Upload ex6 and ex7

2026-01-04 20:15:55 +01:00 · 2026-01-04 20:15:55 +01:00 · 6c2d96ff4d
commit 6c2d96ff4d
parent 1885d64c0a
44 changed files with 15291 additions and 0 deletions
--- a/ex6/adaptivity_schemes.py
+++ b/ex6/adaptivity_schemes.py
@ -0,0 +1,83 @@
+import numpy as np
+
+def flux_jumps(mesh, u):
+    N = len(mesh) - 1   # number of elements
+    jumps = np.zeros(N + 1) # N-1 edges
+    
+    for i in range(1, N):
+        upper = (u[i + 1] - u[i])/(mesh[i + 1] - mesh[i])
+        lower = (u[i] - u[i - 1])/(mesh[i] - mesh[i - 1])
+        jumps[i] = upper - lower
+
+    return jumps
+
+
+def residual_errors(mesh, u):
+    N = len(mesh) - 1   # number of elements
+    errors = np.zeros(N)
+
+    jumps = flux_jumps(mesh, u)
+
+    for i in range(N):
+        errors[i] = np.sqrt((jumps[i]**2 + jumps[i + 1]**2)/2)  # Braess (8.10)
+        
+    #print("errors:\n", errors)
+
+    return errors
+
+
+
+def adapt_h(mesh, u, alpha):
+    N = len(mesh) - 1   # number of elements
+
+    errors = residual_errors(mesh, u)
+    threshhold = alpha * abs(max(errors))
+
+    # refine mesh
+    refined_mesh = [mesh[0]]
+    for i in range(N):
+        if abs(errors[i]) <= threshhold:
+            refined_mesh.append(mesh[i + 1])
+        else:
+            refined_mesh.append(mesh[i] + (mesh[i + 1] - mesh[i])/2)
+            refined_mesh.append(mesh[i + 1])
+
+
+    #print("refined mesh:\n", refined_mesh)
+
+    return refined_mesh
+
+
+def adapt_r(mesh, u):  
+    N = len(mesh) - 1   # number of elements
+
+    rho = np.abs(flux_jumps(mesh, u))  # rho ... mesh density function
+
+    p = np.zeros(N)     # piecewise constant function on the mesh elements
+    for i in range(N):
+        p[i] = (rho[i] + rho[i + 1])/2
+
+    P = np.zeros(N + 1)     # \int_0^{x_j} p(x) dx for j = 1,...,N
+    for j in range(1, N + 1):
+        h_j = mesh[j] - mesh[j - 1]
+        P[j] = P[j - 1] + h_j*p[j - 1]  # add integral over j-th interval
+
+    moved_mesh = np.zeros(N + 1)
+    moved_mesh[0] = mesh[0]
+    moved_mesh[-1] = mesh[-1]
+
+    for j in range(1, N):  # calculate the new nodes with De Boor's algorithm
+        xi_j = j/N
+        k = np.searchsorted(P, xi_j*P[-1], side="left")  # searches for index k, such that xi_j*P[-1] > P[k]
+        assert(P[k - 1] < xi_j*P[-1])
+        assert(xi_j*P[-1] <= P[k])
+
+        moved_mesh[j] = mesh[k - 1] + (xi_j*P[-1] - P[k - 1])/p[k - 1]
+        print("orign_mesh[j] =", mesh[j])
+        print("moved_mesh[j] =", moved_mesh[j])
+    print("done\n")
+
+
+    #print("moved mesh:\n", moved_mesh)
+
+    return moved_mesh
--- a/ex6/ex_6A.py
+++ b/ex6/ex_6A.py
@ -0,0 +1,139 @@
+import numpy as np
+import scipy.integrate as integrate
+import matplotlib.pyplot as plt
+import adaptivity_schemes
+
+np.set_printoptions(precision=2)
+
+
+def Solve_6A(mesh, p):
+    N = len(mesh) - 1   # number of elements
+
+    f = lambda x : 2*p**3*x/((p**2*x**2 + 1)**2)
+    g_b = p/(p**2 + 1)
+
+
+
+    A = np.zeros((N + 1, N + 1))
+    f_vec = np.zeros(N + 1)
+
+    for i in range(1, N + 1):
+        h = mesh[i] - mesh[i - 1]
+
+        a_11 =  1./h
+        a_12 = -1./h
+        a_21 = -1./h
+        a_22 =  1./h
+                                        
+        A[i - 1, i - 1] += a_11
+        A[i - 1, i] += a_12
+        A[i, i - 1] += a_21
+        A[i, i] += a_22
+
+
+        phi_lower = lambda x : (mesh[i] - x)/h
+        f_vec[i-1] += integrate.quad(lambda x : f(x)*phi_lower(x), mesh[i - 1], mesh[i])[0]
+
+        phi_upper = lambda x : (x - mesh[i - 1])/h
+        f_vec[i] += integrate.quad(lambda x : f(x)*phi_upper(x), mesh[i - 1], mesh[i])[0]
+
+
+
+    # take Neumann data into account
+    A[N, N] += 0
+    f_vec[N] += g_b
+
+
+    # take Dirichlet data into account
+    u_g = np.zeros(N + 1)
+    u_g[0] = -np.arctan(p)
+    #print("u_g =\n", u_g)
+
+    # remove first row of A
+    A_g = A[1:N+1, :]
+    #print("A_g =\n", A_g)
+
+    # remove first row of f_vec
+    f_g = f_vec[1:N+1]
+
+    # assemble RHS with dirichlet data
+    f_g -= A_g.dot(u_g)
+    #print("f_g =\n", f_g)
+
+    # matrix for the inner nodes (excluding nodes with dirichlet bcs)
+    A_0 = A[1:N+1, 1:N+1]   
+    #print(A_0)
+
+    # solve for u_0 (free dofs)
+    u_0 = np.linalg.solve(A_0, f_g)
+
+    # assemble "u = u_0 + u_g"
+    u = np.concatenate([[u_g[0]], u_0])
+
+    return u
+
+
+
+p = 100
+########## h-adaptivity ##########
+N = 5   # number of elements
+mesh = np.linspace(-1, 1, N + 1)
+u = Solve_6A(mesh, p)
+
+plt.plot(mesh, u, '-o')
+plt.grid()
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.title("h-adaptivity")
+
+
+N_vec = ["0 refinements, " + str(N) + " elements"]
+refinements = 4   # number of refinements
+for i in range(refinements):
+    mesh = adaptivity_schemes.adapt_h(mesh, u, 0.7)
+    u = Solve_6A(mesh, p)
+    plt.plot(mesh, u, '-o')
+
+    N_vec.append(str(i + 1) + " refinements, " + str(len(mesh) - 1) + " elements")
+
+
+# plot exact solution
+x = np.linspace(-1, 1, 50)
+plt.plot(x, np.arctan(p*x))
+N_vec.append("exact")
+
+plt.legend(N_vec)
+plt.show()
+
+
+
+# ########## r-adaptivity ##########
+N = 5
+mesh = np.linspace(-1, 1, N + 1)
+u = Solve_6A(mesh, p)
+plt.plot(mesh, u, '-o')
+title = "r-adaptivity with " + str(N) + " elements"
+plt.title(title)
+
+adaptations_vec = ["0 adaptations"]
+adaptations = 5   # number of iterations
+for i in range(adaptations):
+    mesh = adaptivity_schemes.adapt_r(mesh, u)
+
+    u = Solve_6A(mesh, p)
+    plt.plot(mesh, u, '-o')
+
