Debuggin linear equations

homework/linear-equations/Makefile

-CFLAGS = -Wall -O1 -std=gnu11 $(shell gsl-config --cflags)
+CFLAGS = -Wall -O3 -std=gnu11 $(shell gsl-config --cflags)
 LDLIBS = -lm $(shell gsl-config --libs)
 
 default: out.txt time_graph.png
@@ -6,6 +6,8 @@ default: out.txt time_graph.png
 out.txt time_test.txt: main
 	./$< > $@
 
+main: main.c functions.c
+
 time_graph.png: time_test.txt Makefile
 	echo '\
 	set terminal png;\

homework/linear-equations/functions.c

+#include "functions.h"
+
+void print_vector(char s[], gsl_vector* v) {
+	printf("%s\n",s);
+	for(int i=0;i<v->size;i++) {
+		printf("%15g",gsl_vector_get(v,i));
+		printf("\n");
+	}
+}
+
+void print_matrix(gsl_matrix* M) {
+    for(int i = 0; i < M->size1; i++) {
+        for(int j = 0; j < M->size2; j++) {
+            printf("%15g\t", gsl_matrix_get(M, i, j));
+        }
+        printf("\n");
+    }
+}
+
+void GS_decomp(gsl_matrix* A, gsl_matrix* R) {
+    int n = A -> size1;
+    int m = A -> size2;
+    for(int i=0;i<m;i++) {
+        gsl_vector_view ai = gsl_matrix_column(A,i);
+        double Rii = gsl_blas_dnrm2(&(ai.vector));
+        gsl_matrix_set(R,i,i,Rii);
+        gsl_vector_scale(&(ai.vector),1/Rii);
+        for(int j=i+1;j<m;j++) {
+            gsl_vector_view aj = gsl_matrix_column(A,j);
+            double Rij;
+            gsl_blas_ddot(&(ai.vector),&(aj.vector),&Rij);
+            gsl_matrix_set(R,i,j,Rij);
+            gsl_vector* qiRij = gsl_vector_alloc(n);
+            gsl_vector_memcpy(qiRij,&(ai.vector));
+            gsl_vector_scale(qiRij,Rij);
+            gsl_vector_sub(&(aj.vector),qiRij);
+        }
+    }
+}
+
+void GS_solve(gsl_matrix* Q, gsl_matrix* R, gsl_vector* b, gsl_vector* x) {
+    assert(Q->size1==Q->size2);
+    int m = Q -> size2;
+    gsl_blas_dgemv(CblasTrans,1,Q,b,0,x);
+    for(int i=m-1;i>=0;i--) {
+        double xi = gsl_vector_get(x,i);
+        for(int j=i+1;j<m;j++) {
+            xi += -gsl_matrix_get(R,i,j)*gsl_vector_get(x,j);
+        }
+        xi /= gsl_matrix_get(R,i,i);
+        gsl_vector_set(x,i,xi);
+    }
+}
+
+void GS_inverse(gsl_matrix* Q, gsl_matrix* R, gsl_matrix* B) {
+    for(int j=0;j<Q->size2;j++) {
+        gsl_vector* ej = gsl_vector_alloc(Q->size1);
+        gsl_vector_set_basis(ej,j);
+        gsl_vector_view Bj = gsl_matrix_column(B,j);
+        GS_solve(Q,R,ej,&(Bj.vector));
+        gsl_vector_free(ej);
+    }
+}
\ No newline at end of file

homework/linear-equations/functions.h

+#ifndef FUNCTIONS_H
+#define FUNCTIONS_H
+
+#include<math.h>
+#include<time.h>
+#include<stdio.h>
+#include<assert.h>
+#include<gsl/gsl_vector.h>
+#include<gsl/gsl_matrix.h>
+#include<gsl/gsl_blas.h>
+#include<gsl/gsl_linalg.h>
+#define RND (double)rand()/RAND_MAX
+
+void print_vector(char s[], gsl_vector* v);
+void print_matrix(gsl_matrix* M);
+void GS_decomp(gsl_matrix* A, gsl_matrix* R);
+void GS_solve(gsl_matrix* Q, gsl_matrix* R, gsl_vector* b, gsl_vector* x);
+void GS_inverse(gsl_matrix* Q, gsl_matrix* R, gsl_matrix* B);
+
+#endif
\ No newline at end of file

