sheet 4

sheet4/B/.vscode/c_cpp_properties.json

@@ -0,0 +1,16 @@
+{
+    "configurations": [
+        {
+            "name": "Linux",
+            "includePath": [
+                "${workspaceFolder}/**"
+            ],
+            "defines": [],
+            "compilerPath": "/usr/bin/gcc",
+            "cStandard": "c17",
+            "cppStandard": "gnu++17",
+            "intelliSenseMode": "linux-gcc-x64"
+        }
+    ],
+    "version": 4
+}

sheet4/B/.vscode/settings.json

@@ -0,0 +1,6 @@
+{
+    "files.associations": {
+        "ostream": "cpp",
+        "iostream": "cpp"
+    }
+}

sheet4/B/Makefile

@@ -0,0 +1,32 @@
+#
+# use GNU-Compiler tools
+COMPILER=GCC_
+# alternatively from the shell
+# export COMPILER=GCC_
+# or, alternatively from the shell
+# make COMPILER=GCC_
+
+# use Intel compilers
+#COMPILER=ICC_
+
+# use PGI compilers
+# COMPILER=PGI_
+
+
+SOURCES = main.cpp 
+OBJECTS = $(SOURCES:.cpp=.o)
+
+PROGRAM	= main.${COMPILER}
+
+# uncomment the next to lines for debugging and detailed performance analysis
+CXXFLAGS += -g
+LINKFLAGS += -g
+# do not use -pg with PGI compilers
+
+ifndef COMPILER
+  COMPILER=GCC_
+endif
+
+include ../${COMPILER}default.mk
+$(PROGRAM): $(OBJECTS)
+	$(CXX) $(CXXFLAGS) $(OBJECTS) -llapacke -lopenblas -o $(PROGRAM)

sheet4/B/main.cpp

@@ -0,0 +1,86 @@
+
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <cmath>
+#include <lapacke.h>
+using namespace std;
+
+int n = 10;
+double threshold = 1.0/sqrt(2);
+double lambda(double x)
+{
+    if(x < threshold)
+    {
+        return 1;
+    }
+    return 10;
+}
+
+double fillOffDiagonal(unsigned int i)
+{
+    
+    double x_l = i/double(n);
+    double x_u = (i+1)/double(n);
+
+    if(x_l < threshold && x_u > threshold)
+    {
+        return -n*n*(threshold-x_l+10*(x_u-threshold));
+    }
+    return -n*lambda(x_l);
+}
+
+double fillDiagonal(int i)
+{
+    double x_l = (i-1)/double(n);
+    double x_u = (i+1)/double(n);
+    if(x_l < threshold && x_u > threshold)
+    {
+        return n*n*(threshold-x_l+10*(x_u-threshold));
+    }
+    return 2*n*lambda(x_l);
+}
+
+int main()
+{   
+    //Ignored the first Row of K cause we now that u(0)=0
+    
+    int rhs = 1;
+    unsigned int nodes = n+1;
+
+
+    //Lapacke overwrites upper/lower diagonal so store twice 
+    vector<double> upperdiagonal(n,0.0);
+    vector<double> lowerdiagonal(n,0.0);
+    vector<double> diagonal(nodes,1.0);
+    vector<double> F(nodes,0.0);
+
+    for(int i=0; i < n; i++)
+    {
+        upperdiagonal[i] = fillOffDiagonal(i);
+        lowerdiagonal[i] = fillOffDiagonal(i);
+        diagonal[i+1] = fillDiagonal(i+1);
+    }
+
+    upperdiagonal[0]=0.0;
+    lowerdiagonal[n-1]=0.0;
+    diagonal[n] = 1.0;
+    F[n] = 1.0;
+    
+
+    //Tridiagonal
+    LAPACKE_dgtsv(LAPACK_COL_MAJOR,nodes,rhs,lowerdiagonal.data(),diagonal.data(),upperdiagonal.data(),F.data(),nodes);
+    
+
+    cout << "Solution u_h at nodes x_0..x_" << n << ":\n";
+    
+    for (unsigned int i = 0; i < nodes; ++i) {
+
+        double xi = double(i) /double(n);
+        cout << "u_h(" << xi << ") = " << F[i] << "\n";
+        // F will be overwritten with sol
+    }
+    return 0;
+
+    
+}