sheet 4

sheet4/A/.vscode/settings.json

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

sheet4/A/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/A/main.cpp

@@ -0,0 +1,53 @@
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <lapacke.h>
+using namespace std;
+
+int main()
+{   
+    int n = 10;
+    unsigned int nodes = n+1;
+    int rhs = 1;
+    double a = 1.0;
+    double alpha = 2.0;
+    double gB = 1.0;
+
+    double d = n + a/3.0/n;
+    double s = - n + a / 6.0 / n;
+
+    cout << d << endl;
+    cout << s << endl;
+
+    //Lapacke overwrites upper/lower diagonal so store twice 
+    vector<double> upperdiagonal(n,s);
+    vector<double> lowerdiagonal(n,s);
+    vector<double> diagonal(nodes,2*d);
+    vector<double> F(nodes,1.0/n);
+
+    diagonal[0]=1.0;
+    diagonal[n]=d+alpha;
+
+    upperdiagonal[0] = 0.0;
+    //
+
+    F[0] = 0;
+    F[n]= 1.0/n/2.0 +alpha*gB;
+    
+
+    //Tridiagonal
+    LAPACKE_dgtsv(LAPACK_COL_MAJOR,nodes,rhs,lowerdiagonal.data(),diagonal.data(),upperdiagonal.data(),F.data(),nodes);
+    
+
+    cout << "Solution u_h at nodes x_1..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;
+
+    
+}  

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;
+
+    
+}  

sheet4/C/.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/C/.vscode/settings.json

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

sheet4/C/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/C/main.cpp

@@ -0,0 +1,51 @@
+
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <cmath>
+#include <lapacke.h>
+using namespace std;
+
+
+int main()
+{   
+    unsigned int ns[5] = {10,20,30,40,70};
+    int p = 70;
+    int rhs = 1;
+    for(unsigned int i = 0; i< sizeof(ns)/sizeof(ns[0]); i++)
+    {
+        int n=ns[i];
+        unsigned int nodes = n+1;
+
+        vector<double> upperdiagonal(n,-n+p/2.0);
+        vector<double> lowerdiagonal(n,-n-p/2.0);
+        vector<double> diagonal(nodes,2*n);
+        vector<double> F(nodes,0.0);
+        upperdiagonal[0]=0.0;
+        lowerdiagonal[n-1]=0.0;
+        diagonal[0] = 1.0;
+        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 j = 0; j < nodes; ++j) {
+
+            double xi = double(j) /double(n);
+            cout << "u_h(" << xi << ") = " << F[j] << "\n";
+            // F will be overwritten with sol
+        }
+    }
+
+    /*
+    From Methode  der finiten Elemente fuer Ingenieure:
+    small n approximates pu' not good espicially if n < p/2=35 therefor this oscillation (see plot) occurs.
+    */
+    return 0;
+
+    
+}  

