From c301992d25a25ef3353dc780342c2617521c1e3c Mon Sep 17 00:00:00 2001 From: Spectre Date: Sun, 22 Sep 2024 00:16:38 +0700 Subject: [PATCH 1/2] elimination added --- main.cpp | 29 +++++++++++++++++++++++++++-- tools/elimination.cpp | 31 +++++++++++++++++++++++++++++++ tools/elimination.h | 13 +++++++++++++ tools/gauss_jordan.cpp | 1 - tools/gauss_jordan.h | 12 ------------ tools/math.h | 1 + 6 files changed, 72 insertions(+), 15 deletions(-) create mode 100644 tools/elimination.cpp create mode 100644 tools/elimination.h delete mode 100644 tools/gauss_jordan.cpp delete mode 100644 tools/gauss_jordan.h diff --git a/main.cpp b/main.cpp index df1ab18..7c89b5e 100644 --- a/main.cpp +++ b/main.cpp @@ -2,6 +2,26 @@ #include "tools/matrix.h" #include "tools/math.h" +Matrix createGeneralMatrix(Matrix& A, ColumnVector& C, ColumnVector& b) { + Matrix generalMatrix(A.getRows() + 1, A.getColumns() + 1); + for (int i = 0; i < A.getColumns(); i++) { + generalMatrix[0][i] = C[i]; + } + + generalMatrix[0][A.getColumns()] = 0; + for (int j = 0; j < A.getRows(); j++) { + generalMatrix[j + 1][A.getColumns()] = b[j]; + } + + for (int i = 0; i < A.getRows(); i++) { + for (int j = 0; j < A.getColumns(); j++) { + generalMatrix[i + 1][j] = A[i][j]; + } + } + + return generalMatrix; +} + int main() { int n, m; std::cin >> n; @@ -12,13 +32,18 @@ int main() { ColumnVector b(n); double eps; double eps_default; + std::cin >> C; std::cin >> A; + std::cin >> b; std::cout << "Вектор C: " << C << std::endl; + std::cout << "Вектор b: " << b << std::endl; std::cout << "Матрица A: " << A << std::endl; - Matrix B(2, 2); - std::cout << B << std::endl; + Matrix E = createGeneralMatrix(A, C, b); + + std::cout << "Новая матрица:" << E << std::endl; + return 0; } diff --git a/tools/elimination.cpp b/tools/elimination.cpp new file mode 100644 index 0000000..8182f67 --- /dev/null +++ b/tools/elimination.cpp @@ -0,0 +1,31 @@ +#include "elimination.h" +#include "matrix.h" +#include "math.h" + +Matrix createGeneralMatrix(Matrix& A, ColumnVector& C, ColumnVector& b) { + Matrix generalMatrix(A.getRows() + 1, A.getColumns() + 1); + for (int i = 0; i < A.getColumns(); i++) { + generalMatrix[0][i] = C[i]; + } + + generalMatrix[0][A.getColumns()] = 0; + for (int j = 0; j < A.getRows(); j++) { + generalMatrix[j + 1][A.getColumns()] = b[j]; + } + + for (int i = 0; i < A.getRows(); i++) { + for (int j = 0; j < A.getColumns(); j++) { + generalMatrix[i + 1][j] = A[i][j]; + } + } + + return generalMatrix; +} + +Matrix elimination(Matrix A, ColumnVector C, ColumnVector b, int pivot_column_index, int pivot_row_index, double eps) { + Matrix generalMatrix = createGeneralMatrix(A, C, b); + + + return generalMatrix; +} + diff --git a/tools/elimination.h b/tools/elimination.h new file mode 100644 index 0000000..a57e6d3 --- /dev/null +++ b/tools/elimination.h @@ -0,0 +1,13 @@ +#ifndef ELIMINATION_H +#define ELIMINATION_H + + + +class Elimination { + public: + Matrix elimination(Matrix A, ColumnVector C, ColumnVector b, int pivot_column_index, int pivot_row_index, double eps); +}; + + + +#endif //ELIMINATION_H diff --git a/tools/gauss_jordan.cpp b/tools/gauss_jordan.cpp deleted file mode 100644 index de26809..0000000 --- a/tools/gauss_jordan.cpp +++ /dev/null @@ -1 +0,0 @@ -#include "gauss_jordan.h" diff --git a/tools/gauss_jordan.h b/tools/gauss_jordan.h deleted file mode 100644 index 0666382..0000000 --- a/tools/gauss_jordan.h +++ /dev/null @@ -1,12 +0,0 @@ -#ifndef GAUSS_JORDAN_H -#define GAUSS_JORDAN_H - - - -class gauss_jordan { - -}; - - - -#endif //GAUSS_JORDAN_H diff --git a/tools/math.h b/tools/math.h index b641471..8ff38f0 100644 --- a/tools/math.h +++ b/tools/math.h @@ -4,6 +4,7 @@ #include class ColumnVector; +class Matrix; class Math { public: From cd6de49b347bea55c6160999a1286f829859fbc8 Mon Sep 17 00:00:00 2001 From: Spectre Date: Sun, 22 Sep 2024 21:53:29 +0700 Subject: [PATCH 2/2] Elimination func created --- main.cpp | 48 ++++++++++++++++++++++---- tools/elimination.cpp | 80 ++++++++++++++++++++++++++++++++++++++++--- tools/elimination.h | 2 +- tools/math.cpp | 56 +++++++++++++++++++++++++++--- tools/math.h | 13 ++++--- 5 files changed, 178 insertions(+), 21 deletions(-) diff --git a/main.cpp b/main.cpp index 7c89b5e..260d587 100644 --- a/main.cpp +++ b/main.cpp @@ -2,15 +2,45 @@ #include "tools/matrix.h" #include "tools/math.h" +struct DestroyMatrix { + Matrix A; + ColumnVector C; + ColumnVector b; +}; + +DestroyMatrix destroyGeneralMatrix(Matrix& generalMatrix) { + int rows = generalMatrix.getRows(); + int cols = generalMatrix.getColumns(); + + Matrix A(rows - 1, cols - 1); + ColumnVector C(cols - 1); + ColumnVector b(rows - 1); + + for (int j = 0; j < cols - 1; ++j) { + C[j] = generalMatrix[0][j]; + } + + for (int i = 1; i < rows; ++i) { + b[i - 1] = generalMatrix[i - 1][cols - 1]; + } + + for (int i = 1; i < rows; ++i) { + for (int j = 0; j < cols - 1; ++j) { + A[i - 1][j] = generalMatrix[i][j]; + } + } + + return {A, C, b}; +} + Matrix createGeneralMatrix(Matrix& A, ColumnVector& C, ColumnVector& b) { Matrix generalMatrix(A.getRows() + 1, A.getColumns() + 1); for (int i = 0; i < A.getColumns(); i++) { generalMatrix[0][i] = C[i]; } - generalMatrix[0][A.getColumns()] = 0; for (int j = 0; j < A.getRows(); j++) { - generalMatrix[j + 1][A.getColumns()] = b[j]; + generalMatrix[j][A.getColumns()] = b[j]; } for (int i = 0; i < A.getRows(); i++) { @@ -28,13 +58,13 @@ int main() { std::cin >> m; ColumnVector C(n); - Matrix A(n, m); - ColumnVector b(n); + Matrix A(m - 1, n); + ColumnVector b(m); double eps; double eps_default; std::cin >> C; - std::cin >> A; std::cin >> b; + std::cin >> A; std::cout << "Вектор C: " << C << std::endl; std::cout << "Вектор b: " << b << std::endl; @@ -42,8 +72,14 @@ int main() { std::cout << "Матрица A: " << A << std::endl; Matrix E = createGeneralMatrix(A, C, b); + std::cout << "Матрица E: " << E << std::endl; + + DestroyMatrix destroyed = destroyGeneralMatrix(E); + std::cout << "Вектор C: " << destroyed.C << std::endl; + std::cout << "Вектор b: " << destroyed.b << std::endl; + + std::cout << "Матрица A: " << destroyed.A << std::endl; - std::cout << "Новая матрица:" << E << std::endl; return 0; } diff --git a/tools/elimination.cpp b/tools/elimination.cpp index 8182f67..183cdbd 100644 --- a/tools/elimination.cpp +++ b/tools/elimination.cpp @@ -2,15 +2,53 @@ #include "matrix.h" #include "math.h" +struct FracturedMatrix { + Matrix A; + ColumnVector C; + ColumnVector b; + int pivot_column_index; + int pivot_row_index; +}; + +struct DestroyMatrix { + Matrix A; + ColumnVector C; + ColumnVector b; +}; + +DestroyMatrix destroyGeneralMatrix(Matrix& generalMatrix) { + int rows = generalMatrix.getRows(); + int cols = generalMatrix.getColumns(); + + Matrix A(rows - 1, cols - 1); + ColumnVector C(cols - 1); + ColumnVector b(rows - 1); + + for (int j = 0; j < cols - 1; ++j) { + C[j] = generalMatrix[0][j]; + } + + for (int i = 1; i < rows; ++i) { + b[i - 1] = generalMatrix[i - 1][cols - 1]; + } + + for (int i = 1; i < rows; ++i) { + for (int j = 0; j < cols - 1; ++j) { + A[i - 1][j] = generalMatrix[i][j]; + } + } + + return {A, C, b}; +} + Matrix createGeneralMatrix(Matrix& A, ColumnVector& C, ColumnVector& b) { Matrix generalMatrix(A.getRows() + 1, A.getColumns() + 1); for (int i = 0; i < A.getColumns(); i++) { generalMatrix[0][i] = C[i]; } - generalMatrix[0][A.getColumns()] = 0; for (int j = 0; j < A.getRows(); j++) { - generalMatrix[j + 1][A.getColumns()] = b[j]; + generalMatrix[j][A.getColumns()] = b[j]; } for (int i = 0; i < A.getRows(); i++) { @@ -22,10 +60,42 @@ Matrix createGeneralMatrix(Matrix& A, ColumnVector& C, ColumnVector& b) { return generalMatrix; } -Matrix elimination(Matrix A, ColumnVector C, ColumnVector b, int pivot_column_index, int pivot_row_index, double eps) { +FracturedMatrix elimination(Matrix A, ColumnVector C, ColumnVector b, int pivot_column_index, int pivot_row_index) { Matrix generalMatrix = createGeneralMatrix(A, C, b); + + int rows = generalMatrix.getRows(); + int cols = generalMatrix.getColumns(); + + double pivotElement = generalMatrix[pivot_row_index][pivot_column_index]; + + for (int j = 0; j < cols; ++j) { + generalMatrix[pivot_row_index][j] /= pivotElement; + } + + for (int i = 0; i < rows; ++i) { + if (i == pivot_row_index) + continue; + + double pivotColumnCoefficient = generalMatrix[i][pivot_column_index]; + + for (int j = 0; j < cols; ++j) { + generalMatrix[i][j] -= pivotColumnCoefficient * generalMatrix[pivot_row_index][j]; + } + } + + DestroyMatrix destroyedMatrix = destroyGeneralMatrix(generalMatrix); + + pivot_column_index = Math::max_index(destroyedMatrix.C); - - return generalMatrix; + ColumnVector ratio_vector(A.getRows()); + + for (int i = 0; i < A.getRows(); i++) { + ratio_vector[i] = b[i] / A[i][pivot_column_index]; + } + + int pivot_row_index = Math::min_index(ratio_vector); + + return {A, C, b, pivot_column_index, pivot_row_index}; } + diff --git a/tools/elimination.h b/tools/elimination.h index a57e6d3..12b6b7a 100644 --- a/tools/elimination.h +++ b/tools/elimination.h @@ -5,7 +5,7 @@ class Elimination { public: - Matrix elimination(Matrix A, ColumnVector C, ColumnVector b, int pivot_column_index, int pivot_row_index, double eps); + Matrix elimination(Matrix A, ColumnVector C, ColumnVector b, double eps); }; diff --git a/tools/math.cpp b/tools/math.cpp index 255124d..122aad5 100644 --- a/tools/math.cpp +++ b/tools/math.cpp @@ -1,7 +1,7 @@ #include "math.h" #include "matrix.h" -double Math::minVector(ColumnVector columnVector) { +double Math::min(ColumnVector columnVector) { double temp = columnVector[0]; for (int j = 0; j < columnVector.getColumns(); j++) { if (columnVector[j] < temp) { @@ -11,7 +11,7 @@ double Math::minVector(ColumnVector columnVector) { return temp; } -double Math::maxVector(ColumnVector columnVector) { +double Math::max(ColumnVector columnVector) { double temp = columnVector[0]; for (int j = 0; j < columnVector.getColumns(); j++) { if (columnVector[j] > temp) { @@ -21,7 +21,31 @@ double Math::maxVector(ColumnVector columnVector) { return temp; } -double Math::minArray(std::vector array) { +int Math::min_index(ColumnVector columnVector) { + int temp_index = 0; + double temp = columnVector[0]; + for (int j = 0; j < columnVector.getColumns(); j++) { + if (columnVector[j] < temp) { + temp_index = j; + temp = columnVector[j]; + } + } + return temp_index; +} + +int Math::max_index(ColumnVector columnVector) { + int temp_index = 0; + double temp = columnVector[0]; + for (int j = 0; j < columnVector.getColumns(); j++) { + if (columnVector[j] > temp) { + temp_index = j; + temp = columnVector[j]; + } + } + return temp_index; +} + +double Math::min(std::vector array) { double temp = array[0]; for (size_t i = 1; i < array.size(); i++) { if (array[i] < temp) { @@ -31,7 +55,7 @@ double Math::minArray(std::vector array) { return temp; } -double Math::maxArray(std::vector array) { +double Math::max(std::vector array) { double temp = array[0]; for (size_t i = 1; i < array.size(); i++) { if (array[i] > temp) { @@ -40,3 +64,27 @@ double Math::maxArray(std::vector array) { } return temp; } + +double Math::min(std::vector array) { + int temp_index = 0; + double temp = array[0]; + for (size_t i = 1; i < array.size(); i++) { + if (array[i] < temp) { + temp_index = i; + temp = array[i]; + } + } + return temp_index; +} + +double Math::max(std::vector array) { + int temp_index = 0; + double temp = array[0]; + for (size_t i = 1; i < array.size(); i++) { + if (array[i] > temp) { + temp_index = i; + temp = array[i]; + } + } + return temp_index; +} \ No newline at end of file diff --git a/tools/math.h b/tools/math.h index 8ff38f0..5dab8e5 100644 --- a/tools/math.h +++ b/tools/math.h @@ -4,14 +4,17 @@ #include class ColumnVector; -class Matrix; class Math { public: - double minVector(ColumnVector columnVector); - double maxVector(ColumnVector columnVector); - double minArray(std::vector array); - double maxArray(std::vector array); + double min(ColumnVector columnVector); + double max(ColumnVector columnVector); + static int min_index(ColumnVector columnVector); + static int max_index(ColumnVector columnVector); + double min(std::vector array); + double max(std::vector array); + int min_index(std::vector array); + int max_index(std::vector array); }; #endif // MATH_H \ No newline at end of file