710 lines
18 KiB
C++
710 lines
18 KiB
C++
/*!
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* 03_matrix.cpp
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*
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* Copyright (c) 2015-2024, NADAL Jean-Baptiste. All rights reserved.
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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* MA 02110-1301 USA
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*
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* @Author: NADAL Jean-Baptiste
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* @Date: 01/02/2024
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*
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*/
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/*---------------------------------------------------------------------------*/
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#include <external/catch.hpp>
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#include "raytracing.h"
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using namespace Raytracer;
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/* ------------------------------------------------------------------------- */
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SCENARIO("Constructing and inspecting a 4x4 matrix", "[features/matrices.feature]")
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{
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GIVEN("rgz following 4x4 matrix M")
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{
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Matrix M = {
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{ 1, 2, 3, 4},
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{ 5.5, 6.5, 7.5, 8.5},
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{ 9, 10, 11, 12},
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{13.5, 14.5, 15.5, 16.5}
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};
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THEN("M.rows = 4")
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{
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REQUIRE(M.rows() == 4);
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}
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AND_THEN("M.cols = 4")
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{
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REQUIRE(M.cols() == 4);
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}
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AND_THEN("M[0][0] = 1")
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{
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REQUIRE(M[0][0] == 1);
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}
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AND_THEN("M[0][3] = 4")
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{
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REQUIRE(M[0][3] == 4);
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}
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AND_THEN("M[1][0] = 5.5")
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{
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REQUIRE(M[1][0] == 5.5);
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}
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AND_THEN("M[1][2] = 7.5")
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{
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REQUIRE(M[1][2] == 7.5);
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}
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AND_THEN("M[2][2] = 11")
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{
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REQUIRE(M[2][2] == 11);
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}
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AND_THEN("M[3][0] = 13.5")
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{
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REQUIRE(M[3][0] == 13.5);
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}
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AND_THEN("M[3][2] = 15.5")
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{
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REQUIRE(M[3][2] == 15.5);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("A 2x2 matrix ought to be representable", "[features/matrices.feature]")
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{
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GIVEN("the following 2x2 matrix M")
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{
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Matrix M = {
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{-3, 5},
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{ 1, -2}
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};
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THEN("M.rows = 2")
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{
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REQUIRE(M.rows() == 2);
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}
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AND_THEN("M.cols = 2")
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{
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REQUIRE(M.cols() == 2);
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}
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AND_THEN("M[0][0] = -3")
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{
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REQUIRE(M[0][0] == -3);
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}
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AND_THEN("M[0][1] = 5")
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{
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REQUIRE(M[0][1] == 5);
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}
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AND_THEN("M[1][0] = 1")
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{
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REQUIRE(M[1][0] == 1);
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}
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AND_THEN("M[1][1] = -2")
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{
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REQUIRE(M[1][1] == -2);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("A 3x3 matrix ought to be representable", "[features/matrices.feature]")
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{
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GIVEN("the following 3x3 matrix M")
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{
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Matrix M = {
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{-3, 5, 0},
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{ 1, -2, -7},
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{ 0, 1, 1}
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};
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THEN("M.rows = 3")
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{
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REQUIRE(M.rows() == 3);
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}
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AND_THEN("M.cols == 3")
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{
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REQUIRE(M.cols() == 3);
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}
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AND_THEN("M[0][0] = -3")
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{
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REQUIRE(M[0][0] == -3);
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}
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AND_THEN("M[1][1] = -2")
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{
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REQUIRE(M[1][1] == -2);
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}
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AND_THEN("M[2][2] = 1")
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{
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REQUIRE(M[2][2] == 1);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Matrix equality with identical matrices", "[features/matrices.feature]")
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{
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GIVEN("the following matrix A")
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{
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Matrix A = {
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{1, 2, 3, 4},
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{5, 6, 7, 8},
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{9, 8, 7, 6},
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{5, 4, 3, 2}
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};
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AND_GIVEN("the following matrix B")
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{