sheet4/C/output.txt

@@ -0,0 +1,180 @@
+Solution u_h at nodes x_0..x_10:
+u_h(0) = -3.51571e-17
+u_h(0.1) = -0.00786414
+u_h(0.2) = 0.00629131
+u_h(0.3) = -0.0191885
+u_h(0.4) = 0.0266752
+u_h(0.5) = -0.0558794
+u_h(0.6) = 0.0927188
+u_h(0.7) = -0.174758
+u_h(0.8) = 0.3067
+u_h(0.9) = -0.559925
+u_h(1) = 1
+Solution u_h at nodes x_0..x_20:
+u_h(0) = -3.2746e-17
+u_h(0.05) = -2.41868e-11
+u_h(0.1) = 6.44981e-11
+u_h(0.15) = -2.6068e-10
+u_h(0.2) = 9.31639e-10
+u_h(0.25) = -3.4402e-09
+u_h(0.3) = 1.25899e-08
+u_h(0.35) = -4.6187e-08
+u_h(0.4) = 1.69328e-07
+u_h(0.45) = -6.20895e-07
+u_h(0.5) = 2.27659e-06
+u_h(0.55) = -8.34752e-06
+u_h(0.6) = 3.06075e-05
+u_h(0.65) = -0.000112228
+u_h(0.7) = 0.000411501
+u_h(0.75) = -0.00150884
+u_h(0.8) = 0.00553241
+u_h(0.85) = -0.0202855
+u_h(0.9) = 0.0743802
+u_h(0.95) = -0.272727
+u_h(1) = 1
+Solution u_h at nodes x_0..x_30:
+u_h(0) = -6.65912e-18
+u_h(0.0333333) = -6.65912e-18
+u_h(0.0666667) = -6.65912e-18
+u_h(0.1) = -6.65912e-18
+u_h(0.133333) = -6.65912e-18
+u_h(0.166667) = -6.65912e-18
+u_h(0.2) = -6.65912e-18
+u_h(0.233333) = -6.65912e-18
+u_h(0.266667) = -6.65912e-18
+u_h(0.3) = -6.65912e-18
+u_h(0.333333) = -6.65907e-18
+u_h(0.366667) = -6.6598e-18
+u_h(0.4) = -6.65023e-18
+u_h(0.433333) = -6.77472e-18
+u_h(0.466667) = -5.1563e-18
+u_h(0.5) = -2.61958e-17
+u_h(0.533333) = 2.47317e-16
+u_h(0.566667) = -3.30835e-15
+u_h(0.6) = 4.29153e-14
+u_h(0.633333) = -5.57992e-13
+u_h(0.666667) = 7.25381e-12
+u_h(0.7) = -9.42996e-11
+u_h(0.733333) = 1.22589e-09
+u_h(0.766667) = -1.59366e-08
+u_h(0.8) = 2.07176e-07
+u_h(0.833333) = -2.69329e-06
+u_h(0.866667) = 3.50128e-05
+u_h(0.9) = -0.000455166
+u_h(0.933333) = 0.00591716
+u_h(0.966667) = -0.0769231
+u_h(1) = 1
+Solution u_h at nodes x_0..x_40:
+u_h(0) = -4.79093e-18
+u_h(0.025) = -4.79093e-18
+u_h(0.05) = -4.79093e-18
+u_h(0.075) = -4.79093e-18
+u_h(0.1) = -4.79093e-18
+u_h(0.125) = -4.79093e-18
+u_h(0.15) = -4.79093e-18
+u_h(0.175) = -4.79093e-18
+u_h(0.2) = -4.79093e-18
+u_h(0.225) = -4.79093e-18
+u_h(0.25) = -4.79093e-18
+u_h(0.275) = -4.79093e-18
+u_h(0.3) = -4.79093e-18
+u_h(0.325) = -4.79093e-18
+u_h(0.35) = -4.79093e-18
+u_h(0.375) = -4.79093e-18
+u_h(0.4) = -4.79093e-18
+u_h(0.425) = -4.79093e-18
+u_h(0.45) = -4.79093e-18
+u_h(0.475) = -4.79093e-18
+u_h(0.5) = -4.79093e-18
+u_h(0.525) = -4.79089e-18
+u_h(0.55) = -4.79026e-18
+u_h(0.575) = -4.78078e-18
+u_h(0.6) = -4.63869e-18
+u_h(0.625) = -2.50728e-18