+    adaptations_vec.append(str(i + 1) + " adaptations")
+
+
+# plot exact solution
+x = np.linspace(-1, 1, 50)
+plt.plot(x, np.arctan(p*x))
+adaptations_vec.append("exact")
+
+
+plt.legend(adaptations_vec)
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.grid()
+plt.show()
--- a/ex6/ex_6B.py
+++ b/ex6/ex_6B.py
@ -0,0 +1,120 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import adaptivity_schemes
+
+np.set_printoptions(precision=2)
+
+
+def lam_func(x):
+    n = len(x)
+    lam_vec = np.zeros(n)
+    for i in range(n):    
+        if (x[i] > 1/np.sqrt(2)):
+            lam_vec[i] = 10
+        else:
+            lam_vec[i] = 1
+    return lam_vec
+    
+
+
+def Solve_6B(mesh):
+    N = len(mesh) - 1   # number of elements
+
+    A = np.zeros((N + 1, N + 1))
+
+    lam_vec = lam_func(mesh)
+
+    for i in range(1, N + 1):
+        h = mesh[i] - mesh[i - 1]
+
+        a_11 = lam_vec[i]/h
+        a_12 = -lam_vec[i]/h
+        a_21 = -lam_vec[i]/h
+        a_22 = lam_vec[i]/h
+                                        
+        A[i - 1, i - 1] += a_11
+        A[i - 1, i] += a_12
+        A[i, i - 1] += a_21
+        A[i, i] += a_22
+
+    #print("A =\n", A)
+    
+    # take dirichlet data into account
+    u_g = np.zeros(N + 1)
+    u_g[0] = 0
+    u_g[N] = 1
+    #print("u_g =\n", u_g)
+
+    # remove first and last row of A
+    A_g = A[1:N, :]
+    #print("A_g =\n", A_g)
+
+    # assemble RHS with dirichlet data
+    f = -A_g.dot(u_g)
+    #print(f)
+
+    # matrix for the inner nodes (excluding nodes with dirichlet bcs)
+    A_0 = A[1:N, 1:N]   
+    #print(A_0)
+
+    # solve for u_0 (free dofs)
+    u_0 = np.linalg.solve(A_0, f)
+
+    # assemble "u = u_0 + u_g"
+    u = np.concatenate([[0], u_0, [1]])
+    #print("u =\n", u)
+
+    return u
+
+
+########## h-adaptivity ##########
+N = 2   # number of elements
+mesh = np.linspace(0, 1, N + 1)
+u = Solve_6B(mesh)
+
+plt.plot(mesh, u, '-o')
+plt.grid()
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.title("h-adaptivity")
+
+
+N_vec = ["0 refinements, " + str(N) + " elements"]
+refinements = 5   # number of refinements
+for i in range(refinements):
+    mesh = adaptivity_schemes.adapt_h(mesh, lam_func(mesh)*u, 0.9)
+    u = Solve_6B(mesh)
+    plt.plot(mesh, u, '-o')
+
+    N_vec.append(str(i + 1) + " refinements, " + str(len(mesh) - 1) + " elements")
+
+plt.legend(N_vec)
+plt.show()
+
+
+
+########## r-adaptivity ##########
+N = 5
+mesh = np.linspace(0, 1, N + 1)
+u = Solve_6B(mesh)
+plt.plot(mesh, u, '-o')
+title = "r-adaptivity with " + str(N) + " elements"
+plt.title(title)
+
+adaptations_vec = ["0 adaptations"]
+adaptations = 4   # number of iterations
+for i in range(adaptations):
+    mesh = adaptivity_schemes.adapt_r(mesh, lam_func(mesh)*u)
+    u = Solve_6B(mesh)
+    plt.plot(mesh, u, '-o')
+
+    adaptations_vec.append(str(i + 1) + " adaptations")
+
+
+plt.legend(adaptations_vec)
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.grid()
+plt.show()
+
+
--- a/ex6/ex_6C.py
+++ b/ex6/ex_6C.py
@ -0,0 +1,127 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import adaptivity_schemes
+
+np.set_printoptions(precision=2)
+
+
+def Solve_6C(mesh, p):
+    N = len(mesh) - 1   # number of elements
+
+    A = np.zeros((N + 1, N + 1))
+
+    for i in range(1, N + 1):
+        h = mesh[i] - mesh[i - 1]
+
+        a_11 =  1./h - p/2.
+        a_12 = -1./h + p/2.
+        a_21 = -1./h - p/2.
+        a_22 =  1./h + p/2.
+                                            
+        A[i - 1, i - 1] += a_11
+        A[i - 1, i] += a_12
+        A[i, i - 1] += a_21
+        A[i, i] += a_22
+
+    #print("A =\n", A)
+
+
+    # take dirichlet data into account
+    u_g = np.zeros(N + 1)
+    u_g[0] = 0
+    u_g[N] = 1
+    #print("u_g =\n", u_g)
+
+    # remove first and last row of A
+    A_g = A[1:N, :]
+    #print("A_g =\n", A_g)
+
+    # assemble RHS with dirichlet data
+    f = -A_g.dot(u_g)
+    #print(f)
+
+    # matrix for the inner nodes (excluding nodes with dirichlet bcs)
+    A_0 = A[1:N, 1:N]   
+    #print(A_0)
+
+    # solve for u_0 (free dofs)
+    u_0 = np.linalg.solve(A_0, f)
+
+    # assemble "u = u_0 + u_g"
+    u = np.concatenate([[0], u_0, [1]])
+
+    return u
+
+
+
+
+
+
+p = 70
+######### h-adaptivity ##########
+N = 5   # number of elements
+mesh = np.linspace(0, 1, N + 1)
+u = Solve_6C(mesh, p)
+
+plt.plot(mesh, u, '-o')
+plt.grid()
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.title("h-adaptivity")
+
+
+N_vec = ["0 refinements, " + str(N) + " elements"]
+refinements = 4   # number of refinements
+for i in range(refinements):
+    mesh = adaptivity_schemes.adapt_h(mesh, u, 0.7)
+    u = Solve_6C(mesh, p)
+    plt.plot(mesh, u, '-o')
+
+    N_vec.append(str(i + 1) + " refinements, " + str(len(mesh) - 1) + " elements")
+
+
+# plot exact solution
+x = np.linspace(0, 1, 50)
+plt.plot(x, (np.exp(p*x) - 1.)/(np.exp(p) - 1.))
+N_vec.append("exact")
+
+plt.legend(N_vec)
+plt.show()
+
+
+
+########## r-adaptivity ##########
+N = 10
+mesh = np.linspace(0, 1, N + 1)
+u = Solve_6C(mesh, p)
+plt.plot(mesh, u, '-o')
+title = "r-adaptivity with " + str(N) + " elements"
+plt.title(title)
+
+adaptations_vec = ["0 adaptations"]
+adaptations = 4   # number of iterations
+for i in range(adaptations):
+    mesh = adaptivity_schemes.adapt_r(mesh, u)
+    u = Solve_6C(mesh, p)
+    plt.plot(mesh, u, '-o')
+
+    adaptations_vec.append(str(i + 1) + " adaptations")
+
+
+# plot exact solution
+x = np.linspace(0, 1, 50)
+plt.plot(x, (np.exp(p*x) - 1.)/(np.exp(p) - 1.))
