? ComputeThinU : 0) | (r_V ? ComputeThinV : 0);

intern/eigen/intern/svd.h

@@ -31,7 +31,7 @@
 extern "C" {
 #endif
 
-void EG3_svd_square_matrix(const int size, const float *matrix, float *r_U, float *r_S, float *r_V);
+void EIG_svd_square_matrix(const int size, const float *matrix, float *r_U, float *r_S, float *r_V);
 
 #ifdef __cplusplus
 }