+u_h(0.65) = 2.94639e-17
+u_h(0.675) = 5.09032e-16
+u_h(0.7) = 7.70256e-15
+u_h(0.725) = 1.15605e-13
+u_h(0.75) = 1.73415e-12
+u_h(0.775) = 2.60123e-11
+u_h(0.8) = 3.90184e-10
+u_h(0.825) = 5.85277e-09
+u_h(0.85) = 8.77915e-08
+u_h(0.875) = 1.31687e-06
+u_h(0.9) = 1.97531e-05
+u_h(0.925) = 0.000296296
+u_h(0.95) = 0.00444444
+u_h(0.975) = 0.0666667
+u_h(1) = 1
+Solution u_h at nodes x_0..x_70:
+u_h(0) = -1.30667e-17
+u_h(0.0142857) = -1.30667e-17
+u_h(0.0285714) = -1.30667e-17
+u_h(0.0428571) = -1.30667e-17
+u_h(0.0571429) = -1.30667e-17
+u_h(0.0714286) = -1.30667e-17
+u_h(0.0857143) = -1.30667e-17
+u_h(0.1) = -1.30667e-17
+u_h(0.114286) = -1.30667e-17
+u_h(0.128571) = -1.30667e-17
+u_h(0.142857) = -1.30667e-17
+u_h(0.157143) = -1.30667e-17
+u_h(0.171429) = -1.30667e-17
+u_h(0.185714) = -1.30667e-17
+u_h(0.2) = -1.30667e-17
+u_h(0.214286) = -1.30667e-17
+u_h(0.228571) = -1.30667e-17
+u_h(0.242857) = -1.30667e-17
+u_h(0.257143) = -1.30667e-17
+u_h(0.271429) = -1.30667e-17
+u_h(0.285714) = -1.30667e-17
+u_h(0.3) = -1.30667e-17
+u_h(0.314286) = -1.30667e-17
+u_h(0.328571) = -1.30667e-17
+u_h(0.342857) = -1.30666e-17
+u_h(0.357143) = -1.30664e-17
+u_h(0.371429) = -1.30657e-17
+u_h(0.385714) = -1.30637e-17
+u_h(0.4) = -1.30576e-17
+u_h(0.414286) = -1.30393e-17
+u_h(0.428571) = -1.29845e-17
+u_h(0.442857) = -1.282e-17
+u_h(0.457143) = -1.23265e-17
+u_h(0.471429) = -1.08459e-17
+u_h(0.485714) = -6.40428e-18
+u_h(0.5) = 6.92065e-18
+u_h(0.514286) = 4.68954e-17
+u_h(0.528571) = 1.6682e-16
+u_h(0.542857) = 5.26593e-16
+u_h(0.557143) = 1.60591e-15
+u_h(0.571429) = 4.84387e-15
+u_h(0.585714) = 1.45577e-14
+u_h(0.6) = 4.36994e-14
+u_h(0.614286) = 1.31124e-13
+u_h(0.628571) = 3.93399e-13
+u_h(0.642857) = 1.18022e-12
+u_h(0.657143) = 3.54069e-12
+u_h(0.671429) = 1.06221e-11
+u_h(0.685714) = 3.18663e-11
+u_h(0.7) = 9.55991e-11
+u_h(0.714286) = 2.86797e-10
+u_h(0.728571) = 8.60392e-10
+u_h(0.742857) = 2.58117e-09
+u_h(0.757143) = 7.74352e-09
+u_h(0.771429) = 2.32306e-08
+u_h(0.785714) = 6.96917e-08
+u_h(0.8) = 2.09075e-07
+u_h(0.814286) = 6.27225e-07
+u_h(0.828571) = 1.88168e-06
+u_h(0.842857) = 5.64503e-06
+u_h(0.857143) = 1.69351e-05
+u_h(0.871429) = 5.08053e-05
+u_h(0.885714) = 0.000152416
+u_h(0.9) = 0.000457247
+u_h(0.914286) = 0.00137174
+u_h(0.928571) = 0.00411523
+u_h(0.942857) = 0.0123457
+u_h(0.957143) = 0.037037
+u_h(0.971429) = 0.111111
+u_h(0.985714) = 0.333333
+u_h(1) = 1

