Lab 4

Lab4/M.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_M_good.csv'); % reading csv file 
+X = data(:,1);
+Y = data(:,2); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('M(Eps)');
+title("$\bf M(Eps)$", 'Interpreter','latex');
+xlabel('Eps')
+ylabel('M')

Lab4/M_bad.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_M_bad.csv'); % reading csv file 
+X = data(:,1);
+Y = data(:,2); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('M(Eps)');
+title("$\bf M(Eps)$", 'Interpreter','latex');
+xlabel('Eps')
+ylabel('M')

Lab4/M_tol.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_M_good_tol.csv'); % reading csv file 
+X = data(:,2);
+Y = data(:,1); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('Eps(M)');
+title("$\bf Eps(M)$", 'Interpreter','latex');
+xlabel('M')
+ylabel('Eps')

Lab4/M_tol_bad.m

@@ -0,0 +1,10 @@
+data=csvread('lab_4_M_bad_tol.csv'); % reading csv file 
+X = data(:,2);
+Y = data(:,1); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('Eps(M)');
+title("$\bf Eps(M)$", 'Interpreter','latex');
+xlabel('M')
+ylabel('Eps')

Lab4/cond.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_cond.csv'); % reading csv file 
+X = data(:,1);
+Y = data(:,2); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('Error(Cond)');
+title("$\bf Error(Condition)$", 'Interpreter','latex');
+xlabel('Condition')
+ylabel('Error')

Lab4/error.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_error_good.csv'); % reading csv file 
+X = data(:,1);
+Y = data(:,2); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('Error(Eps)');
+title("$\bf Error(Eps)$", 'Interpreter','latex');
+xlabel('Eps')
+ylabel('Error')

Lab4/error_bad.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_error_bad.csv'); % reading csv file 
+X = data(:,1);
+Y = data(:,2); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('Error(Eps)');
+title("$\bf Error(Eps)$", 'Interpreter','latex');
+xlabel('Eps')
+ylabel('Error')

