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# This file is part of CasADi.
#
# CasADi -- A symbolic framework for dynamic optimization.
# Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl,
# KU Leuven. All rights reserved.
# Copyright (C) 2011-2014 Greg Horn
#
# CasADi is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 3 of the License, or (at your option) any later version.
#
# CasADi 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
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
# Linear solvers
# =================
#
# We demonstrate solving a dense system A.x=b by using different linear solvers.
from casadi import *
from numpy import *
import time
n=100
# We generate $A \in \mathbf{R}^{n \times n}$, $x \in \mathbf{R}^{n}$ with $n=100$
A=DM([[cos(i*j)-sin(i) for i in range(n)] for j in range(n)])
x=DM([tan(i) for i in range(n)])
# We generate the b vector:
b= mtimes(A,x)
# Commented out pendling completion #1615
# # We demonstrate the LinearSolver API with CSparse:
# s = LinearSolver("s", "csparse", A.sparsity())
# # Give it the matrix A
# s.setInput(A,"A")
# # Do the LU factorization
# s.prepare()
# # Give it the matrix b
# s.setInput(b,"B")
# # And we are off to find x...
# s.solve()
# x_ = s.getOutput("X")
# # By looking at the residuals between the x we knew in advance and the computed x, we see that the CSparse solver works
# print "Sum of residuals = %.2e" % norm_1(x-x_)
# # Comparison of different linear solvers
# # ======================================
# for solver in ("lapacklu","lapackqr","csparse"):
# s = LinearSolver("s", solver, A.sparsity()) # We create a solver
# s.setInput(A,"A") # Give it the matrix A
# t0 = time.time()
# for i in range(100):
# s.prepare() # Do the LU factorization
# pt = (time.time()-t0)/100
# s.setInput(b,"B") # Give it the matrix b
# t0 = time.time()
# for i in range(100):
# s.solve()
# st = (time.time()-t0)/100
# x_ = s.getOutput("X")
# print ""
# print solver
# print "=" * 10
# print "Sum of residuals = %.2e" % norm_1(x-x_)
# print "Preparation time = %0.2f ms" % (pt*1000)
# print "Solve time = %0.2f ms" % (st*1000)
# assert(norm_1(x-x_)<1e-9)
# # Note that these
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