Start Task 3

2025.03.28/02Ex/a.txt

@@ -0,0 +1,5 @@
+4 1 0 0 0
+1 4 1 0 0
+0 1 4 1 0
+0 0 1 4 1
+0 0 0 1 4

2025.03.28/02Ex/matrix.c

@@ -8,12 +8,9 @@ void init_vec_b(const double * restrict a, double * restrict b, int n)
 	{
 		double sum = 0;
 
-//		#pragma omp simd reduction(+:sum)
-//		for (int k = 1; k < n; k+=2)
-//			sum += a[i * n + k];
-		
-		for (int k = 0; k < (n-1)/2; ++k)
-			sum += a[i*n + 2*k+1];
+		#pragma omp simd reduction(+:sum)
+		for (int k = 1; k < n; k+=2)
+			sum += a[i * n + k];
 
 		b[i] = sum;
 	}

2025.03.28/02Ex/solve.c

@@ -5,7 +5,6 @@
 
 void t2_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, int n, int m, double t)
 {
-	#pragma omp parallel for
 	for (int k = 0; k < m; ++k)
 	{
 		double * swap_temp;
@@ -20,7 +19,7 @@ void t2_solve(const double * restrict A, double * restrict x_0, const double * r
 		x_0 = swap_temp;
 	}
 
-	if (m % 2 == 0)	
+	if (m % 2 == 0) // Проверил 100 раз	
 		for (int i = 0; i < n; i++)
 		{
 			double temp = x[i];
@@ -62,18 +61,18 @@ double t2_get_r1(const double * restrict A, const double * restrict x_k, const d
 
 double t2_get_r2_value(const double * restrict x_k, int n)
 {
-	double r2 = 0;
-	double abs_xi = 0;
-	double abs_i = 0;
+	double relative_error = 0;
+	double total_diff = 0;
+	double template_sum = 0;
 
-	#pragma omp parallel for reduction(+:abs_xi, abs_i)
+	#pragma omp parallel for reduction(+:total_diff, template_sum)
 	for (int i = 0; i < n; ++i)
 	{
 		short int modi = i ^ 1;
-		abs_xi += fabs(x_k[i] - modi);
-		abs_i += modi;
+		total_diff += fabs(x_k[i] - modi);
+		template_sum += modi;
 	}
 
-	r2 = abs_xi / abs_i;
-	return r2;
+	relative_error = total_diff / template_sum;
+	return relative_error;
 }

2025.03.28/02Ex/t.txt

@@ -0,0 +1,5 @@
+0
+0
+0
+0
+0

2025.03.28/03Ex/Makefile

@@ -0,0 +1,30 @@
+CFLAGS = -mfpmath=sse -fstack-protector-all -W -Wall -Wextra -Wunused \
+-Wempty-body -Wlogical-op -Wold-style-declaration -Wmissing-parameter-type \
+-Wignored-qualifiers -Winit-self -Wshadow -Wtype-limits \
+-Wpointer-arith -Wformat-security -Wmissing-format-attribute -Wformat=1 \
+-Wdeclaration-after-statement -Wbad-function-cast -Wnested-externs \
+-Wmissing-prototypes -Wmissing-declarations -Wold-style-definition \
+-Wcast-align -Werror -pedantic -pedantic-errors -Wfloat-equal \
+-Wwrite-strings -Wno-long-long -std=gnu99 -Wstrict-prototypes \
+-Wmissing-field-initializers -Wpointer-sign -fopenmp -O3
+
+TARGET = a01.out
+OBJ = main.o solve.o array_io.o init_f.o
+
+$(TARGET): $(OBJ)
+	gcc $^ -o $@ -lm -fopenmp 
+
+main.o: main.c
+	gcc $(CFLAGS) -c $^
+
+solve.o: solve.c
+	gcc $(CFLAGS) -c $^
+
+array_io.o: array_io.c
+	gcc $(CFLAGS) -c $^
+
+init_f.o: init_f.c
+	gcc $(CFLAGS) -c $^
+
+clean:
+	rm *.o *.out