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Matrix B = {
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{1, 2, 3, 4},
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{5, 6, 7, 8},
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{9, 8, 7, 6},
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{5, 4, 3, 2}
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};
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THEN("A = B")
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{
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REQUIRE(A == B);
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}
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Matrix equality with different matrices", "[features/matrices.feature]")
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{
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GIVEN("the following matrix A")
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{
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Matrix A = {
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{1, 2, 3, 4},
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{5, 6, 7, 8},
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{9, 8, 7, 6},
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{5, 4, 3, 2}
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};
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AND_GIVEN("the following matrix B")
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{
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Matrix B = {
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{2, 3, 4, 5},
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{6, 7, 8, 9},
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{8, 7, 6, 5},
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{4, 3, 2, 1}
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};
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THEN("A != B")
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{
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REQUIRE(A != B);
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}
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Multiplying two matrices", "[features/matrices.feature]")
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{
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GIVEN("the following matrix A")
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{
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Matrix A = {
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{1, 2, 3, 4},
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{5, 6, 7, 8},
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{9, 8, 7, 6},
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{5, 4, 3, 2}
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};
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AND_GIVEN("the following matrix B")
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{
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Matrix B = {
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{-2, 1, 2, 3},
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{ 3, 2, 1, -1},
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{ 4, 3, 6, 5},
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{ 1, 2, 7, 8}
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};
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AND_GIVEN("the following matrix C")
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{
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Matrix C = {
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{20, 22, 50, 48},
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{44, 54, 114, 108},
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{40, 58, 110, 102},
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{16, 26, 46, 42}
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};
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THEN("A * B = C")
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REQUIRE((A * B) == C);
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}
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("A matrix multiplied by a tuple", "[features/matrices.feature]")
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{
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GIVEN("the following matrix A")
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{
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Matrix A = {
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{1, 2, 3, 4},
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{2, 4, 4, 2},
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{8, 6, 4, 1},
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{0, 0, 0, 1}
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};
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AND_GIVEN("b <- tuple(1, 2, 3, 1)")
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{
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Tuple b(1, 2, 3, 1);
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THEN("A * b = tuple(18, 24, 33, 1)")
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{
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REQUIRE((A * b) == Tuple(18, 24, 33, 1));
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}
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Multiplying a matrix by the identity matrix", "[features/matrices.feature]")
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{
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GIVEN("the following matrix A")
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{
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Matrix A = {
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{0, 1, 2, 4},
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{1, 2, 4, 8},
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{2, 4, 8, 16},
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{4, 8, 16, 32}
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};
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THEN("A * identity_matrix = A")
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{
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REQUIRE((A * Matrix::identity()) == A);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Multiplying the identity matrix by a tuple", "[features/matrices.feature]")
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{
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GIVEN("a <- tuple(1, 2, 3, 4)")
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{
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Tuple a(1, 2, 3, 4);
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THEN("identity_matrix * a = a")
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{
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REQUIRE((Matrix::identity() * a) == a);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Transposing a matrix", "[features/matrices.feature]")
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{
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GIVEN("the following matrix A")
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{
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Matrix A = {
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{0, 9, 3, 0},
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{9, 8, 0, 8},
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{1, 8, 5, 3},
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{0, 0, 5, 8}
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};
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THEN("transpose(A) is the following matrix")
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{
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Matrix transposed = {
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{0, 9, 1, 0},
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{9, 8, 8, 0},
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{3, 0, 5, 5},
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{0, 8, 3, 8}
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};
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REQUIRE(A.transpose() == transposed);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Transposing the identity matrix", "[features/matrices.feature]")
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{
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GIVEN("A <- transpose(identity_matrix)")
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{
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Matrix A = Matrix::identity().transpose();
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THEN("A = identity_matrix")
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{
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REQUIRE(A == Matrix::identity());
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Calculating the determinant of a 2x2 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 2x2 matrix A")
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{
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Matrix A = {