sheet4/CLANG_default.mk

@@ -0,0 +1,124 @@
+# Basic Defintions for using GNU-compiler suite sequentially
+# requires setting of COMPILER=CLANG_
+
+#CLANGPATH=//usr/lib/llvm-10/bin/
+CC     = ${CLANGPATH}clang
+CXX    = ${CLANGPATH}clang++
+#CXX   = ${CLANGPATH}clang++ -lomptarget  -fopenmp-targets=nvptx64-nvidia-cuda --cuda-path=/opt/pgi/linux86-64/2017/cuda/8.0
+#F77   = gfortran
+LINKER = ${CXX}
+
+#http://clang.llvm.org/docs/UsersManual.html#options-to-control-error-and-warning-messages
+WARNINGS += -Weverything 
+WARNINGS += -Wno-c++98-compat -Wno-c++98-compat-pedantic -Wno-sign-conversion -Wno-date-time -Wno-shorten-64-to-32 -Wno-padded 
+WARNINGS += -Wdocumentation -Wconversion -Wshadow -Wfloat-conversion -pedantic -ferror-limit=1
+#-fsyntax-only -Wdocumentation -Wconversion -Wshadow -Wfloat-conversion -pedantic
+
+CXXFLAGS += -O3 -std=c++17 -ferror-limit=1 ${WARNINGS}
+# don't use -Ofast
+# -ftrapv
+LINKFLAGS += -O3
+
+# different libraries in Ubuntu or manajaró
+ifndef UBUNTU
+UBUNTU=1
+endif
+
+# BLAS, LAPACK
+LINKFLAGS += -llapack -lblas
+# -lopenblas
+ifeq ($(UBUNTU),1)
+# ubuntu
+else
+# on  archlinux
+LINKFLAGS += -lcblas
+endif
+
+# interprocedural optimization
+CXXFLAGS  += -flto
+LINKFLAGS += -flto
+
+#   very good check
+# http://clang.llvm.org/extra/clang-tidy/
+#   good check, see:  http://llvm.org/docs/CodingStandards.html#include-style
+SWITCH_OFF=,-readability-magic-numbers,-readability-redundant-control-flow,-readability-redundant-member-init
+SWITCH_OFF+=,-readability-redundant-member-init,-readability-isolate-declaration
+#READABILITY=,readability*${SWITCH_OFF}
+#TIDYFLAGS = -checks=llvm-*,-llvm-header-guard -header-filter=.* -enable-check-profile -extra-arg="-std=c++17" -extra-arg="-fopenmp"
+TIDYFLAGS = -checks=llvm-*,-llvm-header-guard${READABILITY} -header-filter=.* -enable-check-profile -extra-arg="-std=c++17" -extra-arg="-fopenmp"
+#TIDYFLAGS += -checks='modernize*
+#   ???
+#TIDYFLAGS = -checks='cert*'  -header-filter=.*
+#   MPI checks ??
+#TIDYFLAGS = -checks='mpi*'
+#   ??
+#TIDYFLAGS = -checks='performance*'   -header-filter=.*
+#TIDYFLAGS = -checks='portability-*'  -header-filter=.*
+#TIDYFLAGS = -checks='readability-*'  -header-filter=.*
+
+default: ${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+
+clean:
+	@rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+codecheck: tidy_check
+tidy_check:
+	clang-tidy ${SOURCES} ${TIDYFLAGS} -- ${SOURCES}
+# see also http://clang-developers.42468.n3.nabble.com/Error-while-trying-to-load-a-compilation-database-td4049722.html
+
+run: clean ${PROGRAM}
+#	time  ./${PROGRAM} ${PARAMS}
+	./${PROGRAM} ${PARAMS}
+
+# tar the current directory
+MY_DIR = `basename ${PWD}`
+tar: clean_all
+	@echo "Tar the directory: " ${MY_DIR}
+	@cd .. ;\
+	tar cf ${MY_DIR}.tar ${MY_DIR} *default.mk ;\
+	cd ${MY_DIR}
+# 	tar cf `basename ${PWD}`.tar *
+
+doc:
+	doxygen Doxyfile
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+
+.c.o:
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+.f.o:
+	$(F77) -c $(FFLAGS) -o $@ $<
+
+##################################################################################################
+#    some tools
+# Cache behaviour (CXXFLAGS += -g  tracks down to source lines; no -pg in linkflags)
+cache: ${PROGRAM}
+	valgrind --tool=callgrind --simulate-cache=yes ./$^  ${PARAMS}
+#	kcachegrind callgrind.out.<pid> &
+	kcachegrind `ls -1tr  callgrind.out.* |tail -1`
+
+# Check for wrong memory accesses, memory leaks, ...
+# use smaller data sets
+mem: ${PROGRAM}
+	valgrind -v --leak-check=yes --tool=memcheck --undef-value-errors=yes --track-origins=yes --log-file=$^.addr.out --show-reachable=yes ./$^  ${PARAMS}
+
+#  Simple run time profiling of your code
+#  CXXFLAGS += -g -pg
+#  LINKFLAGS += -pg
+prof: ${PROGRAM}
+	perf record ./$^  ${PARAMS}
+	perf report
+#	gprof -b ./$^ > gp.out
+#	kprof -f gp.out -p gprof &
+
+codecheck: tidy_check