2025.03.28/03Ex/a.txt

@@ -0,0 +1,2 @@
+1.0001 0
+0 1

2025.03.28/03Ex/array_io.c

@@ -0,0 +1,40 @@
+#include <stdio.h>
+#include "array_io.h"
+
+io_status read_matrix(double *a, int m, int n, const char *name)
+{
+	int i, j;
+	FILE *fp;
+	if (!(fp = fopen(name, "r"))) return ERROR_OPEN;
+	for (i = 0; i < m; i++)
+		for (j = 0; j < n; j++)
+			if (fscanf(fp, "%lf", a + i * n + j) != 1) 
+				{fclose(fp); return ERROR_READ;}
+	fclose(fp);
+	return SUCCESS;
+}
+
+void print_matrix(const double *a, int m, int n, int p)
+{
+	int mp = (m > p ? p : m);
+	int np = (n > p ? p : n);
+	int i, j;
+
+	for (i = 0; i < mp; i++)
+	{
+		for (j = 0; j < np; j++)
+			printf(" %10.3e", a[i * n + j]);
+		printf("\n");
+	}
+}
+
+void init_matrix(double *a, int m, int n, int k)
+{
+	double (*q)(int, int, int, int);
+	double (*f[])(int, int, int, int) = {f1, f2, f3, f4};
+	int i, j;
+	q = f[k-1];
+	for (i = 0; i < m; i++)
+		for (j = 0; j < n; j++)
+			a[i * n + j] = q(m, n, i+1, j+1);
+}

2025.03.28/03Ex/array_io.h

@@ -0,0 +1,11 @@
+#ifndef ARRAY_IO_H
+#define ARRAY_IO_H
+
+#include "io_status.h"
+#include "init_f.h"
+
+io_status read_matrix(double *a, int m, int n, const char *name);
+void print_matrix(const double *a, int m, int n, int p);
+void init_matrix(double *a, int m, int n, int k);
+
+#endif

2025.03.28/03Ex/init_f.c

@@ -0,0 +1,30 @@
+#include "init_f.h"
+#include <stdlib.h>
+
+#define MAX(n, m) (n < m ? m : n)
+
+double f1(int m, int n, int i, int j)
+{
+	return MAX(n, m) - MAX(i, j) + 1;
+}
+
+double f2(int m, int n, int i, int j)
+{
+	(void)n;
+	(void)m;
+	return MAX(i, j);
+}
+
+double f3(int m, int n, int i, int j)
+{
+	(void)n;
+	(void)m;
+	return abs(i - j);
+}
+
+double f4(int m, int n, int i, int j)
+{
+	(void)n;
+	(void)m;
+	return 1./(i+j-1);
+}

2025.03.28/03Ex/init_f.h

@@ -0,0 +1,9 @@
+#ifndef INIT_F_H
+#define INIT_F_H
+
+double f1(int m, int n, int i, int j);
+double f2(int m, int n, int i, int j);
+double f3(int m, int n, int i, int j);
+double f4(int m, int n, int i, int j);
+
+#endif

2025.03.28/03Ex/io_status.h

@@ -0,0 +1,13 @@
+#ifndef IO_STATUS_H
+#define IO_STATUS_H
+
+#define LEN 1234
+
+typedef enum _io_status
+{
+	SUCCESS,
+	ERROR_OPEN,
+	ERROR_READ
+} io_status;
+
+#endif