homework/linear-equations/main.c

-#include<math.h>
-#include<time.h>
-#include<stdio.h>
-#include<gsl/gsl_vector.h>
-#include<gsl/gsl_matrix.h>
-#include<gsl/gsl_blas.h>
-#include<gsl/gsl_linalg.h>
-#define RND (double)rand()/RAND_MAX
-
-void print_vector(char s[], gsl_vector* v) {
-	printf("%s\n",s);
-	for(int i=0;i<v->size;i++) {
-		printf("%15g",gsl_vector_get(v,i));
-		printf("\n");
-	}
-}
-
-void print_matrix(gsl_matrix* M) {
-    for(int i = 0; i < M->size1; i++) {
-        for(int j = 0; j < M->size2; j++) {
-            printf("%15g\t", gsl_matrix_get(M, i, j));
-        }
-        printf("\n");
-    }
-}
-
-void GS_decomp(gsl_matrix* A, gsl_matrix* R) {
-    int n = A -> size1;
-    int m = A -> size2;
-    for(int i=0;i<m;i++) {
-        gsl_vector_view ai = gsl_matrix_column(A,i);
-        double Rii = gsl_blas_dnrm2(&(ai.vector));
-        gsl_matrix_set(R,i,i,Rii);
-        gsl_vector_scale(&(ai.vector),1/Rii);
-        for(int j=i+1;j<m;j++) {
-            gsl_vector_view aj = gsl_matrix_column(A,j);
-            double Rij;
-            gsl_blas_ddot(&(ai.vector),&(aj.vector),&Rij);
-            gsl_matrix_set(R,i,j,Rij);
-            gsl_vector* qiRij = gsl_vector_alloc(n);
-            gsl_vector_memcpy(qiRij,&(ai.vector));
-            gsl_vector_scale(qiRij,Rij);
-            gsl_vector_sub(&(aj.vector),qiRij);
-        }
-    }
-}
-
-void GS_solve(gsl_matrix* Q, gsl_matrix* R, gsl_vector* b, gsl_vector* x) {
-    int m = Q -> size2;
-    gsl_blas_dgemv(CblasTrans,1,Q,b,0,x);
-    for(int i=m-1;i>=0;i--) {
-        double xi = gsl_vector_get(x,i);
-        for(int j=i+1;j<m;j++) {
-            xi += -gsl_matrix_get(R,i,j)*gsl_vector_get(x,j);
-        }
-        xi /= gsl_matrix_get(R,i,i);
-        gsl_vector_set(x,i,xi);
-    }
-}
-
-void GS_inverse(gsl_matrix* Q, gsl_matrix* R, gsl_matrix* B) {
-    for(int j=0;j<Q->size2;j++) {
-        gsl_vector* ej = gsl_vector_alloc(Q->size1);
-        gsl_vector_set_basis(ej,j);
-        gsl_vector_view Bj = gsl_matrix_column(B,j);
-        GS_solve(Q,R,ej,&(Bj.vector));
-        gsl_vector_free(ej);
-    }
-}
+#include "functions.h"
 
 int main() {
     int n =3;
@@ -139,42 +71,35 @@ int main() {
     print_matrix(AB);
 
     FILE* time_test_out_stream = fopen("time_test.txt","w");
-    for(int N=2;N<100;N++) {
-        int iterations = 200;
+    for(int N=300;N<500;N++) {
         gsl_matrix* My_time_test_A = gsl_matrix_alloc(N,N);
+        gsl_matrix* Gsl_time_test_A = gsl_matrix_alloc(N,N);
         gsl_matrix* My_time_test_R = gsl_matrix_alloc(N,N);
         gsl_vector* Gsl_time_test_v = gsl_vector_alloc(N);
 
+        for(int k=0; k<My_time_test_A->size1;k++) {
+		    for(int j=0; j<My_time_test_A->size2;j++) {
+		        double kj=RND;
+			    gsl_matrix_set(My_time_test_A,k,j,kj);
+		    }
+	    }
+        gsl_matrix_memcpy(Gsl_time_test_A,My_time_test_A);
+
         clock_t my_time1 = clock();
-        for(int i=0;i<iterations;i++) {
-            for(int k=0; k<My_time_test_A->size1;k++) {
-		        for(int j=0; j<My_time_test_A->size2;j++) {
-			        double kj=RND;
-			        gsl_matrix_set(My_time_test_A,k,j,kj);
-		        }
-	        }
-            GS_decomp(My_time_test_A,My_time_test_R);
-        }
+        GS_decomp(My_time_test_A,My_time_test_R);
         clock_t my_time2 = clock();
         double my_time = (double)(my_time2-my_time1);
 
         clock_t gsl_time1 = clock();
-        for(int i=0;i<iterations;i++) {
-            for(int k=0; k<My_time_test_A->size1;k++) {
-		        for(int j=0; j<My_time_test_A->size2;j++) {
-			        double kj=RND;
-			        gsl_matrix_set(My_time_test_A,k,j,kj);
-		        }
-	        }
-            gsl_linalg_QR_decomp(My_time_test_A,Gsl_time_test_v);
-        }
+        gsl_linalg_QR_decomp(Gsl_time_test_A,Gsl_time_test_v);
         clock_t gsl_time2 = clock();
         double gsl_time = (double)(gsl_time2-gsl_time1);
 
-        my_time /= iterations; my_time /= CLOCKS_PER_SEC;
-        gsl_time /= iterations; gsl_time /= CLOCKS_PER_SEC;
-        fprintf(time_test_out_stream,"%i %g %g\n",N,my_time/iterations,gsl_time/iterations);
+        my_time /= CLOCKS_PER_SEC;
+        gsl_time /= CLOCKS_PER_SEC;
+        fprintf(time_test_out_stream,"%i %g %g\n",N,my_time,gsl_time);
         gsl_matrix_free(My_time_test_A);
+        gsl_matrix_free(Gsl_time_test_A);
         gsl_matrix_free(My_time_test_R);
         gsl_vector_free(Gsl_time_test_v);
     }

homework/linear-equations/out.txt

@@ -55,5 +55,4 @@ A*B:
    -1.73472e-16	   -5.41234e-16	              1	
 B*A:
               1	   -3.33067e-16	    1.38778e-17	
-    3.88578e-16	              1	   -6.76542e-17	
-     1.7486e-15	   -8.60423e-16	              1	
+    3.88578e-16	   
\ No newline at end of file