sheet4/GCC_default.mk

@@ -0,0 +1,183 @@
+# Basic Defintions for using GNU-compiler suite sequentially
+# requires setting of COMPILER=GCC_
+
+CC	= gcc
+CXX     = g++
+F77	= gfortran
+LINKER  = ${CXX}
+
+#LINKFLAGS   += -lblas
+# The <cblas.h> header requires extern "C".
+
+WARNINGS = -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow \
+           -Wredundant-decls -Winline -fmax-errors=1
+#  -Wunreachable-code
+#CXXFLAGS += -ffast-math -march=native ${WARNINGS}
+CXXFLAGS += -O0 -funroll-all-loops -std=c++17 ${WARNINGS}
+#-msse3
+# -ftree-vectorizer-verbose=2  -DNDEBUG
+# -ftree-vectorizer-verbose=5
+# -ftree-vectorize -fdump-tree-vect-blocks=foo.dump  -fdump-tree-pre=stderr
+
+# CFLAGS	= -ffast-math -O0 -DNDEBUG -msse3 -fopenmp -fdump-tree-vect-details
+# CFLAGS	= -ffast-math -O0 -funroll-loops -DNDEBUG -msse3 -fopenmp -ftree-vectorizer-verbose=2
+# #CFLAGS	= -ffast-math -O0 -DNDEBUG -msse3 -fopenmp
+# FFLAGS	= -ffast-math -O0 -DNDEBUG -msse3 -fopenmp
+# LFLAGS  = -ffast-math -O0 -DNDEBUG -msse3 -fopenmp
+LINKFLAGS   += -O0
+
+#architecture
+#CPU = -march=znver2
+CXXFLAGS  += ${CPU}
+LINKFLAGS += ${CPU}
+
+# different libraries in Ubuntu or manajaró
+ifndef UBUNTU
+UBUNTU=1
+endif
+
+# BLAS, LAPACK
+ifeq ($(UBUNTU),1)
+LINKFLAGS += -llapack -lblas
+# -lopenblas
+else
+# on  archlinux
+LINKFLAGS += -llapack -lopenblas -lcblas
+endif
+
+# interprocedural optimization
+CXXFLAGS  += -flto
+LINKFLAGS += -flto
+
+# for debugging purpose (save code)
+# -fsanitize=leak         # only one out the three can be used
+# -fsanitize=address
+# -fsanitize=thread
+SANITARY =  -fsanitize=address  -fsanitize=undefined -fsanitize=null -fsanitize=return \
+ -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow \
+ -fsanitize=bool -fsanitize=enum -fsanitize=vptr
+#CXXFLAGS  += ${SANITARY}
+#LINKFLAGS += ${SANITARY}
+
+# profiling tools
+#CXXFLAGS  += -pg
+#LINKFLAGS += -pg
+
+default: ${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+
+clean:
+	@rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	-@rm -f *_ *~ *.bak *.log *.out *.tar *.orig *.optrpt
+	-@rm -rf html
+
+run: clean ${PROGRAM}
+#run: ${PROGRAM}
+#	time  ./${PROGRAM} ${PARAMS}
+	./${PROGRAM} ${PARAMS}
+
+# tar the current directory
+MY_DIR = `basename ${PWD}`
+tar: clean_all
+	@echo "Tar the directory: " ${MY_DIR}
+	@cd .. ;\
+	tar cf ${MY_DIR}.tar ${MY_DIR} *default.mk ;\
+	cd ${MY_DIR}
+# 	tar cf `basename ${PWD}`.tar *
+
+zip: clean
+	@echo "Zip the directory: " ${MY_DIR}
+	@cd .. ;\
+	zip -r ${MY_DIR}.zip ${MY_DIR} *default.mk ;\
+	cd ${MY_DIR}
+
+doc:
+	doxygen Doxyfile
+
+#########################################################################
+.SUFFIXES: .f90
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+#	$(CXX) -c $(CXXFLAGS) -o $@ $<  2>&1 | tee -a $<.log 
+#	$(CXX) -c $(CXXFLAGS) -o $@ $<  2>&1 | tee -a $(<:.cpp=.log)
+
+.c.o:
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+.f.o:
+	$(F77) -c $(FFLAGS) -o $@ $<
+
+.f90.o:
+	$(F77) -c $(FFLAGS) -o $@ $<
+
+##################################################################################################
+#    some tools
+# Cache behaviour (CXXFLAGS += -g  tracks down to source lines; no -pg in linkflags)
+cache: ${PROGRAM}
+	valgrind --tool=callgrind --simulate-cache=yes ./$^  ${PARAMS}
+#	kcachegrind callgrind.out.<pid> &
+	kcachegrind `ls -1tr  callgrind.out.* |tail -1`
+
+# Check for wrong memory accesses, memory leaks, ...
+# use smaller data sets
+# no "-pg"  in compile/link options
+mem: ${PROGRAM}
+	valgrind -v --leak-check=yes --tool=memcheck --undef-value-errors=yes --track-origins=yes --log-file=$^.addr.out --show-reachable=yes ./$^  ${PARAMS}
+# Graphical interface
+# valkyrie
+
+#  Simple run time profiling of your code
+#  CXXFLAGS += -g -pg
+#  LINKFLAGS += -pg
+prof: ${PROGRAM}
+	perf record ./$^  ${PARAMS}
+	perf report
+#	gprof -b ./$^ > gp.out
+#	kprof -f gp.out -p gprof &
+
+#  perf in Ubuntu 20.04:   https://www.howtoforge.com/how-to-install-perf-performance-analysis-tool-on-ubuntu-20-04/
+#  * install 
+#  * sudo vi /etc/sysctl.conf
+#                add   kernel.perf_event_paranoid = 0
+
+#Trace your heap:
+#> heaptrack ./main.GCC_
+#> heaptrack_gui heaptrack.main.GCC_.<pid>.gz
+heap: ${PROGRAM}
+	heaptrack ./$^  ${PARAMS} 11
+	heaptrack_gui  `ls -1tr  heaptrack.$^.* |tail -1` &
+
+codecheck: $(SOURCES)
+	cppcheck --enable=all --inconclusive --std=c++17 --suppress=missingIncludeSystem $^
+
+
+########################################################################
+#  get the detailed  status of all optimization flags
+info:
+	echo "detailed  status of all optimization flags"
+	$(CXX) --version
+	$(CXX) -Q $(CXXFLAGS) --help=optimizers
+	lscpu
+	inxi -C
+	lstopo
+
+# Excellent hardware info
+#	hardinfo
+# Life monitoring of CPU frequency etc.
+#	sudo i7z
+
+# Memory  consumption
+#	vmstat -at -SM 3
+#	xfce4-taskmanager
+
+
+# https://www.tecmint.com/check-linux-cpu-information/
+#https://www.tecmint.com/monitor-cpu-and-gpu-temperature-in-ubuntu/
+
+# Debugging:
+# https://wiki.archlinux.org/index.php/Debugging