2025.03.28/03Ex/main.c

@@ -0,0 +1,141 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#include "array_io.h"
+#include "io_status.h"
+#include "solve.h"
+
+/* ./a.out m n p k_a [filename_a] k_x [filename_x] */
+int main(int argc, char *argv[])
+{
+	double t, r1, r2, *a, *x_0, *b, *x;
+	int n, m, p, k_a, k_x, task = 3;
+	char *name_a = 0, *name_x = 0;
+	if (!((argc == 6 || argc == 7 || argc == 8) && 
+				sscanf(argv[1], "%d", &m) == 1 && 
+				sscanf(argv[2], "%d", &n) == 1 && 
+				sscanf(argv[3], "%d", &p) == 1 && 
+				sscanf(argv[4], "%d", &k_a) == 1 && 
+				(k_a >= 0 && k_a <= 4) &&
+				(!(k_a == 0 && argc == 6)) && 
+				((k_a == 0 && sscanf(argv[6], "%d", &k_x) == 1) || 
+				 (k_a != 0 && sscanf(argv[5], "%d", &k_x) == 1)) &&
+				(k_x >= 0 && k_x <= 4) && 
+				(!(k_x == 0 && argc == 6)) && 
+				(!((k_a == 0 && k_x == 0) && argc != 8))))
+	{
+		printf("Usage: %s m n p k_a [filename_a] k_x [filename_x]\n", argv[0]);
+		return 1;
+	}
+	if (argc != 6) 
+	{
+		int i_x = 6;
+		if (k_a == 0) {name_a = argv[5];i_x++;}
+		if (k_x == 0) name_x = argv[i_x];
+	}
+
+	a = (double *)malloc((size_t)n * (size_t)n * sizeof(double));
+	if (!a)
+	{
+		printf("Not enough memory\n");
+		return 2;
+	}
+	x_0 = (double *)malloc((size_t)n * sizeof(double));
+	if (!x_0)
+	{
+		free(a);
+		printf("Not enough memory\n");
+		return 2;
+	}
+	b = (double *)malloc((size_t)n * sizeof(double));
+	if (!b)
+	{
+		free(a);
+		free(x_0);
+		printf("Not enough memory\n");
+		return 2;
+	}
+	x = (double *)malloc((size_t)n * sizeof(double));
+	if (!x)
+	{
+		free(a);
+		free(x_0);
+		free(b);
+		printf("Not enough memory\n");
+		return 2;
+	}
+
+	if (name_a)
+	{ /* из файла */
+		io_status ret;
+		ret = read_matrix(a, n, n, name_a);
+		do {
+			switch (ret)
+			{
+				case SUCCESS:
+					continue;
+				case ERROR_OPEN:
+					printf("Cannot open %s\n", name_a);
+					break;
+				case ERROR_READ:
+					printf("Cannot read %s\n", name_a);
+					break;
+			}
+			free(a);
+			free(x_0);
+			free(b);
+			free(x);
+			return 3;
+		} while (0);
+	} else init_matrix(a, n, n, k_a);
+
+	if (name_x)
+	{
+		io_status ret;
+		ret = read_matrix(x_0, n, 1, name_x);
+		do {
+			switch (ret)
+			{
+				case SUCCESS:
+					continue;
+				case ERROR_OPEN:
+					printf("Cannot open %s\n", name_x);
+					break;
+				case ERROR_READ:
+					printf("Cannot read %s\n", name_x);
+					break;
+			}
+			free(a);
+			free(x_0);
+			free(b);
+			free(x);
+			return 3;
+		} while (0);
+	} else init_matrix(x_0, n, 1, k_x);
+
+	init_vec_b(a, b, n);
+
+	printf("Matrix A:\n");
+	print_matrix(a, n, n, p);
+	printf("Vector x_0:\n");
+	print_matrix(x_0, 1, n, p);
+	printf("Vector b:\n");
+	print_matrix(b, 1, n, p);
+
+	t = clock();
+	t3_solve(a, x_0, x, n, m);
+	t = (clock() - t) / CLOCKS_PER_SEC;
+	
+	r1 = get_r1(a, x, b, n);
+	r2 = get_r2_value(x, n);
+
+	printf("Vector x_m:\n");
+	print_matrix(x, 1, n, p);
+	printf("%s : Task = %d Res1 = %e Res2 = %e Elapsed = %.2f\n", argv[0], task, r1, r2, t);
+
+	free(a);
+	free(x_0);
+	free(x);
+
+	return 0;
+}

2025.03.28/03Ex/matrix.c

@@ -0,0 +1,38 @@
+#include "matrix.h"
+#include <math.h>
+
+void init_vec_b(const double * restrict a, double * restrict b, int n)
+{
+	#pragma omp parallel for
+	for (int i = 0; i < n; ++i)
+	{
+		double sum = 0;
+
+		#pragma omp simd reduction(+:sum)
+		for (int k = 1; k < n; k+=2)
+			sum += a[i * n + k];
+
+		b[i] = sum;
+	}
+}
+
+/*
+ * OLD VERSION
+void matvec_mul(int n, const double * restrict A, const double * restrict x, double * restrict x_k)
+{
+	#pragma	omp parallel for
+	for (int i = 0; i < n; i++)
+	{
+		double sum = 0;
+		#pragma omp simd reduction(+:sum)
+		for (int j = 0; j < n; j++)
+			sum += A[i * n + j] * x[j];
+		x_k[i] = sum;
+	}	
+}
+*/
+
+void matvec_mul(int n, const double * restrict A, const double * restrict x, double * restrict x_k)
+{
+	cblas_dgemv(CblasRowMajor, CblasdNoTrans, n, n, 1.0, A, n, x, 1, 0.0, x_k, 1);	
+}

2025.03.28/03Ex/matrix.h

@@ -0,0 +1,7 @@
+#ifndef MATRIX_H
+#define MATRIX_H
+
+void init_vec_b(const double * restrict a, double * restrict b, int n);
+void matvec_mul(int n, const double * restrict A, const double * restrict x, double * restrict x_k);
+
+#endif