Lab4/lab.c

@@ -0,0 +1,261 @@
+#define _USE_MATH_DEFINES
+#include<stdio.h>
+#include<stdlib.h>
+#include<math.h>
+#include<time.h>
+
+// Необязательный флаг для дебага (можно удалить)
+#define DEBUG 0
+
+// Фиксированная размерность матрицы (обрабатывается препроцессором, просто alias)
+#define N 10
+
+//
+struct N_eps {
+	double eps;
+	int I;	
+};
+
+// Тип вектора
+typedef double vec[N];
+
+// Тип матрицы
+typedef double mat[N][N];
+
+// Скалярное произведение
+double dot(vec v, vec u) {
+    double res = 0;
+    for(int i = 0; i < N; i++) res += v[i]*u[i];
+
+    return res;
+}
+
+// Прибавление вектора
+void add(vec v, vec u, vec result) {
+    for(int i = 0; i < N; i++) {
+        result[i] = v[i] + u[i];
+    }
+}
+
+// Вычитание вектора
+void sub(vec v, vec u, vec result) {
+    for(int i = 0; i < N; i++) {
+        result[i] = v[i] - u[i];
+    }
+}
+
+// Умножение на скаляр
+void mul(vec v, double a) {
+    for(int i = 0; i < N; i++) {
+        v[i] *= a;
+    }
+}
+
+// Умножение матрицы на вектор (res = m*v)
+void apply(mat m, vec v, vec res) {   
+    for(int i = 0; i < N; i++) {
+        res[i] = 0;
+        for(int j = 0; j < N; j++) {
+            res[i] += m[i][j] * v[j]; 
+        }
+    }
+}
+
+
+// Копирование матрицы (copy = m)
+void copy_vec(vec copy, vec x) {
+    for(int i = 0; i < N; i++) {
+        copy[i] = x[i];
+    }
+}
+
+//Ошибка между двумя векторами
+double error(vec a, vec b){
+    double error = 0;
+    for (int i = 0; i < N; i++) {
+		if (error < fabs(a[i] - b[i])) {
+			error = fabs(a[i] - b[i]);
+		}
+	}
+    return error;
+}
+
+// Чтение матрицы из файла
+void mat_from_file(FILE* f, mat m) {
+	double d;
+	for (int i = 0; i < N; i++) {
+		for (int j = 0; j < N; j++) {
+			fscanf(f, "%lf,", &d);
+			m[i][j] = d;
+		}
+	}
+}
+// Чтение матрицы из файла
+void min_max_from_file(FILE* f, vec v) {
+	double d;
+	for (int i = 0; i < 2; i++) {
+		fscanf(f, "%lf,", &d);
+		v[i] = d;
+	}
+}
+
+// Красивая печать матрицы
+void print_mat(mat m) {
+    for(int j = 0; j < N; j++) {
+        printf("-----------|");
+    }
+    printf("\n");
+    for(int i = 0; i < N; i++) {
+        for(int j = 0; j < N; j++) {
+            printf("%10.4lf |", m[i][j]);
+        }
+        printf("\n");
+        for(int j = 0; j < N; j++) {
+            printf("-----------|");
+        }
+        printf("\n");
+    }
+}
+
+// Красивая печать вектора
+void print_vec(vec v) {
+    for(int j = 0; j < N; j++) {
+        printf("%10.4lf |", v[j]);
+    }
+    printf("\n");
+}
+
+void mx_b(mat m, vec x, vec b, vec result){
+    apply(m,x,result);
+    sub(b,result,result);
+}
+
+// Решение СЛАУ методом Ричардсона
+struct N_eps solve(mat m, double eps, int M, double min, double max) {
+    struct N_eps result;
+    result.I = 0;
+    vec x = { 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9};
+    vec x1;
+    vec b;
+    vec var;
+    vec x_k = { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
+    apply(m,x_k,b);
+    print_vec(b);
+
+    for (int k = 0; k < M; k++) {
+        
+
+
+        double t = cos(M_PI * (2 * (k + 1) - 1) / (2 * M));
+        printf("\n t = %lf\n", t);
+        double alpha  = 2.0 / ((min + max) + ((max - min)*t));
+    
+        mx_b(m, x, b, var);
+        //print_vec(var);
+
+        mul(var,alpha);
+        //print_vec(var);
+
+        add(x,var,x1);
+        print_vec(x1);
+
+        if (error(x,x1) < eps){
+            result.eps = error(x,x1);
+            result.I += 1;
+            break;
+        }
+        result.eps = error(x,x1);
+        result.I += 1;
+        copy_vec(x,x1);
+        print_vec(x);
+    }
+    return result;
+}
+
+//взять из мат лаба
+int main(){
+    FILE* f;
+    FILE* f2;
+	if ((f = fopen("lab4_1.txt", "r")) == NULL) return 1;
+    if ((f2 = fopen("min_max.txt", "r")) == NULL) return 1;
+    mat m;
+    vec min_max;
+    FILE* file;
+    FILE* file2;
+    if ((file = fopen("lab_4_cond.csv", "w+")) == NULL) return 1;
+    if ((file2 = fopen("lab_4_time.csv", "w+")) == NULL) return 1;
+    for (int k = 0; k < 8; k++){
+        mat_from_file(f, m);
+        min_max_from_file(f2, min_max);
+        clock_t begin = clock();
+        struct N_eps result = solve(m, pow(10, -5), 1000, min_max[0], min_max[1]);
+        clock_t end = clock();
+        printf("\n\n\n");
+        fprintf(file, "%.5lf, %e\n", pow(10, k), result.eps);
+        fprintf(file2, "%.5lf, %e\n", pow(10, k), ((float)(end - begin) / CLOCKS_PER_SEC));
+    }
+    fclose(f);
+    fclose(f2); 
+    fclose(file);
+    fclose(file2);
+
+    FILE* fbad = fopen("lab_4_error_bad.txt", "r");
+    FILE* fminbad = fopen("min_max2.txt", "r");
+    FILE* fbade = fopen("lab_4_error_bad.csv", "w+");
+    FILE* fbadm = fopen("lab_4_M_bad.csv", "w+");
+    mat_from_file(fbad,m);
+    min_max_from_file(fminbad, min_max);
+    for (int i = 1; i < 6; i++) {
+        struct N_eps result = solve(m, pow(10, -i), 1000, min_max[0], min_max[1]);
+        fprintf(fbade, "%e, %e\n", pow(10, -i), result.eps);
+        fprintf(fbadm, "%e, %d\n", pow(10, -i), result.I);
+    }
+    fclose(fbad);
+    fclose(fminbad);
+    fclose(fbade);
+    fclose(fbadm);
+
+
+    FILE* fgood = fopen("lab_4_error_good.txt", "r");\
+    FILE* fmingood = fopen("min_max3.txt", "r");
+    FILE* fgoode = fopen("lab_4_error_good.csv", "w+");
+    FILE* fgoodm = fopen("lab_4_M_good.csv", "w+");
+    mat_from_file(fgood,m);
+    min_max_from_file(fmingood, min_max);
+    for (int i = 1; i < 16; i++) {
+        struct N_eps result = solve(m, pow(10, -i), 1000, min_max[0], min_max[1]);
+        fprintf(fgoodm, "%e, %d\n", pow(10, -i), result.I);
+        fprintf(fgoode, "%e, %e\n", pow(10, -i), result.eps);
+    }
+    fclose(fgood);
+    fclose(fmingood);
+    fclose(fgoode);
+    fclose(fgoodm);
+
+
+    FILE* fbad2 = fopen("lab_4_error_bad.txt", "r");
+    FILE* fminbad2 = fopen("min_max2.txt", "r");
+    FILE* fbadmt = fopen("lab_4_M_bad_tol.csv", "w+");
+    mat_from_file(fbad2,m);
+    min_max_from_file(fminbad2, min_max);
+    for (int i = 0; i < 41; i++) {
+        struct N_eps result = solve(m, pow(10, -15), i, min_max[0], min_max[1]);
+        fprintf(fbadmt, "%e, %d\n", result.eps, result.I);
+    }
+    fclose(fbad2);
+    fclose(fminbad2);
+    fclose(fbadmt);
+
+    FILE* fgood2 = fopen("lab_4_error_good.txt", "r");
+    FILE* fmindoof2 = fopen("min_max3.txt", "r");
+    FILE* fgoodmt2 = fopen("lab_4_M_good_tol.csv", "w+");
+    mat_from_file(fgood2,m);
+    min_max_from_file(fmindoof2, min_max);
+    for (int i = 0; i < 41; i++) {
+        struct N_eps result = solve(m, pow(10, -15), i, min_max[0], min_max[1]);
+        fprintf(fgoodmt2, "%e, %d\n", result.eps, i);
+    }
+    fclose(fgood2);
+    fclose(fmindoof2);
+    fclose(fgoodmt2);
+}