sheet4/ICC_default.mk

@@ -0,0 +1,125 @@
+# Basic Defintions for using INTEL compiler suite sequentially
+# requires setting of COMPILER=ICC_
+
+#BINDIR = /opt/intel/bin/
+
+CC	= ${BINDIR}icc
+CXX     = ${BINDIR}icpc
+F77	= ${BINDIR}ifort
+LINKER  = ${CXX}
+
+
+WARNINGS = -Wall -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -wd2015,2012 -wn3
+#    -Winline -Wredundant-decls -Wunreachable-code
+CXXFLAGS +=  -O3 -fargument-noalias -std=c++17 -DNDEBUG ${WARNINGS} -mkl
+# profiling tools
+#CXXFLAGS  += -pg
+#LINKFLAGS += -pg
+# -vec-report=3
+# -qopt-report=5 -qopt-report-phase=vec
+# -guide -parallel
+# -guide-opts=string  -guide-par[=n]  -guide-vec[=n]
+# -auto-p32 -simd -msse3
+
+LINKFLAGS += -O3
+
+# LAPACK, BLAS: use MKL by INTEL
+# LINKFLAGS += -L${BINDIR}../composer_xe_2013.1.117/mkl/lib/intel64 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lpthread
+CXXFLAGS  += -mkl
+LINKFLAGS += -mkl
+
+# interprocedural optimization
+#CXXFLAGS  += -ipo
+#LINKFLAGS += -ipo
+
+# annotated assembler file
+ANNOTED = -fsource-asm -S
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+
+clean:
+	rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+run: clean ${PROGRAM}
+	./${PROGRAM}
+
+# tar the current directory
+MY_DIR = `basename ${PWD}`
+tar: clean_all
+	@echo "Tar the directory: " ${MY_DIR}
+	@cd .. ;\
+	tar cf ${MY_DIR}.tar ${MY_DIR} *default.mk ;\
+	cd ${MY_DIR}
+# 	tar cf `basename ${PWD}`.tar *
+
+doc:
+	doxygen Doxyfile
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+
+.c.o:
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+.f.o:
+	$(F77) -c $(FFLAGS) -o $@ $<
+
+##################################################################################################
+# #    some tools
+# # Cache behaviour (CXXFLAGS += -g  tracks down to source lines)
+# cache: ${PROGRAM}
+# 	valgrind --tool=callgrind --simulate-cache=yes ./$^
+# #	kcachegrind callgrind.out.<pid> &
+#
+# # Check for wrong memory accesses, memory leaks, ...
+# # use smaller data sets
+# mem: ${PROGRAM}
+# 	valgrind -v --leak-check=yes --tool=memcheck --undef-value-errors=yes --track-origins=yes --log-file=$^.addr.out --show-reachable=yes ./$^
+#
+# #  Simple run time profiling of your code
+# #  CXXFLAGS += -g -pg
+# #  LINKFLAGS += -pg
+# prof: ${PROGRAM}
+# 	./$^
+# 	gprof -b ./$^ > gp.out
+# #	kprof -f gp.out -p gprof &
+#
+
+
+mem: inspector
+prof: amplifier
+cache: amplifier
+
+gap_par_report:
+	${CXX}  -c -guide -parallel $(SOURCES) 2> gap.txt
+
+# GUI for performance report
+amplifier: ${PROGRAM}
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+#	alternatively to the solution abouve:
+            #edit file  /etc/sysctl.d/10-ptrace.conf     and set variable   kernel.yama.ptrace_scope   variable to 0 .
+	vtune-gui &
+
+# GUI for Memory and Thread analyzer (race condition)
+inspector: ${PROGRAM}
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	inspxe-gui &
+
+advisor:
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	vtune-gui &
+
+icc-info:
+	icpc -# main.cpp
+
+
+
+