+adaptations_vec.append("exact")
+
+
+plt.legend(adaptations_vec)
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.grid()
+plt.show()
+
+
+
+
+
+
--- a/ex7/ex7_2/GCC_default.mk
+++ b/ex7/ex7_2/GCC_default.mk
@ -0,0 +1,154 @@
+# Basic Defintions for using GNU-compiler suite sequentially
+# requires setting of COMPILER=GCC_
+
+#startmake as follows to avoid warnings caused by OpenMPI code
+#  make 2>&1 | grep -v openmpi
+
+
+MPI_ROOT=/usr/bin/
+
+CC	= ${MPI_ROOT}mpicc
+CXX     = ${MPI_ROOT}mpicxx
+F77	= ${MPI_ROOT}mpif77
+LINKER  = ${CXX}
+
+# If you 'mpirun ...' reports some error "... not enough slots .." then use the option '--oversubscribe'
+MPIRUN  = ${MPI_ROOT}mpirun --oversubscribe -display-map
+#MPIRUN  = ${MPI_ROOT}mpiexec
+
+# 2023, Oct 23:  ""WARNING: There is at least non-excluded one OpenFabrics device found,"
+# solution according to https://github.com/open-mpi/ompi/issues/11063
+MPIRUN += -mca btl ^openib 
+
+# KFU:sauron
+CXXFLAGS += -I/software/boost/1_72_0/include
+
+WARNINGS = -Wall -pedantic -Woverloaded-virtual -Wfloat-equal -Wshadow \
+           -Wredundant-decls -Wunreachable-code -Winline -fmax-errors=1
+
+# WARNINGS += -Weffc++ -Wextra
+# -Wno-pragmas
+CXXFLAGS += -std=c++17 -ffast-math -O3 -march=native ${WARNINGS}
+# -ftree-vectorizer-verbose=5  -DNDEBUG
+#          -ftree-vectorizer-verbose=2
+# CFLAGS	= -ffast-math -O3 -DNDEBUG -msse3 -fopenmp -fdump-tree-vect-details
+# CFLAGS	= -ffast-math -O3 -funroll-loops -DNDEBUG -msse3 -fopenmp -ftree-vectorizer-verbose=2
+
+# info on vectorization
+#VECTORIZE = -ftree-vectorize -fdump-tree-vect-blocks=foo.dump
+#-fdump-tree-pre=stderr
+VECTORIZE = -ftree-vectorize -fopt-info -ftree-vectorizer-verbose=5
+#CXXFLAGS += ${VECTORIZE}
+
+# -funroll-all-loops   -msse3
+#GCC  -march=knl -march=broadwell -march=haswell
+
+# for debugging purpose (save code)
+# -fsanitize=leak         # only one out the trhee 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}
+
+# OpenMP
+CXXFLAGS += -fopenmp
+LINKFLAGS += -fopenmp
+
+default: ${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+clean:
+	@rm -f ${PROGRAM} ${OBJECTS} gmon.out
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar *.orig
+	@rm -rf html latex
+
+run: ${PROGRAM}
+	${MPIRUN} -np 8 ./$^
+
+# 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
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+#	 2>&1 | grep -v openmpi
+
+# special: get rid of compiler warnings genermaeate by openmpi-files
+#.cpp.o:
+# 	@$(CXX) -c $(CXXFLAGS) $< 2>/tmp/t.txt || grep -sv openmpi /tmp/t.txt
+# 	|grep -sv openmpi
+
+.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: ${PROGRAM}
+	valgrind --tool=callgrind --simulate-cache=yes ./$^
+#	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 mpirun -np 8 ./$^
+	# Graphical interface
+	# valkyrie
+
+#  Simple run time profiling of your code
+#  CXXFLAGS += -g -pg
+#  LINKFLAGS += -pg
+prof: ${PROGRAM}
+	perf record ./$^
+	perf report
+#	gprof -b ./$^ > gp.out
+#	kprof -f gp.out -p gprof &
+
+#Trace your heap:
+#> heaptrack ./main.GCC_
+#> heaptrack_gui heaptrack.main.GCC_.<pid>.gz
+heap: ${PROGRAM}
+	heaptrack ./$^ 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
--- a/ex7/ex7_2/ex7_2/Makefile
+++ b/ex7/ex7_2/ex7_2/Makefile
@ -0,0 +1,54 @@
+#
+# use GNU-Compiler tools
+COMPILER=GCC_
+# COMPILER=GCC_SEQ_
+# alternatively from the shell
+# export COMPILER=GCC_
+# or, alternatively from the shell
+# make COMPILER=GCC_
+
+MAIN = main
+SOURCES = ${MAIN}.cpp greetings.cpp
+
+OBJECTS = $(SOURCES:.cpp=.o)
+
+PROGRAM	= ${MAIN}.${COMPILER}
+
+# uncomment the next to lines for debugging and detailed performance analysis
+CXXFLAGS += -g
+# -DNDEBUG
+# -pg slows down the code on my laptop when using CLANG_
+LINKFLAGS += -g
+#-pg
+#CXXFLAGS += -Q --help=optimizers
+#CXXFLAGS += -fopt-info
+
+include ../${COMPILER}default.mk
+
+#############################################################################
+# additional specific cleaning in this directory
+clean_all::
+	@rm -f t.dat*
+
+
+#############################################################################
+# special testing
+# NPROCS	= 4
+#
+TFILE	= t.dat
+# TTMP	= t.tmp
+#
+graph: $(PROGRAM)
+# 	@rm -f $(TFILE).*
+	# next two lines only sequentially
+	./$(PROGRAM)
+	@mv  $(TFILE).000 $(TFILE)
+# 	$(MPIRUN) $(MPIFLAGS) -np $(NPROCS) $(PROGRAM)
+# 	@echo " "; echo "Manipulate data for graphics."; echo " "
+# 	@cat $(TFILE).* > $(TTMP)
+# 	@sort -b -k 2    $(TTMP)   -o $(TTMP).1
+# 	@sort -b -k 1    $(TTMP).1 -o $(TTMP).2
+# 	@awk  -f nl.awk  $(TTMP).2  > $(TFILE)
+# 	@rm -f $(TTMP).* $(TTMP) $(TFILE).*
+#
+	-gnuplot jac.dem
--- a/ex7/ex7_2/ex7_2/greetings.cpp
+++ b/ex7/ex7_2/ex7_2/greetings.cpp
@ -0,0 +1,89 @@
+#include "greetings.h"
+#include <cassert>
+#include <cstring>
+#include <iostream>
+#include <mpi.h>                                  // MPI
+#include <string>
+using namespace std;
+ 
+// see  http://www.open-mpi.org/doc/current
+// for details on MPI functions
+ 
+void greetings(MPI_Comm const &icomm)
+{
+    int myrank, numprocs;
+    MPI_Comm_rank(icomm, &myrank);                // my MPI-rank
+    MPI_Comm_size(icomm, &numprocs);              // #MPI processes
+    char *name  = new char [MPI_MAX_PROCESSOR_NAME],
+         *chbuf = new char [MPI_MAX_PROCESSOR_NAME];
+ 
+    int reslen, ierr;
+    MPI_Get_processor_name( name, &reslen);
+ 
+    if (0==myrank) {
+        cout << "   " << myrank << " runs on " << name << endl;
+        for (int i = 1; i < numprocs; ++i) {
+            MPI_Status stat;
+            stat.MPI_ERROR = 0;            // M U S T   be initialized!!