2025.03.28/03Ex/solve.c

@@ -0,0 +1,99 @@
+#include "solve.h"
+#include "matrix.h"
+#include <math.h>
+
+
+void t3_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, double * restrict r, int n, int m)
+{
+	for (int k = 0; k < m; ++k)
+	{
+		double * swap_temp = 0;
+		double t = 0;
+		double dot_r_r = 0, dot_Ar_r = 0;
+	
+		for (int i = 0; i < n; ++i)
+		{
+			double sum = 0;
+			for (int j = 0; j < n; ++j)
+				sum += A[i*n + j] * x_0[j];
+			r = sum - b[i];
+		}
+
+		for (int i = 0; i < n; ++i)
+		{
+			double ri = r[i];
+			double sum = 0;
+			for (int j = 0; j < n; ++j)
+				sum += A[i*n + j] * r[j];
+			
+			dot_Ar_r += sum * ri;
+			dot_r_r += ri * ri;
+		}
+		
+		t = dot_r_r / dot_Ar_r;
+		
+		for (int i = 0; i < n; ++i)
+			x[i] = x_0[i] - r[i]*t;
+		
+		swap_temp = x;
+		x = x_0;
+		x_0 = swap_temp;
+	}
+
+	if (m % 2 == 0) // Проверил 100 раз	
+		for (int i = 0; i < n; i++)
+		{
+			double temp = x[i];
+			x[i] = x_0[i];
+			x_0[i] = temp;
+		}
+	else
+	{
+		double * swap_temp = x;
+		x = x_0;
+		x_0 = swap_temp;
+	}
+}
+
+double get_r1(const double * restrict A, const double * restrict x_k, const double * restrict b, int n)
+{
+	double norm_r1x_1 = 0;
+	double residual_norm_1 = 0;
+	double r1 = 0;
+
+	#pragma omp parallel for reduction(+:residual_norm_1, norm_r1x_1)
+	for (int i = 0; i < n; ++i)
+	{
+		double bi = b[i];
+		double sum = 0;
+		
+		#pragma omp simd reduction(+:sum)
+		for (int j = 0; j < n; ++j)
+			sum += A[i*n + j] * x_k[j];
+		
+		residual_norm_1 += fabs(sum - bi);
+		norm_r1x_1 += fabs(bi);
+	}
+
+	r1 = residual_norm_1 / norm_r1x_1;
+
+	return r1;
+}
+
+double get_r2_value(const double * restrict x_k, int n)
+{
+	double relative_error = 0;
+	double total_diff = 0;
+	double template_sum = 0;
+
+	#pragma omp parallel for reduction(+:total_diff, template_sum)
+	for (int i = 0; i < n; ++i)
+	{
+		short int modi = i ^ 1;
+		total_diff += fabs(x_k[i] - modi);
+		template_sum += modi;
+	}
+
+	relative_error = total_diff / template_sum;
+	return relative_error;
+}

2025.03.28/03Ex/solve.h

@@ -0,0 +1,8 @@
+#ifndef SOLVE_H
+#define SOLVE_H
+
+void t2_solve(const double * restrict A, double * restrict x_0, const double * restrict b, double * restrict x, int n, int m, double t);
+double t2_get_r1(const double * restrict A, const double * restrict x_k, const double * restrict b, int n);
+double t2_get_r2_value(const double * restrict x_k, int n);
+
+#endif

2025.03.28/03Ex/v.txt

@@ -0,0 +1,2 @@
+1
+1

2025.03.28/Matvecmul/solve.c

@@ -1,6 +1,7 @@
 #include "solve.h"
 #include <math.h>
 
+
 #define eps 1e-17
 
 int compare(const double a, const double b)
@@ -38,3 +39,5 @@ void matvec_mul(int n, double * restrict A, double * restrict x, double * restri
 		x_k[i] = sum;
 	}	
 }
+
+

2025.03.28/dist/Sustavov/a.txt

@@ -0,0 +1,5 @@
+4 1 0 0 0
+1 4 1 0 0
+0 1 4 1 0
+0 0 1 4 1
+0 0 0 1 4

2025.03.28/dist/Sustavov/t.txt

@@ -0,0 +1,5 @@
+0
+0
+0
+0
+0

2025.03.28/dist/Ulyanov/a.txt

@@ -0,0 +1,5 @@
+4 1 0 0 0
+1 4 1 0 0
+0 1 4 1 0
+0 0 1 4 1
+0 0 0 1 4

2025.03.28/dist/Ulyanov/t.txt

@@ -0,0 +1,5 @@
+0
+0
+0
+0
+0