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{ 1, 5},
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{-3, 2}
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};
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THEN("determinant(A) = 17")
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{
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REQUIRE(A.determinant() == 17);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("A submatrix of a 3x3 matrix is a 2x2 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 3x3 matrix A")
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{
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Matrix A = {
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{ 1, 5, 0},
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{-3, 2, 7},
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{ 0, 6, -3}
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};
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Matrix B = {
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{-3, 2},
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{ 0, 6}
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};
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THEN("submatrix(A,0,2) is the following 2x2 matrix")
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{
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REQUIRE(A.sub_matrix(0, 2) == B);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("A submatrix of a 4x4 matrix is a 3x3 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
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{-6, 1, 1, 6},
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{-8, 5, 8, 6},
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{-1, 0, 8, 2},
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{-7, 1, -1, 1}
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};
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Matrix B = {
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{-6, 1, 6},
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{-8, 8, 6},
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{-7, -1, 1}
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};
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THEN("submatrix(B,2,1) is the following 3x3 matrix")
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{
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REQUIRE(A.sub_matrix(2, 1) == B);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Calculating a minor of a 3x3 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 3x3 matrix A")
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{
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Matrix A = {
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{3, 5, 0},
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{2, -1, -7},
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{6, -1, 5}
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};
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AND_GIVEN("B <- submatrix(A,1,0)")
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{
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Matrix B = A.sub_matrix(1, 0);
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THEN("determinant(B) = 25")
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{
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REQUIRE(B.determinant() == 25);
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}
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AND_THEN("minor(A,1,0)=25")
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{
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REQUIRE(A.minor(1, 0) == 25);
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}
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Calculating a cofactor of a 3x3 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 3x3 matrix A")
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{
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Matrix A = {
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{3, 5, 0},
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{2, -1, -7},
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{6, -1, 5}
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};
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THEN("minor(A, 0, 0) = -12")
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{
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REQUIRE(A.minor(0, 0) == -12);
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}
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AND_THEN("cofactor(A, 0, 0) = -12")
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{
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REQUIRE(A.cofactor(0, 0) == -12);
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}
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AND_THEN("minor(A, 1, 0) = 25")
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{
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REQUIRE(A.minor(1, 0) == 25);
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}
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AND_THEN("cofactor(A, 1, 0) = -25")
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{
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REQUIRE(A.cofactor(1, 0) == -25);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Calculating the determinant of a 3x3 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 3x3 matrix A")
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{
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Matrix A = {
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{ 1, 2, 6},
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{-5, 8, -4},
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{ 2, 6, 4}
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};
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THEN("cofactor(A, 0, 0) = 56")
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{
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REQUIRE(A.cofactor(0, 0) == 56);
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}
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AND_THEN("cofactor(A, 0, 1) = 12")
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{
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REQUIRE(A.cofactor(0, 1) == 12);
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}
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AND_THEN("cofactor(A, 0, 2) = -46")
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{
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REQUIRE(A.cofactor(0, 2) == -46);
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}
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AND_THEN("determinant(A) = -196")
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{
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REQUIRE(A.determinant() == -196);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Calculating the determinant of a 4x4 matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
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{-2, -8, 3, 5},
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{-3, 1, 7, 3},
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{ 1, 2, -9, 6},
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{-6, 7, 7, -9}
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};
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THEN("cofactor(A, 0, 0) = 690")
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{
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REQUIRE(A.cofactor(0, 0) == 690);
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}
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AND_THEN("cofactor(A, 0, 1) = 447")
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{
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REQUIRE(A.cofactor(0, 1) == 447);
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}
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AND_THEN("cofactor(A, 0, 2) = 210")
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{
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REQUIRE(A.cofactor(0, 2) == 210);
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}
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AND_THEN("cofactor(A, 0, 3) = 51")
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{
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REQUIRE(A.cofactor(0, 3) == 51);
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}
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AND_THEN("determinant(A) = -4071")
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{
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REQUIRE(A.determinant() == -4071);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Testing an invertible matrix for invertibility", "[features/matrices.feature]")
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{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
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{6, 4, 4, 4},
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{5, 5, 7, 6},