+ 
+
+            //ierr = MPI_Recv(chbuf, MPI_MAX_PROCESSOR_NAME, MPI_CHAR, MPI_ANY_SOURCE, MPI_ANY_TAG, icomm, &stat);
+            ierr = MPI_Recv(chbuf, MPI_MAX_PROCESSOR_NAME, MPI_CHAR, i, i, icomm, &stat);
+            assert(0==ierr);
+ 
+            cout << "   " << stat.MPI_SOURCE << " runs on " << chbuf;
+            int count;
+            MPI_Get_count(&stat, MPI_CHAR, &count); // size of received data
+            cout << " (length: " << count << " )" << endl;
+            //  stat.Get_error()        // Error code
+        }
+    }
+    else {
+        int dest = 0;
+        ierr = MPI_Send(name, strlen(name) + 1, MPI_CHAR, dest, myrank, icomm);
+        assert(0==ierr);
+    }
+    delete [] chbuf;
+    delete [] name;
+    return;
+}
+ 
+ 
+void greetings_cpp(MPI_Comm const &icomm)
+{
+    int myrank, numprocs;
+    MPI_Comm_rank(icomm, &myrank);                // my MPI-rank
+    MPI_Comm_size(icomm, &numprocs);              // #MPI processes
+    string name(MPI_MAX_PROCESSOR_NAME,'#'),      // C++
+           recvbuf(MPI_MAX_PROCESSOR_NAME,'#');   // C++: receive buffer, don't change size
+ 
+    int reslen, ierr;
+    MPI_Get_processor_name(name.data(), &reslen);
+    name.resize(reslen);                          // C++
+
+ 
+    if (0==myrank) {
+        cout << "   " << myrank << " runs on " << name << endl;
+        for (int i = 1; i < numprocs; ++i) {
+            MPI_Status stat;
+            stat.MPI_ERROR = 0;            // M U S T   be initialized!!
+ 
+            //ierr = MPI_Recv(recvbuf.data(), MPI_MAX_PROCESSOR_NAME, MPI_CHAR, MPI_ANY_SOURCE, MPI_ANY_TAG, icomm, &stat);
+            ierr = MPI_Recv(recvbuf.data(), MPI_MAX_PROCESSOR_NAME, MPI_CHAR, i, i, icomm, &stat);
+            assert(0==ierr);
+ 
+            int count;
+            MPI_Get_count(&stat, MPI_CHAR, &count); // size of received data
+            string const chbuf(recvbuf,0,count);    // C++
+            cout << "   " << stat.MPI_SOURCE << " runs on " << chbuf;
+            cout << " (length: " << count << " )" << endl;
+            //  stat.Get_error()        // Error code
+        }
+    }
+    else {
+        int dest = 0;
+        ierr = MPI_Send(name.data(), name.size(), MPI_CHAR, dest, myrank, icomm);
+        assert(0==ierr);
+    }
+    return;
+}
--- a/ex7/ex7_2/ex7_2/greetings.h
+++ b/ex7/ex7_2/ex7_2/greetings.h
@ -0,0 +1,11 @@
+//      general header for all functions in directory
+ 
+#ifndef GREETINGS_FILE
+#define GREETINGS_FILE
+ 
+#include <mpi.h>
+ 
+void greetings(MPI_Comm const &icomm);
+void greetings_cpp(MPI_Comm const &icomm);
+ 
+#endif
--- a/ex7/ex7_2/ex7_2/main.cpp
+++ b/ex7/ex7_2/ex7_2/main.cpp
@ -0,0 +1,40 @@
+#include <iostream>
+#include <mpi.h> 
+
+#include "greetings.h"
+
+using namespace std;
+
+
+int main(int argc , char **argv )
+{
+    // -------------------- E2 --------------------
+    MPI_Init(&argc, &argv);     // Initializes the MPI execution environment 
+
+    // -------------------- E1 --------------------
+    MPI_Comm const icomm(MPI_COMM_WORLD);   // MPI_COMM_WORLD ... all processes
+
+    // -------------------- E3 --------------------
+    int rank;
+    MPI_Comm_rank(icomm, &rank);   // Determines the rank of the calling process in the communicator. 
+    
+    if (rank == 0)
+    {
+        int size;
+        MPI_Comm_size(icomm, &size); // Returns the size of the group associated with a communicator. 
+        cout << "Process " << rank << " says: " << size << " proesses are running." << endl;
+    }
+    // To vary number of processes: changed number in GCC_default.mk file
+    // alternatively, call in terminal:
+    // /usr/bin/mpirun --oversubscribe -display-map -mca btl ^openib  -np 4 ./main.GCC_
+    // or
+    // /usr/bin/mpirun --oversubscribe -display-map -mca btl ^openib  -np 8 ./main.GCC_
+
+
+    // -------------------- E4 --------------------
+    greetings_cpp(MPI_COMM_WORLD);  // greetings with sorted output
+
+
+    MPI_Finalize();     // Terminates MPI execution environment
+    return 0;
+}
--- a/ex7/ex7_3/GCC_default.mk
+++ b/ex7/ex7_3/GCC_default.mk
@ -0,0 +1,154 @@
+# Basic Defintions for using GNU-compiler suite sequentially
+# requires setting of COMPILER=GCC_
+
+#startmake as follows to avoid warnings caused by OpenMPI code
+#  make 2>&1 | grep -v openmpi
+
+
+MPI_ROOT=/usr/bin/
+
+CC	= ${MPI_ROOT}mpicc
+CXX     = ${MPI_ROOT}mpicxx
+F77	= ${MPI_ROOT}mpif77
+LINKER  = ${CXX}
+
+# If you 'mpirun ...' reports some error "... not enough slots .." then use the option '--oversubscribe'
+MPIRUN  = ${MPI_ROOT}mpirun --oversubscribe -display-map
+#MPIRUN  = ${MPI_ROOT}mpiexec
+
+# 2023, Oct 23:  ""WARNING: There is at least non-excluded one OpenFabrics device found,"
+# solution according to https://github.com/open-mpi/ompi/issues/11063
+MPIRUN += -mca btl ^openib 
+
+# KFU:sauron
+CXXFLAGS += -I/software/boost/1_72_0/include
+
+WARNINGS = -Wall -pedantic -Woverloaded-virtual -Wfloat-equal -Wshadow \
+           -Wredundant-decls -Wunreachable-code -Winline -fmax-errors=1
+
+# WARNINGS += -Weffc++ -Wextra
+# -Wno-pragmas
+CXXFLAGS += -std=c++17 -ffast-math -O3 -march=native ${WARNINGS}
+# -ftree-vectorizer-verbose=5  -DNDEBUG
+#          -ftree-vectorizer-verbose=2
+# CFLAGS	= -ffast-math -O3 -DNDEBUG -msse3 -fopenmp -fdump-tree-vect-details
+# CFLAGS	= -ffast-math -O3 -funroll-loops -DNDEBUG -msse3 -fopenmp -ftree-vectorizer-verbose=2
+
+# info on vectorization
+#VECTORIZE = -ftree-vectorize -fdump-tree-vect-blocks=foo.dump
+#-fdump-tree-pre=stderr
+VECTORIZE = -ftree-vectorize -fopt-info -ftree-vectorizer-verbose=5
+#CXXFLAGS += ${VECTORIZE}
+
+# -funroll-all-loops   -msse3
+#GCC  -march=knl -march=broadwell -march=haswell
+
+# for debugging purpose (save code)
+# -fsanitize=leak         # only one out the trhee 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}
+
+# OpenMP
+CXXFLAGS += -fopenmp
+LINKFLAGS += -fopenmp
+
+default: ${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+clean:
+	@rm -f ${PROGRAM} ${OBJECTS} gmon.out
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar *.orig
+	@rm -rf html latex
+
+run: ${PROGRAM}
+	${MPIRUN} -np 4 ./$^
+
+# 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