Lab4/lab4_1.txt

@@ -0,0 +1,80 @@
+2.0181 0.7868 0.8209 1.1553 0.6649 0.8245 1.1792 1.0289 0.7177 1.1886
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Lab4/lab_4_M_bad.csv

@@ -0,0 +1,5 @@
+1.000000e-01, 2
+1.000000e-02, 2
+1.000000e-03, 2
+1.000000e-04, 2
+1.000000e-05, 2

Lab4/lab_4_M_bad_tol.csv

@@ -0,0 +1,41 @@
+1.079005e-311, 0
+2.547581e-01, 1
+1.390307e-01, 2
+1.138031e-01, 3
+9.305394e-02, 4
+7.106301e-02, 5
+4.712831e-02, 6
+2.183628e-02, 7
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+8.994934e+01, 36
+3.196828e+02, 37
+1.006674e+03, 38
+3.341589e+03, 39
+1.138087e+04, 40

Lab4/lab_4_M_good.csv

@@ -0,0 +1,15 @@
+1.000000e-01, 2
+1.000000e-02, 2
+1.000000e-03, 13
+1.000000e-04, 34
+1.000000e-05, 56
+1.000000e-06, 78
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+1.000000e-11, 183
+1.000000e-12, 203
+1.000000e-13, 223
+1.000000e-14, 242
+1.000000e-15, 262

Lab4/lab_4_M_good_tol.csv

@@ -0,0 +1,41 @@
+1.079005e-311, 0
+2.173891e-01, 1
+8.802993e-02, 2
+3.685533e-02, 3
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+5.647824e-08, 37
+6.710773e-08, 38
+8.244036e-08, 39
+1.250861e-09, 40

Lab4/lab_4_cond.csv

@@ -0,0 +1,8 @@
+1.00000, 9.645124e-06
+10.00000, 9.928609e-06
+100.00000, 2.928609e-05
+1000.00000, 3.186230e-05
+10000.00000, 4.075690e-05
+100000.00000, 6.840757e-05
+1000000.00000, 9.195746e-05
+10000000.00000, 6.665259e-05

Lab4/lab_4_error_bad.csv

@@ -0,0 +1,5 @@
+1.000000e-01, 1.305911e-05
+1.000000e-02, 1.305911e-05
+1.000000e-03, 1.305911e-05
+1.000000e-04, 1.305911e-05
+1.000000e-05, 1.305911e-05

