Update.

CMakeLists.txt

-cmake_minimum_required(VERSION 3.14)
+cmake_minimum_required(VERSION 3.0)
 project(GaussSeidel Fortran)
 
 
 enable_language(Fortran)
-add_executable(GaussSeidel main.f gauss_seidel.f tril.f90 triu.f90)
\ No newline at end of file
+add_executable(GaussSeidel main.f90 matop.f90)

Makefile

-FC = gfortran
-OPT = -g
+# CMAKE generated file: DO NOT EDIT!
+# Generated by "Unix Makefiles" Generator, CMake Version 3.15
 
-gss: main.f gauss_seidel.o
-	$(FC) $(OPT) main.f gauss_seidel.o -o main
+# Default target executed when no arguments are given to make.
+default_target: all
 
-gauss_seidel.o: gauss_seidel.f
-	$(FC) $(OPT) gauss_seidel.f -c
+.PHONY : default_target
 
+# Allow only one "make -f Makefile2" at a time, but pass parallelism.
+.NOTPARALLEL:
+
+
+#=============================================================================
+# Special targets provided by cmake.
+
+# Disable implicit rules so canonical targets will work.
+.SUFFIXES:
+
+
+# Remove some rules from gmake that .SUFFIXES does not remove.
+SUFFIXES =
+
+.SUFFIXES: .hpux_make_needs_suffix_list
+
+
+# Suppress display of executed commands.
+$(VERBOSE).SILENT:
+
+
+# A target that is always out of date.
+cmake_force:
+
+.PHONY : cmake_force
+
+#=============================================================================
+# Set environment variables for the build.
+
+# The shell in which to execute make rules.
+SHELL = /bin/sh
+
+# The CMake executable.
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+
+# The command to remove a file.
+RM = /home/epierre01/Documents/Programs/clion-2019.2.3/bin/cmake/linux/bin/cmake -E remove -f
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+# The top-level source directory on which CMake was run.
+CMAKE_SOURCE_DIR = /home/epierre01/Documents/GM3/Projet/gauss-seidel
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+# The top-level build directory on which CMake was run.
+CMAKE_BINARY_DIR = /home/epierre01/Documents/GM3/Projet/gauss-seidel
+
+#=============================================================================
+# Targets provided globally by CMake.
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+# Special rule for the target rebuild_cache
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+.PHONY : rebuild_cache
+
+# Special rule for the target rebuild_cache
+rebuild_cache/fast: rebuild_cache
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+.PHONY : rebuild_cache/fast
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+# Special rule for the target edit_cache
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+# Special rule for the target edit_cache
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+# The main all target
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+	$(MAKE) -f CMakeFiles/Makefile2 all
+	$(CMAKE_COMMAND) -E cmake_progress_start /home/epierre01/Documents/GM3/Projet/gauss-seidel/CMakeFiles 0
+.PHONY : all
+
+# The main clean target
 clean:
-	rm main *.o *.mod *.exe
\ No newline at end of file
+	$(MAKE) -f CMakeFiles/Makefile2 clean
+.PHONY : clean
+
+# The main clean target
+clean/fast: clean
+
+.PHONY : clean/fast
+
+# Prepare targets for installation.
+preinstall: all
+	$(MAKE) -f CMakeFiles/Makefile2 preinstall
+.PHONY : preinstall
+
+# Prepare targets for installation.
+preinstall/fast:
+	$(MAKE) -f CMakeFiles/Makefile2 preinstall
+.PHONY : preinstall/fast
+
+# clear depends
+depend:
+	$(CMAKE_COMMAND) -S$(CMAKE_SOURCE_DIR) -B$(CMAKE_BINARY_DIR) --check-build-system CMakeFiles/Makefile.cmake 1
+.PHONY : depend
+
+#=============================================================================
+# Target rules for targets named GaussSeidel
+
+# Build rule for target.
+GaussSeidel: cmake_check_build_system
+	$(MAKE) -f CMakeFiles/Makefile2 GaussSeidel
+.PHONY : GaussSeidel
+
+# fast build rule for target.
+GaussSeidel/fast:
+	$(MAKE) -f CMakeFiles/GaussSeidel.dir/build.make CMakeFiles/GaussSeidel.dir/build
+.PHONY : GaussSeidel/fast
+
+main.o: main.f90.o
+
+.PHONY : main.o
+
+# target to build an object file
+main.f90.o:
+	$(MAKE) -f CMakeFiles/GaussSeidel.dir/build.make CMakeFiles/GaussSeidel.dir/main.f90.o
+.PHONY : main.f90.o
+
+main.i: main.f90.i
+
+.PHONY : main.i
+
+# target to preprocess a source file
+main.f90.i:
+	$(MAKE) -f CMakeFiles/GaussSeidel.dir/build.make CMakeFiles/GaussSeidel.dir/main.f90.i
+.PHONY : main.f90.i
+
+main.s: main.f90.s
+
+.PHONY : main.s
+
+# target to generate assembly for a file
+main.f90.s:
+	$(MAKE) -f CMakeFiles/GaussSeidel.dir/build.make CMakeFiles/GaussSeidel.dir/main.f90.s
+.PHONY : main.f90.s
+
+matop.o: matop.f90.o
+
+.PHONY : matop.o
+
+# target to build an object file
+matop.f90.o:
+	$(MAKE) -f CMakeFiles/GaussSeidel.dir/build.make CMakeFiles/GaussSeidel.dir/matop.f90.o
+.PHONY : matop.f90.o
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+.PHONY : matop.i
+
+# target to preprocess a source file
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+.PHONY : matop.s
+
+# target to generate assembly for a file
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+.PHONY : matop.f90.s
+
+# Help Target
+help:
+	@echo "The following are some of the valid targets for this Makefile:"
+	@echo "... all (the default if no target is provided)"
+	@echo "... clean"
+	@echo "... depend"
+	@echo "... rebuild_cache"
+	@echo "... GaussSeidel"
+	@echo "... edit_cache"
+	@echo "... main.o"
+	@echo "... main.i"
+	@echo "... main.s"
+	@echo "... matop.o"
+	@echo "... matop.i"
+	@echo "... matop.s"
+.PHONY : help
+
+
+
+#=============================================================================
+# Special targets to cleanup operation of make.
+
+# Special rule to run CMake to check the build system integrity.
+# No rule that depends on this can have commands that come from listfiles
+# because they might be regenerated.
+cmake_check_build_system:
+	$(CMAKE_COMMAND) -S$(CMAKE_SOURCE_DIR) -B$(CMAKE_BINARY_DIR) --check-build-system CMakeFiles/Makefile.cmake 0
+.PHONY : cmake_check_build_system
+