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+#	 2>&1 | grep -v openmpi
+
+# special: get rid of compiler warnings genermaeate by openmpi-files
+#.cpp.o:
+# 	@$(CXX) -c $(CXXFLAGS) $< 2>/tmp/t.txt || grep -sv openmpi /tmp/t.txt
+# 	|grep -sv openmpi
+
+.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: ${PROGRAM}
+	valgrind --tool=callgrind --simulate-cache=yes ./$^
+#	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 mpirun -np 4 ./$^
+	# Graphical interface
+	# valkyrie
+
+#  Simple run time profiling of your code
+#  CXXFLAGS += -g -pg
+#  LINKFLAGS += -pg
+prof: ${PROGRAM}
+	perf record ./$^
+	perf report
+#	gprof -b ./$^ > gp.out
+#	kprof -f gp.out -p gprof &
+
+#Trace your heap:
+#> heaptrack ./main.GCC_
+#> heaptrack_gui heaptrack.main.GCC_.<pid>.gz
+heap: ${PROGRAM}
+	heaptrack ./$^ 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
--- a/ex7/ex7_3/ex7_3/Makefile
+++ b/ex7/ex7_3/ex7_3/Makefile
@ -0,0 +1,54 @@
+#
+# use GNU-Compiler tools
+COMPILER=GCC_
+# COMPILER=GCC_SEQ_
+# alternatively from the shell
+# export COMPILER=GCC_
+# or, alternatively from the shell
+# make COMPILER=GCC_
+
+MAIN = main
+SOURCES = ${MAIN}.cpp vector_operations.cpp
+
+OBJECTS = $(SOURCES:.cpp=.o)
+
+PROGRAM	= ${MAIN}.${COMPILER}
+
+# uncomment the next to lines for debugging and detailed performance analysis
+CXXFLAGS += -g
+# -DNDEBUG
+# -pg slows down the code on my laptop when using CLANG_
+LINKFLAGS += -g
+#-pg
+#CXXFLAGS += -Q --help=optimizers
+#CXXFLAGS += -fopt-info
+
+include ../${COMPILER}default.mk
+
+#############################################################################
+# additional specific cleaning in this directory
+clean_all::
+	@rm -f t.dat*
+
+
+#############################################################################
+# special testing
+# NPROCS	= 4
+#
+TFILE	= t.dat
+# TTMP	= t.tmp
+#
+graph: $(PROGRAM)
+# 	@rm -f $(TFILE).*
+	# next two lines only sequentially
+	./$(PROGRAM)
+	@mv  $(TFILE).000 $(TFILE)
+# 	$(MPIRUN) $(MPIFLAGS) -np $(NPROCS) $(PROGRAM)
+# 	@echo " "; echo "Manipulate data for graphics."; echo " "
+# 	@cat $(TFILE).* > $(TTMP)
+# 	@sort -b -k 2    $(TTMP)   -o $(TTMP).1
+# 	@sort -b -k 1    $(TTMP).1 -o $(TTMP).2
+# 	@awk  -f nl.awk  $(TTMP).2  > $(TFILE)
+# 	@rm -f $(TTMP).* $(TTMP) $(TFILE).*
+#
+	-gnuplot jac.dem
--- a/ex7/ex7_3/ex7_3/main.cpp
+++ b/ex7/ex7_3/ex7_3/main.cpp
@ -0,0 +1,107 @@
+#include <iostream>
+#include <mpi.h> 
+#include <vector>
+
+#include "vector_operations.h"
+
+using namespace std;
+
+
+int main(int argc , char **argv)
+{
+    MPI_Init(&argc, &argv);     // Initializes the MPI execution environment 
+    MPI_Comm const icomm(MPI_COMM_WORLD);
+    int myrank;
+    MPI_Comm_rank(icomm, &myrank);
+
+    int n = 20;
+    vector<double> x(n);
+    vector<double> y = x;
+    for (int i = 0; i < n; ++i)
+    {
+        x[i] = myrank*100 + (i % 5)*10 + i;
+        y[i] = 1.0/(x[i]);
+    }
+
+    if(myrank == 0) // so scalar product is well defined (avoid division by 0)
+        y[0] = 0;
+    
+
+    // -------------------- E5 --------------------
+    if (myrank == 0) cout << "-------------------- E5 --------------------" << endl;
+    DebugVector(x, icomm);
+
+
+    cout.flush();
+    MPI_Barrier(icomm);
+    // -------------------- E6 --------------------
+    if (myrank == 0) cout << "-------------------- E6 --------------------" << endl;
+    double scalar_product = par_scalar(x, y, icomm);
+
+    if (myrank == 0)
+    {
+        cout << "<x,y> = " << scalar_product << endl << endl;
+    }
+    
+
+    cout.flush();
+    MPI_Barrier(icomm);
+    // -------------------- E7 --------------------
+    if (myrank == 0) cout << "-------------------- E7 --------------------" << endl;
+    double xmin, xmax;
+    par_minmax(x, xmin, xmax, icomm);
+
+    if (myrank == 0)
+    {
+        cout << "Global min: " << xmin << endl;
+        cout << "Global max: " << xmax << endl << endl;
+    }
+
+    cout.flush();
+    MPI_Barrier(icomm);
+    // -------------------- E8 --------------------
+    if (myrank == 0) cout << "-------------------- E8 --------------------" << endl;
+    vector<double> x_new(n);
+
+
+    cout.flush();
+    MPI_Barrier(icomm);
+    // All to all
+    if (myrank == 0) cout << "----- All to all -----" << endl;
+    auto sendbuf = x.data();
+    int sendcount = 5;
+    auto recvbuf = x_new.data();
+    int recvcount = 5;
+    MPI_Alltoall(sendbuf, sendcount, MPI_DOUBLE, recvbuf, recvcount, MPI_DOUBLE, icomm);
+
+    DebugVector(x_new, icomm);
+
+
+    cout.flush();
+    MPI_Barrier(icomm);
+    // All to all v
+    if (myrank == 0) cout << "----- All to all v -----" << endl;
+    int sendcounts[4] = {5, 5, 5, 5};
+    int senddispls[4] = {0, 5, 10, 15};
+    int rcvcounts[4] = {5, 5, 5, 5};
+    int rcvdispls[4] = {0, 5, 10, 15};
+    MPI_Alltoallv(x.data(), sendcounts, senddispls, MPI_DOUBLE, x_new.data(), rcvcounts, rcvdispls, MPI_DOUBLE, icomm);
+
+    DebugVector(x_new, icomm);
+
+
+    cout.flush();
+    MPI_Barrier(icomm);
+    // All to all (in place), sendcount and sendtype are ignored
+    if (myrank == 0) cout << "----- All to all (in place) -----" << endl;
+    MPI_Alltoall(MPI_IN_PLACE, sendcount, MPI_DOUBLE, x.data(), recvcount, MPI_DOUBLE, icomm);
+
+    DebugVector(x, icomm);
+
+
+
+    
+    MPI_Finalize();     // Terminates MPI execution environment
+
+    return 0;
+}
--- a/ex7/ex7_3/ex7_3/vector_operations.cpp
+++ b/ex7/ex7_3/ex7_3/vector_operations.cpp
@ -0,0 +1,110 @@
+#include "vector_operations.h"
+#include <cassert>
+#include <cfloat>
+
+void DebugVector(const vector<double> &xin, const MPI_Comm &icomm)
+{
+    int myrank, numprocs;
+    MPI_Comm_rank(icomm, &myrank);                // my MPI-rank
+    MPI_Comm_size(icomm, &numprocs);              // #MPI processes
+    int ierr;
+    
+
+    int n = xin.size();
+    
+    
+    int chosen_process;
+    for (int k = 0; k < numprocs; ++k)
+    {   
+        MPI_Barrier(icomm);
+
+        if (myrank == 0)
+        {   
+            cout << "Choose next process: ";
+            cin >> chosen_process;
+            
+        }
+        ierr = MPI_Bcast(&chosen_process, 1, MPI_INT, 0, icomm); // broadcast value of "chosen_process" to all processes