sheet4/ONEAPI_default.mk

@@ -0,0 +1,176 @@
+# Basic Defintions for using INTEL compiler suite sequentially
+# requires setting of COMPILER=ONEAPI_
+
+#         https://software.intel.com/content/www/us/en/develop/tools/oneapi/components/onemkl/link-line-advisor.html
+# requires
+# source /opt/intel/oneapi/setvars.sh
+# on  AMD:    export MKL_DEBUG_CPU_TYPE=5
+
+#BINDIR = /opt/intel/oneapi/compiler/latest/linux/bin/
+#MKL_ROOT = /opt/intel/oneapi/mkl/latest/
+#export KMP_AFFINITY=verbose,compact
+
+CC	= ${BINDIR}icc
+CXX     = ${BINDIR}dpcpp
+F77	= ${BINDIR}ifort
+LINKER  = ${CXX}
+
+## Compiler flags
+WARNINGS = -Wall -Weffc++ -Woverloaded-virtual -Wfloat-equal -Wshadow -pedantic
+WARNINGS += -Wpessimizing-move -Wredundant-move
+#-wd2015,2012,2014 -wn3
+#    -Winline -Wredundant-decls -Wunreachable-code
+# -qopt-subscript-in-range
+# -vec-threshold0
+
+CXXFLAGS += -O3 -std=c++17  ${WARNINGS}
+#CXXFLAGS += -DMKL_ILP64  -I"${MKLROOT}/include"
+#CXXFLAGS += -DMKL_ILP32  -I"${MKLROOT}/include"
+LINKFLAGS += -O3
+
+# interprocedural optimization
+CXXFLAGS  += -ipo
+LINKFLAGS += -ipo
+LINKFLAGS += -flto
+
+# annotated Assembler file
+ANNOTED = -fsource-asm -S 
+
+#architecture
+CPU  = -march=core-avx2
+#CPU += -mtp=zen
+# -xCORE-AVX2
+# -axcode COMMON-AVX512 -axcode MIC-AVX512 -axcode CORE-AVX512 -axcode CORE-AVX2
+CXXFLAGS  += ${CPU}
+LINKFLAGS += ${CPU}
+
+# use MKL by INTEL
+# https://software.intel.com/content/www/us/en/develop/tools/oneapi/components/onemkl/link-line-advisor.html
+# sequential MKL
+#                              use the 32 bit interface (LP64) instead of 64 bit interface (ILP64)
+CXXFLAGS +=  -qmkl=sequential  -UMKL_ILP64
+LINKFLAGS += -O3 -qmkl=sequential -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lpthread
+#LINKFLAGS += -O3 -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lpthread
+
+# shared libs:  https://aur.archlinux.org/packages/intel-oneapi-compiler-static
+#     install intel-oneapi-compiler-static   
+# or 
+LINKFLAGS += -shared-intel
+
+
+OPENMP = -qopenmp
+CXXFLAGS += ${OPENMP}
+LINKFLAGS += ${OPENMP}
+
+
+# profiling tools
+#CXXFLAGS  += -pg
+#LINKFLAGS += -pg
+# -vec-report=3
+# -qopt-report=5 -qopt-report-phase=vec -qopt-report-phase=openmp
+# -guide -parallel
+# -guide-opts=string  -guide-par[=n]  -guide-vec[=n]
+# -auto-p32 -simd
+
+# Reports: https://software.intel.com/en-us/articles/getting-the-most-out-of-your-intel-compiler-with-the-new-optimization-reports
+#CXXFLAGS +=  -qopt-report=5 -qopt-report-phase=vec,par
+#CXXFLAGS +=  -qopt-report=5 -qopt-report-phase=cg
+# Redirect report from *.optrpt to stderr
+#    -qopt-report-file=stderr
+# Guided paralellization
+#    -guide -parallel
+#    -guide-opts=string  -guide-par[=n]  -guide-vec[=n]
+#    -auto-p32 -simd
+
+## run time checks
+# https://www.intel.com/content/www/us/en/develop/documentation/fortran-compiler-oneapi-dev-guide-and-reference/top/compiler-reference/compiler-options/offload-openmp-and-parallel-processing-options/par-runtime-control-qpar-runtime-control.html
+
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+
+clean:
+	rm -f ${PROGRAM} ${OBJECTS} *.optrpt
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+run: clean ${PROGRAM}
+	./${PROGRAM}
+
+# tar the current directory
+MY_DIR = `basename ${PWD}`
+tar: clean_all
+	@echo "Tar the directory: " ${MY_DIR}
+	@cd .. ;\
+	tar cf ${MY_DIR}.tar ${MY_DIR} *default.mk ;\
+	cd ${MY_DIR}
+# 	tar cf `basename ${PWD}`.tar *
+
+doc:
+	doxygen Doxyfile
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+
+.c.o:
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+.f.o:
+	$(F77) -c $(FFLAGS) -o $@ $<
+
+##################################################################################################
+#    some tools
+# Cache behaviour (CXXFLAGS += -g  tracks down to source lines)
+# https://software.intel.com/content/www/us/en/develop/documentation/vtune-help/top/analyze-performance/microarchitecture-analysis-group/memory-access-analysis.html
+
+mem: inspector
+prof: vtune
+cache: inspector
+
+gap_par_report:
+	${CXX}  -c -guide -parallel $(SOURCES) 2> gap.txt
+
+# GUI for performance report
+amplifier: ${PROGRAM}
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	echo 0 | sudo tee /proc/sys/kernel/perf_event_paranoid
+	amplxe-gui &
+
+# GUI for Memory and Thread analyzer (race condition)
+inspector: ${PROGRAM}
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+#	inspxe-gui &
+	vtune-gui ./${PROGRAM} &
+
+advisor:
+	source /opt/intel/oneapi/advisor/2021.2.0/advixe-vars.sh
+#	/opt/intel/oneapi/advisor/latest/bin64/advixe-gui &
+	advisor --collect=survey ./${PROGRAM} 
+#	advisor --collect=roofline ./${PROGRAM} 
+	advisor --report=survey --project-dir=./ src:r=./ --format=csv --report-output=./out/survey.csv
+
+vtune:
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+#	https://software.intel.com/en-us/articles/intel-advisor-2017-update-1-what-s-new
+	export ADVIXE_EXPERIMENTAL=roofline
+	vtune -collect hotspots ./${PROGRAM}
+	vtune -report hotspots -r r000hs > vtune.out
+#	vtune-gui ./${PROGRAM} &	
+
+icc-info:
+	icpc -# main.cpp
+
+# MKL on AMD
+# https://www.computerbase.de/2019-11/mkl-workaround-erhoeht-leistung-auf-amd-ryzen/
+#
+# https://sites.google.com/a/uci.edu/mingru-yang/programming/mkl-has-bad-performance-on-an-amd-cpu
+# export MKL_DEBUG_CPU_TYPE=5
+# export MKL_NUM_THRAEDS=1
+# export MKL_DYNAMIC=false
+#  on Intel compiler
+# http://publicclu2.blogspot.com/2013/05/intel-complier-suite-reference-card.html