Lab4/lab_4_error_bad.txt

@@ -0,0 +1,10 @@
+12297.8016 10048.2946 11332.6820 9577.6572 10016.8382 10691.0788 12203.2811 11346.9002 9904.2825 7738.3639
+10098.6997 8251.8236 9306.1674 7865.4000 8225.9401 8780.0036 10020.6257 9317.4457 8133.2139 6353.9544
+12921.9560 10558.2317 11907.2271 10064.5653 10525.4282 11234.2783 12823.0188 11923.2111 10407.2010 8130.4166
+12339.2819 10081.8974 11370.5923 9610.4352 10051.4064 10727.3507 12244.0725 11385.2234 9938.5866 7764.1476
+8708.3958 7114.8499 8024.7758 6782.1939 7092.5523 7571.1405 8640.9919 8034.8875 7013.9085 5479.2480
+9595.2145 7839.5697 8841.4358 7473.1363 7814.9084 8340.7850 9520.4424 8852.7223 7727.4187 6036.8177
+13589.5911 11103.1305 12522.4831 10583.3942 11069.0080 11813.8909 13484.9705 12537.9708 10944.7430 8549.8037
+14897.1169 12171.9616 13726.6597 11602.1343 12133.7171 12950.8644 14782.2116 13744.1940 11998.0423 9373.4282
+12417.7676 10146.8528 11442.7411 9671.0181 10114.4790 10795.4821 12322.0659 11457.7915 10001.6746 7812.9811
+6783.0769 5541.7266 6249.6225 5282.0186 5524.7929 5896.7245 6729.9699 6258.3133 5462.2929 4267.5979

Lab4/lab_4_error_good.csv

@@ -0,0 +1,15 @@
+1.000000e-01, 2.870504e-03
+1.000000e-02, 5.870504e-03
+1.000000e-03, 9.012270e-04
+1.000000e-04, 9.855859e-05
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+1.000000e-07, 9.892614e-08
+1.000000e-08, 9.220616e-09
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+1.000000e-10, 9.154311e-11
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+1.000000e-12, 9.898748e-13
+1.000000e-13, 9.681145e-14
+1.000000e-14, 9.992007e-15
+1.000000e-15, 7.771561e-16

Lab4/lab_4_error_good.txt

@@ -0,0 +1,10 @@
+2.0181 0.7868 0.8209 1.1553 0.6649 0.8245 1.1792 1.0289 0.7177 1.1886
+0.7868 1.6081 0.6344 0.8929 0.5138 0.6372 0.9113 0.7952 0.5547 0.9186
+0.8209 0.6344 1.6619 0.9315 0.5361 0.6648 0.9508 0.8296 0.5787 0.9583
+1.1553 0.8929 0.9315 2.3109 0.7545 0.9356 1.3381 1.1675 0.8144 1.3487
+0.6649 0.5138 0.5361 0.7545 1.4342 0.5384 0.7701 0.6719 0.4687 0.7762
+0.8245 0.6372 0.6648 0.9356 0.5384 1.6677 0.9550 0.8332 0.5812 0.9626
+1.1792 0.9113 0.9508 1.3381 0.7701 0.9550 2.3658 1.1917 0.8312 1.3767
+1.0289 0.7952 0.8296 1.1675 0.6719 0.8332 1.1917 2.0398 0.7253 1.2012
+0.7177 0.5547 0.5787 0.8144 0.4687 0.5812 0.8312 0.7253 1.5059 0.8379
+1.1886 0.9186 0.9583 1.3487 0.7762 0.9626 1.3767 1.2012 0.8379 2.3876

Lab4/lab_4_time.csv

@@ -0,0 +1,8 @@
+1.00000, 2.500000e-02
+10.00000, 1.000000e-02
+100.00000, 9.000000e-03
+1000.00000, 8.000000e-03
+10000.00000, 8.000000e-03
+100000.00000, 5.000000e-03
+1000000.00000, 4.000000e-03
+10000000.00000, 3.000000e-03

Lab4/min_max.txt

@@ -0,0 +1,8 @@
+1.000000e+00 1.000000e+01
+1.000000e+00 1.000000e+02
+1.000000e+00 1.000000e+03
+1.000000e+00 1.000000e+04
+1.000000e+00 1.000000e+05
+1.000000e+00 1.000000e+06
+1.000000e+00 1.000000e+07
+1.000000e+00 1.000000e+08

Lab4/min_max2.txt

@@ -0,0 +1 @@
+1.000000e+00 1.000000e+05

Lab4/min_max3.txt

@@ -0,0 +1 @@
+1.000000e+00 1.000000e+01

Lab4/time.m

@@ -0,0 +1,11 @@
+X = logspace(-16, -1, 16);
+data=csvread('lab_4_time.csv'); % reading csv file 
+X = data(:,1);
+Y = data(:,2); 
+figure;
+loglog(X, Y, '-o');
+grid on;
+legend('Time(Cond)');
+title("$\bf Time(Condition)$", 'Interpreter','latex');
+xlabel('Condition')
+ylabel('Time')