+        assert(ierr == 0);
+
+        MPI_Barrier(icomm);
+
+        if (chosen_process == myrank)
+        {
+            for (int i = 0; i < n; ++i)
+            {
+                cout << "x_" << i << " = " << xin[i] << "\t(Process " << myrank << ")" << endl;
+            }
+            cout.flush();
+        }
+    }
+    return;
+}
+
+
+
+double par_scalar(const vector<double> &x, const vector<double> &y, const MPI_Comm &icomm)
+{
+    int n = x.size();
+    assert(n == (int)y.size());
+
+    double sum = 0.0;
+    double local_sum = 0.0;
+
+    
+    for (int i = 0; i < n; ++i)
+    {
+        local_sum += x[i]*y[i];
+    }
+
+    int ierr = MPI_Allreduce(&local_sum, &sum, 1, MPI_DOUBLE, MPI_SUM, icomm);  // reduce local sums to global sum
+    assert(ierr == 0);
+
+
+    return sum;
+}
+
+
+void par_minmax(const vector<double> &x, double &global_min, double &global_max, const MPI_Comm &icomm)
+{
+    int myrank, numprocs;
+    MPI_Comm_rank(icomm, &myrank);                // my MPI-rank
+    MPI_Comm_size(icomm, &numprocs);              // #MPI processes
+
+    int n = x.size();
+
+    double local_min = DBL_MAX;
+    double local_max = -DBL_MAX;
+    
+    for (int i = 0; i < n; ++i)
+    {
+        if (x[i] < local_min)
+            local_min = x[i];
+        if (x[i] > local_max)
+            local_max = x[i];
+    }
+
+    vector<double> local_mins(numprocs);
+    vector<double> local_maxs(numprocs);
+    MPI_Gather(&local_min, 1, MPI_DOUBLE, local_mins.data(), 1, MPI_DOUBLE, 0, icomm);
+    MPI_Gather(&local_max, 1, MPI_DOUBLE, local_maxs.data(), 1, MPI_DOUBLE, 0, icomm);
+
+    if (myrank == 0)
+    {
+        global_min = DBL_MAX;
+        global_max = -DBL_MAX;
+
+        for (int i = 0; i < numprocs; ++i)
+        {
+            if (local_mins[i] < global_min)
+                global_min = local_mins[i];
+            if (local_maxs[i] > global_max)
+                global_max = local_maxs[i];
+        }
+    }
+
+    MPI_Bcast(&global_min, 1, MPI_DOUBLE, 0, icomm); // make sure every process is up to date
+    MPI_Bcast(&global_max, 1, MPI_DOUBLE, 0, icomm);
+
+    return;
+}
--- a/ex7/ex7_3/ex7_3/vector_operations.h
+++ b/ex7/ex7_3/ex7_3/vector_operations.h
@ -0,0 +1,10 @@
+#include <mpi.h>
+#include <vector>
+
+using namespace std;
+
+void DebugVector(const vector<double> &xin, const MPI_Comm &icomm);
+
+double par_scalar(const vector<double> &x, const vector<double> &y, const MPI_Comm &icomm);
+
+void par_minmax(const vector<double> &x, double &global_min, double &global_max, const MPI_Comm &icomm);
--- a/ex7/ex7_4/GCC_default.mk
+++ b/ex7/ex7_4/GCC_default.mk
@ -0,0 +1,154 @@
+# Basic Defintions for using GNU-compiler suite sequentially
+# requires setting of COMPILER=GCC_
+
+#startmake as follows to avoid warnings caused by OpenMPI code
+#  make 2>&1 | grep -v openmpi
+
+
+MPI_ROOT=/usr/bin/
+
+CC	= ${MPI_ROOT}mpicc
+CXX     = ${MPI_ROOT}mpicxx
+F77	= ${MPI_ROOT}mpif77
+LINKER  = ${CXX}
+
+# If you 'mpirun ...' reports some error "... not enough slots .." then use the option '--oversubscribe'
+MPIRUN  = ${MPI_ROOT}mpirun --oversubscribe -display-map
+#MPIRUN  = ${MPI_ROOT}mpiexec
+
+# 2023, Oct 23:  ""WARNING: There is at least non-excluded one OpenFabrics device found,"
+# solution according to https://github.com/open-mpi/ompi/issues/11063
+MPIRUN += -mca btl ^openib 
+
+# KFU:sauron
+CXXFLAGS += -I/software/boost/1_72_0/include
+
+WARNINGS = -Wall -pedantic -Woverloaded-virtual -Wfloat-equal -Wshadow \
+           -Wredundant-decls -Wunreachable-code -Winline -fmax-errors=1
+
+# WARNINGS += -Weffc++ -Wextra
+# -Wno-pragmas
+CXXFLAGS += -std=c++17 -ffast-math -O3 -march=native ${WARNINGS}
+# -ftree-vectorizer-verbose=5  -DNDEBUG
+#          -ftree-vectorizer-verbose=2
+# CFLAGS	= -ffast-math -O3 -DNDEBUG -msse3 -fopenmp -fdump-tree-vect-details
+# CFLAGS	= -ffast-math -O3 -funroll-loops -DNDEBUG -msse3 -fopenmp -ftree-vectorizer-verbose=2
+
+# info on vectorization
+#VECTORIZE = -ftree-vectorize -fdump-tree-vect-blocks=foo.dump
+#-fdump-tree-pre=stderr
+VECTORIZE = -ftree-vectorize -fopt-info -ftree-vectorizer-verbose=5
+#CXXFLAGS += ${VECTORIZE}
+
+# -funroll-all-loops   -msse3
+#GCC  -march=knl -march=broadwell -march=haswell
+
+# for debugging purpose (save code)
+# -fsanitize=leak         # only one out the trhee 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}
+
+# OpenMP
+CXXFLAGS += -fopenmp
+LINKFLAGS += -fopenmp
+
+default: ${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+clean:
+	@rm -f ${PROGRAM} ${OBJECTS} gmon.out
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar *.orig
+	@rm -rf html latex
+
+run: ${PROGRAM}
+	${MPIRUN} -np 4 ./$^
+
+# 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
+
+#########################################################################
+
+.cpp.o:
+	$(CXX) -c $(CXXFLAGS) -o $@ $<
+#	 2>&1 | grep -v openmpi
+
+# special: get rid of compiler warnings genereate by openmpi-files
+#.cpp.o:
+# 	@$(CXX) -c $(CXXFLAGS) $< 2>/tmp/t.txt || grep -sv openmpi /tmp/t.txt
+# 	|grep -sv openmpi
+
+.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: ${PROGRAM}
+	valgrind --tool=callgrind --simulate-cache=yes ./$^
+#	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 mpirun -np 4 ./$^
+	# Graphical interface
+	# valkyrie
+
+#  Simple run time profiling of your code
+#  CXXFLAGS += -g -pg
+#  LINKFLAGS += -pg
+prof: ${PROGRAM}
+	perf record ./$^
+	perf report
+#	gprof -b ./$^ > gp.out
+#	kprof -f gp.out -p gprof &
+
+#Trace your heap:
+#> heaptrack ./main.GCC_
+#> heaptrack_gui heaptrack.main.GCC_.<pid>.gz
+heap: ${PROGRAM}
+	heaptrack ./$^ 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
--- a/ex7/ex7_4/ICC_NATIVE_default.mk
+++ b/ex7/ex7_4/ICC_NATIVE_default.mk
@ -0,0 +1,107 @@
+# Basic Defintions for using INTEL-MPI with its compilers
+# requires setting of COMPILER=ICC_NATIVE_
+
+# MPI_ROOT should be defined by shell
+#   path to  icpc  is contained in $PATH
+MPI_BIN = $(shell dirname `which icpc` | sed 's/bin\/intel64/mpi\/intel64\/bin/g')/
+MPI_LIB = $(shell echo ${MPI_BIN} | sed 's/bin/lib/g')
+
+#  Intel-MPI wrappers used gcc as default !!