dmain

-2
-0.000001
-3 1 2 4
-3 3
-1 1
\ No newline at end of file

gauss_seidel.f

-      subroutine gauss_seidel(A, n, nmax, b, x)
-          implicit none
-          integer :: n, nmax, i, j
-          double precision :: A(nmax,nmax), b(nmax), x(nmax), tmp
-
-          do i=1,n(1)
-            tmp = 0
-            do j=1,n(1)
-              if (j /= i) then
-                tmp = tmp + A(i,j) * x(j)
-              endif
-            enddo
-            x(i) = (b(i) - tmp) / A(i, i)
-          enddo
-      end
\ No newline at end of file

inv_trig_inf.f90

-function inv_trig_inf(L, nmax, n)
-    integer :: nmax, n, i, j
-    real :: L(nmax, nmax), inv_trig_inf(nmax, nmax), diag
-    inv_trig_inf = 0
-    ! inv(1,1) = 1/L(1,1)
-    ! inv(1,2) =
-    ! inv(2,1) = 0
-    diag = 1
-    do i = 1,n
-        inv_trig_inf(i,i) = 1/L(i,i)
-        diag = diag * L(i,i)
-        x(l) = b(l)
-        do j = 1, n
-            x(l) = x(l) - L(l, c) * x(c)
-        enddo
-        x(l) = x(l) / L(l, l)
-    enddo
-end
\ No newline at end of file