sheet4/PGI_default.mk

@@ -0,0 +1,94 @@
+# Basic Defintions for using PGI-compiler suite sequentially
+# requires setting of COMPILER=PGI_
+# OPTIRUN = optirun
+
+
+CC	= pgcc
+CXX     = pgc++
+F77	= pgfortran
+LINKER  = ${CXX}
+
+#LINKFLAGS   += -llapack -lblas
+# on mephisto:
+#CXXFLAGS  += -I/share/apps/atlas/include
+#LINKFLAGS += -L/share/apps/atlas/lib
+#LINKFLAGS   += -lcblas -latlas
+
+#LINKFLAGS   += -lblas
+# Der <cblas.h> Header muss mit extern "C" versehen werden, damit g++ alles findet.
+
+WARNINGS = -Minform=warn
+# -Wall -pedantic -Wextra -Weffc++ -Woverloaded-virtual -W -Wfloat-equal -Wshadow  -Wredundant-decls
+#           -pedantic -Wunreachable-code -Wextra -Winline
+#  -Wunreachable-code
+
+#PGI_PROFILING = -Minfo=ccff,loop,vect,opt,intensity,mp,accel
+PGI_PROFILING = -Minfo=ccff,accel,ipa,loop,lre,mp,opt,par,unified,vect,intensity
+# -Minfo
+# -Mprof=time
+# -Mprof=lines
+#        take care with option      -Msafeptr
+CXXFLAGS += -O3 -std=c++17 ${WARNINGS}
+#CXXFLAGS += -O3 -std=c++11  -DNDEBUG ${PGI_PROFILING} ${WARNINGS}
+#  -fastsse  -fargument-noalias ${WARNINGS}  -msse3 -vec-report=3
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+
+clean:
+	@rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+run: clean ${PROGRAM}
+	./${PROGRAM}
+
+# tar the current directory
+MY_DIR = `basename ${PWD}`
+tar: clean_all
+	@echo "Tar the directory: " ${MY_DIR}
+	@cd .. ;\
+	tar cf ${MY_DIR}.tar ${MY_DIR} *default.mk ;\
+	cd ${MY_DIR}
+# 	tar cf `basename ${PWD}`.tar *
+
+doc:
+	doxygen Doxyfile
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+
+.c.o:
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+.f.o:
+	$(F77) -c $(FFLAGS) -o $@ $<
+
+##################################################################################################
+# #    some tools
+# #  Simple run time profiling of your code
+# #  CXXFLAGS += -g -pg
+# #  LINKFLAGS += -pg
+
+
+# Profiling options PGI, see: pgcollect -help
+# CPU_PROF = -allcache
+CPU_PROF = -time
+# GPU_PROF = -cuda=gmem,branch,cc13 -cudainit
+#GPU_PROF = -cuda=branch:cc20
+#
+PROF_FILE = pgprof.out
+
+cache: prof
+
+prof: ${PROGRAM}
+	${OPTIRUN} ${BINDIR}pgcollect $(CPU_PROF) ./$^
+	${OPTIRUN} ${BINDIR}pgprof -exe ./$^  $(PROF_FILE) &
+
+info:
+	pgaccelinfo -v