+CC	= ${MPI_BIN}mpicc  -cc=icc
+CXX = ${MPI_BIN}mpicxx -cxx=icpc
+F77	= ${MPI_BIN}mpif77 -f77=ifort
+LINKER  = ${CXX}
+
+MPIRUN  = ${MPI_BIN}mpirun
+
+WARNINGS = -Wall  -Wextra -pedantic -Woverloaded-virtual  -Wfloat-equal -Wshadow
+           #  -Weffc++ -Wunreachable-code -Winline
+CXXFLAGS += -O3 -fargument-noalias  -DNDEBUG -std=c++17 ${WARNINGS} ${MPI_COMPILE_FLAGS}
+CFLAGS   += -O3 -fargument-noalias  -DNDEBUG -Wall  -Wextra -pedantic -Wfloat-equal \
+            -Wshadow ${MPI_COMPILE_FLAGS}
+# -vec-report=3 -mkl
+# -guide -parallel
+# -guide-opts=string  -guide-par[=n]  -guide-vec[=n]
+# -auto-p32 -simd
+
+# use MKL by INTEL
+LINKFLAGS += -mkl ${MPI_LINK_FLAGS}
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+clean:
+	rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+run: ${PROGRAM}
+	(export LD_LIBRARY_PATH=${MPI_LIB}:${LD_LIBRARY_PATH} ;${MPIRUN} -np 4 ./$^ ${PROG_ARGS})
+
+# 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}
+	${BINDIR}../vtune_amplifier_xe_2013/bin64/amplxe-gui &
+
+# GUI for Memory and Thread analyzer (race condition)
+inspector: ${PROGRAM}
+# http://askubuntu.com/questions/41629/after-upgrade-gdb-wont-attach-to-process
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	${BINDIR}../inspector_xe_2013/bin64/inspxe-gui & 
--- a/ex7/ex7_4/ICC_default.mk
+++ b/ex7/ex7_4/ICC_default.mk
@ -0,0 +1,112 @@
+# Basic Defintions for using INTEL compilers with OpenMPI headers and libraries
+# requires setting of COMPILER=ICC_
+
+# MPI_ROOT should be defined by shell
+MPI_ROOT=/usr
+
+CC	= icc
+CXX = icpc
+F77	= ifort
+LINKER  = ${CXX}
+
+MPIRUN  = ${MPI_ROOT}/bin/mpirun
+
+# no differences when C or C++ is used !!  (always used options from mpicxx)
+MPI_COMPILE_FLAGS = `${MPI_ROOT}/bin/mpicxx -showme:compile`
+MPI_LINK_FLAGS    = `${MPI_ROOT}/bin/mpicxx -showme:link`
+# MPI_LINK_FLAGS    = -pthread -L/usr/lib/openmpi/lib -lmpi_cxx -lmpi -lopen-rte -lopen-pal -ldl -Wl,--export-dynamic -lnsl -lutil -lm -ldl
+
+
+WARNINGS = -Wall  -Wextra -pedantic -Woverloaded-virtual  -Wfloat-equal -Wshadow
+           #  -Weffc++ -Wunreachable-code -Winline
+CXXFLAGS += -O3 -std=c++17 -fargument-noalias  -DNDEBUG  ${WARNINGS} ${MPI_COMPILE_FLAGS}
+CFLAGS   += -O3 -fargument-noalias  -DNDEBUG -Wall  -Wextra -pedantic -Wfloat-equal \
+            -Wshadow ${MPI_COMPILE_FLAGS}
+# -vec-report=3 -mkl
+# -guide -parallel
+# -guide-opts=string  -guide-par[=n]  -guide-vec[=n]
+# -auto-p32 -simd
+
+# use MKL by INTEL
+LINKFLAGS += -mkl 
+# use MPI by Compiler
+LINKFLAGS += ${MPI_LINK_FLAGS}
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+clean:
+	rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+run: ${PROGRAM}
+	${MPIRUN} -np 4 ./$^
+
+# 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}
+	${BINDIR}../vtune_amplifier_xe_2013/bin64/amplxe-gui &
+
+# GUI for Memory and Thread analyzer (race condition)
+inspector: ${PROGRAM}
+# http://askubuntu.com/questions/41629/after-upgrade-gdb-wont-attach-to-process
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	${BINDIR}../inspector_xe_2013/bin64/inspxe-gui & 
--- a/ex7/ex7_4/OPENMPI_CLANG_default.mk
+++ b/ex7/ex7_4/OPENMPI_CLANG_default.mk
@ -0,0 +1,128 @@
+# Basic Defintions for using OpenMPI with CLANG compilers
+# requires setting of COMPILER=OPENMPI_CLANG_
+
+# Pass CLANG Compilers to the OpenMPI wrappers
+#    see: https://www.open-mpi.org/faq/?category=mpi-apps#override-wrappers-after-v1.0
+EXPORT = export OMPI_CXX=clang++; export OMPI_CC=clang; export OMPI_mpifort=flang
+
+CC	= mpicc
+CXX = mpicxx
+F77	= mpifort
+LINKER  = ${CXX}
+
+MPIRUN  = ${MPI_BIN}mpirun
+
+#http://clang.llvm.org/docs/UsersManual.html#options-to-control-error-and-warning-messages
+SILENCE_MPI = -Wno-weak-vtables -Wno-old-style-cast -Wno-cast-align -Wno-deprecated 
+SILENCE_MPI+= -Wno-sign-conversion -Wno-reserved-id-macro -Wno-c++98-compat-pedantic
+SILENCE_MPI+= -Wno-zero-as-null-pointer-constant -Wno-source-uses-openmp
+WARNINGS = -Weverything -Wno-c++98-compat -Wno-weak-vtables -ferror-limit=3 ${SILENCE_MPI}
+#-fsyntax-only -Wdocumentation -Wconversion -Wshadow -Wfloat-conversion -pedantic
+CXXFLAGS += -Ofast -std=c++17  ${WARNINGS} 
+#CXXFLAGS += -Ofast -std=c++17 
+# -ftrapv
+#
+CFLAGS   +=  -Ofast -Weverything -ferror-limit=3 ${MPI_COMPILE_FLAGS}
+
+# OpenMP
+#CXXFLAGS += -fopenmp
+#LINKFLAGS += -fopenmp
+
+# tidy_check
+SWITCH_OFF=,-readability-magic-numbers,-readability-redundant-control-flow,-readability-redundant-member-init
+SWITCH_OFF+=,-readability-redundant-member-init,-readability-isolate-declaration
+#READABILITY=,readability*${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${READABILITY} -header-filter=.* -enable-check-profile -extra-arg="-std=c++17" -extra-arg="-fopenmp"
+#TIDYFLAGS += -checks='modernize*
+
+MPI_COMPILE_FLAGS = `${MPI_BIN}mpicxx -showme:compile`
+MPI_LINK_FLAGS    = `${MPI_BIN}mpicxx -showme:link`
+#TIDYFLAGS += ${MPI_COMPILE_FLAGS}
+TIDYFLAGS += -extra-arg="-I/usr/lib/x86_64-linux-gnu/openmpi/include"
+#check:
+#	echo ${MPI_COMPILE_FLAGS}
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	@( ${EXPORT}; $(LINKER)  $^  ${LINKFLAGS} -o $@ )