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{4, -9, 3, -7},
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{9, 1, 7, -6}
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};
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THEN("determinant(A) = -2120")
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{
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REQUIRE(A.determinant() == -2120);
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}
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AND_THEN("A is invertible")
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{
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REQUIRE(A.invertible() == true);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Testing an noninvertible matrix for invertibility", "[features/matrices.feature]")
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{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
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{-4, 2, -2, -3},
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{ 9, 6, 2, 6},
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{ 0, -5, 1, -5},
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{ 0, 0, 0, 0}
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};
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THEN("determinant(A) = 0")
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{
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REQUIRE(A.determinant() == 0);
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}
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AND_THEN("A is not invertible")
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{
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REQUIRE(A.invertible() == false);
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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SCENARIO("Calculating the inverse of a matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
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{-5, 2, 6, -8},
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{ 1, -5, 1, 8},
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{ 7, 7, -6, -7},
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{ 1, -3, 7, 4}
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};
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Matrix a_inverted = {
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{ 0.21805, 0.45113, 0.24060, -0.04511},
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{-0.80827, -1.45677, -0.44361, 0.52068},
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{-0.07895, -0.22368, -0.05263, 0.19737},
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{-0.52256, -0.81391, -0.30075, 0.30639}
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};
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AND_GIVEN("B <- inverse(A)")
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{
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Matrix B = A.inverse();
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THEN("determinant(A) = 532")
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{
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REQUIRE(A.determinant() == 532);
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}
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AND_THEN("cofactor(A, 2, 3) = -160")
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{
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REQUIRE(A.cofactor(2, 3) == -160);
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}
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AND_THEN("B[3][2] = -160.0 / 532.0")
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{
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REQUIRE(B[3][2] == -160.0 / 532.0);
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}
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AND_THEN("cofactor(A, 3, 2) = 105")
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{
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REQUIRE(A.cofactor(3, 2) == 105);
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}
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AND_THEN("B[2][3] = 105.0 / 532.0")
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{
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REQUIRE(B[2][3] == 105.0 / 532.0);
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}
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AND_THEN("B is the following 4x4 matrix")
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{
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REQUIRE(B == a_inverted);
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}
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}
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}
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}
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/* ------------------------------------------------------------------------- */
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|
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SCENARIO("Calculating the inverse of another matrix", "[features/matrices.feature]")
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|
{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
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{ 8, -5, 9, 2},
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{ 7, 5, 6, 1},
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{-6, 0, 9, 6},
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{-3, 0, -9, -4}
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};
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Matrix a_inverted = {
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{-0.15385, -0.15385, -0.28205, -0.53846},
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{-0.07692, 0.12308, 0.02564, 0.03077},
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{ 0.35897, 0.35897, 0.43590, 0.92308},
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{-0.69231, -0.69231, -0.76923, -1.92308}
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};
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THEN("inverse(A) is the following matrix")
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{
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REQUIRE(A.inverse() == a_inverted);
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}
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}
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}
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|
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/* ------------------------------------------------------------------------- */
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|
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SCENARIO("Calculating the inverse of third matrix", "[features/matrices.feature]")
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{
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GIVEN("the following 4x4 matrix A")
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{
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Matrix A = {
|
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{ 9, 3, 0, 9},
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{-5, -2, -6, -3},
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{-4, 9, 6, 4},
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{-7, 6, 6, 2}
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};
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Matrix a_inverted = {
|
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{-0.04074, -0.07778, 0.14444, -0.22222},
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{-0.07778, 0.03333, 0.36667, -0.33333},
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{-0.02901, -0.14630, -0.10926, 0.12963},
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{ 0.17778, 0.06667, -0.26667, 0.33333}
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};
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THEN("inverse(A) is the following matrix")
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{
|
|
REQUIRE(A.inverse() == a_inverted);
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}
|
|
}
|
|
}
|
|
|
|
/* ------------------------------------------------------------------------- */
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|
|
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SCENARIO("Multiplying a product by its inverse", "[features/matrices.feature]")
|
|
{
|
|
GIVEN("the following 4x4 matrix A")
|
|
{
|
|
Matrix A = {
|
|
{ 3, -9, 7, 3},
|
|
{ 3, -8, 2, -9},
|
|
{-4, 4, 4, 1},
|
|
{-6, 5, -1, 1}
|
|
};
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AND_GIVEN("the following 4x4 matrix B")
|
|
{
|
|
Matrix B = {
|
|
{8, 2, 2, 2},
|
|
{3, -1, 7, 0},
|
|
{7, 0, 5, 4},
|
|
{6, -2, 0, 5}
|
|
};
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AND_GIVEN("C <- A * B")
|
|
{
|
|
Matrix C = A * B;
|
|
THEN("C * inverse(B) = A")
|
|
{
|
|
REQUIRE(C * B.inverse() == A);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|