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+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: ${PROGRAM}
+	${MPIRUN} -np 4 ./$^ ${PROG_ARGS}
+
+# 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:
+	@( ${EXPORT}; $(CXX) -c $(CXXFLAGS) -o $@ $< )
+
+.c.o:
+	@( ${EXPORT}; $(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}
+	${BINDIR}../vtune_amplifier_xe_2013/bin64/amplxe-gui &
+
+# GUI for Memory and Thread analyzer (race condition)
+inspector: ${PROGRAM}
+# http://askubuntu.com/questions/41629/after-upgrade-gdb-wont-attach-to-process
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	${BINDIR}../inspector_xe_2013/bin64/inspxe-gui & 
--- a/ex7/ex7_4/OPENMPI_ICC_default.mk
+++ b/ex7/ex7_4/OPENMPI_ICC_default.mk
@ -0,0 +1,107 @@
+# Basic Defintions for using OpenMPI with Intel compilers
+# requires setting of COMPILER=OPENMPI_ICC_
+
+# Pass Intel Compilers to the OpenMPI wrappers
+#    see: https://www.open-mpi.org/faq/?category=mpi-apps#override-wrappers-after-v1.0
+EXPORT = export OMPI_CXX=icpc; export OMPI_CC=icc; export OMPI_mpifort=ifort
+
+CC	= mpicc
+CXX = mpicxx
+F77	= mpifort
+LINKER  = ${CXX}
+
+MPIRUN  = ${MPI_BIN}mpirun
+
+WARNINGS = -Wall  -Wextra -pedantic -Woverloaded-virtual  -Wfloat-equal -Wshadow
+           #  -Weffc++ -Wunreachable-code -Winline
+CXXFLAGS += -fast -fargument-noalias  -DNDEBUG -std=c++17 ${WARNINGS}
+CFLAGS   += -O3 -fargument-noalias  -DNDEBUG -Wall  -Wextra -pedantic -Wfloat-equal -Wshadow
+# -vec-report=3 -mkl
+# -guide -parallel
+# -guide-opts=string  -guide-par[=n]  -guide-vec[=n]
+# -auto-p32 -simd
+
+# use MKL by INTEL
+LINKFLAGS += -O3 -mkl ${MPI_LINK_FLAGS}
+# ipo: warning #11021: unresolved __GI_memset
+# see:  https://software.intel.com/en-us/articles/ipo-warning-11021-unresolved-symbols-referenced-a-dynamic-library
+LINKFLAGS += 
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	@( ${EXPORT}; $(LINKER)  $^  ${LINKFLAGS} -o $@ )
+	@echo
+	@echo "Start with :  $(MPIRUN) -np num_proc $(MPIFLAGS) $(PROGRAM)"
+	@echo
+
+clean:
+	rm -f ${PROGRAM} ${OBJECTS}
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+run: ${PROGRAM}
+	${MPIRUN} -np 4 ./$^ ${PROG_ARGS}
+
+# 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:
+	@( ${EXPORT}; $(CXX) -c $(CXXFLAGS) -o $@ $< )
+
+.c.o:
+	@( ${EXPORT}; $(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}
+	${BINDIR}../vtune_amplifier_xe_2013/bin64/amplxe-gui &
+
+# GUI for Memory and Thread analyzer (race condition)
+inspector: ${PROGRAM}
+# http://askubuntu.com/questions/41629/after-upgrade-gdb-wont-attach-to-process
+	echo 0 | sudo tee /proc/sys/kernel/yama/ptrace_scope
+	${BINDIR}../inspector_xe_2013/bin64/inspxe-gui & 
--- a/ex7/ex7_4/PGI_NATIVE_default.mk
+++ b/ex7/ex7_4/PGI_NATIVE_default.mk
@ -0,0 +1,125 @@
+# Use the MPI-wrappers from the PGI compiler suite.
+# requires setting of COMPILER=PGI_MPI_
+#
+# requires
+#          sudo apt install librdmacm1
+
+
+
+# Details for run time information
+# export PGI_ACC_TIME=1
+# unset PGI_ACC_TIME
+# export PGI_ACC_NOTIFY=1
+# export PGI_ACC_NOTIFY=3
+# unset PGI_ACC_NOTIFY
+
+
+PGI_PATH =  /opt/pgi/linux86-64/2019/bin
+#ifeq "$(HOSTNAME)" "mephisto.uni-graz.at"
+#  # mephisto
+#  PGI_PATH =  /share/apps/pgi/linux86-64/2016/bin
+#endif
+
+
+#MPI_ROOT=${PGI_PATH}mpi/mpich/bin/
+MPI_ROOT= ${PGI_PATH}/../mpi/openmpi-3.1.3/bin/
+MPIRUN  = ${MPI_ROOT}mpirun
+
+CC  = ${MPI_ROOT}mpicc
+CXX = ${MPI_ROOT}mpicxx
+#F77 = ${MPI_ROOT}mpif77
+ifndef LINKER
+  LINKER  = ${CC}
+endif
+LINKER  = ${CXX}
+
+WARNINGS = -Minform=warn
+
+PGI_PROFILING += -Minfo=loop,vect,opt,intensity,mp,accel
+#PGI_PROFILING += -Mprof=lines –Minfo=ccff
+
+CXXFLAGS +=  -e3 -std=c++17 -fast ${PGI_PROFILING} ${WARNINGS} -Mnodepchk
+CFLAGS   +=  -fast ${PGI_PROFILING} ${WARNINGS} -Mnodepchk
+#
+#  for OpenACC
+# Target architecture (nvidia,host)
+TA_ARCH = host
+#TA_ARCH = nvidia,host
+#TA_ARCH = -ta=nvidia:cc2+,cuda5.5,fastmath
+#TA_ARCH = -acc -DNDEBUG -ta=nvidia:cc2+,cuda5.5,fastmath,keepgpu
+#TA_ARCH = -acc -DNDEBUG -ta=nvidia:cc2+,fastmath,keepgpu
+
+#,keepgpu
+# CFLAGS = -O3 -ta=$(TA_ARCH)
+#CFLAGS   += -B -gopt $(TA_ARCH)
+#CXXFLAGS += -B -gopt $(TA_ARCH)
+#  -Minfo=all
+
+# libcudart.a is needed for direct CUDA calls
+#LINKFLAGS  = -gopt $(TA_ARCH) -L${BINDIR}../lib $(PGI_PROFILING)
+# -lcudart
+
+default:	${PROGRAM}
+
+${PROGRAM}:	${OBJECTS}
+	$(LINKER)  $^  ${LINKFLAGS} -o $@
+
+clean:
+	rm -f ${PROGRAM} ${OBJECTS} *.gpu *gprof.out
+
+clean_all:: clean
+	@rm -f *_ *~ *.bak *.log *.out *.tar
+
+#run: clean ${PROGRAM}
+run: ${PROGRAM}
+	${MPIRUN} -np 4 ${OPTIRUN} ./${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
+GPU_PROF = -cuda=gmem,branch,cc13 -cudainit
+#GPU_PROF = -cuda=branch:cc20
+#
+PROF_FILE = pgprof.out
+
+prof: ${PROGRAM}
+#	./$^
+#	$(CUDA_HOME)/bin/nvvp &
+#	export LD_LIBRARY_PATH=/state/partition1/apps/pgi/linux86-64/12.9/lib:$LD_LIBRARY_PATH
+	${OPTIRUN} ${BINDIR}pgcollect $(GPU_PROF) ./$^
+	${OPTIRUN} ${BINDIR}pgprof -exe ./$^  $(PROF_FILE) &
+
+
+# Memory checker (slooooow!!!):
+# see doc at /usr/local/cuda/doc/cuda-memcheck.pdf
+# mem: ${PROGRAM}
+# 	$(CUDA_HOME)memcheck ./$^
--- a/Show more
+++ b/Show more