main.f

-      program main
-      implicit none
-      integer, parameter :: nmax=5
-      integer i, j, n
-      real :: A(nmax,nmax), F(nmax,nmax), G(nmax,nmax), D1(nmax,nmax), L(nmax,nmax), LI(nmax,nmax), U(nmax,nmax), Id(nmax,nmax), b(nmax), x(nmax)
-      real :: prec,res
-  
-      read (*,*) n, prec
-
-      read (*,*) A
-      read (*,*) b
-      read (*,*) x
-
-      D1 = 0
-      Id = 0
-
-      do i=1,n
-        D1(i,i) = 1.0/A(i,i)
-        Id(i,i) = 1
-      enddo
-      do i=1,n
-        do j=1,n
-          L(i, j) = A
-        enddo
-      enddo
-
-      L = tril(matmul(D1, A), nmax, n) - Id
-      U = triu(matmul(D1, A), nmax, n) - Id
-
-      LI = inv(L+Id)
-
-      F = -matmul(LI, U)
-      G = matmul(matmul(LI, D1), b)
-
-      do i=1,nmax
-        call solve_system(A, b, x)
-        res = norm2(matmul(A, x) - b)
-        write(*,*) i, res
-        if ( res < prec) then
-          exit
-        endif
-      enddo
-      
-      end

main.f90

+program main
+	use matop
+    implicit none
+    integer i, j, n, nmax
+    real, allocatable, dimension(:,:) :: A, F, D1, L, LI, U, Eye, tmp
+    real, allocatable, dimension(:) :: b, x, G
+    real :: prec, res
+	
+    read (*, *) n, prec, nmax
+	
+	allocate(A(n,n))
+	allocate(F(n,n))
+	allocate(D1(n,n))
+	allocate(L(n,n))
+	allocate(LI(n,n))
+	allocate(U(n,n))
+	allocate(Eye(n,n))
+	allocate(tmp(n,n))
+	
+	allocate(b(n))
+	allocate(x(n))
+	allocate(G(n))
+	
+    read (*, *) A
+    read (*, *) b
+    read (*, *) x
+
+    D1 = 0
+    Eye = 0
+
+    do i = 1, n
+        D1(i, i) = 1.0 / A(i, i)
+        Eye(i, i) = 1
+    enddo
+	tmp = matmul(D1, A)
+	call tril(tmp, L)
+	call triu(tmp, U)
+	U = U - Eye
+	
+    call inv_trig_inf(L, LI)
+
+    F = -matmul(LI, U)
+    G = matmul(matmul(LI, D1), b)
+	
+	deallocate(D1)
+	deallocate(L)
+	deallocate(LI)
+	deallocate(U)
+	deallocate(Eye)
+	deallocate(tmp)
+
+    do i = 1, nmax
+		x = matmul(F, x) + G
+        res = norm2(matmul(A, x) - b)
+        write(*, *) i, res
+        if (res < prec) then
+            exit
+        endif
+    enddo
+	
+	write (*,*) x, matmul(A, x)
+	deallocate(F)
+	deallocate(G)
+	deallocate(x)
+	deallocate(A)
+	deallocate(b)
+end
\ No newline at end of file

matop.f90

+module matop
+    implicit none
+
+contains
+    subroutine tril(M, L)
+        implicit none
+        integer :: n, i
+        real, dimension(:,:) :: M, L
+        n = size(M, 1)
+        L = 0
+        do i=1,n
+            L(i,1:i) = M(i,1:i)
+        end do
+    end subroutine tril
+
+    subroutine triu(M, U)
+        implicit none
+        integer :: n, p, i
+        real :: M(:,:), U(:,:)
+        n = size(M, 1)
+        p = size(M, 2)
+        U = 0
+        do i=1,n
+            U(i,i:p) = M(i,i:p)
+        end do
+    end subroutine triu
+
+    subroutine inv_trig_inf(L, inv)
+        implicit none
+        integer :: i, j, n
+        real, allocatable, dimension(:,:) :: L(:,:), inv
+        real, dimension(size(L,1),size(L,2)) :: Eye
+        n = size(L, 1)
+
+        inv = 0;
+        Eye = 0
+        do i=1,n
+            Eye(i,i) = 1
+        enddo
+        do i=1,n
+            inv(i,:) = (Eye(i,:) - matmul(L(i,1:i-1),inv(1:i-1,:))) / L(i,i)
+        enddo
+        return
+    end subroutine inv_trig_inf
+end module matop
\ No newline at end of file

src/Makefile

-FC = gfortran
-OPT = -g
-
-gss : main.f gauss_seidel.o
-	$(FC) $(OPT) main.f gauss_seidel.o -o gss 
-
-gauss_seidel.o: gauss_seidel.f
-	$(FC) $(OPT) gauss_seidel.f -c
-
-clean:
-	rm gss  *.o *.mod *.exe

src/dgss

-2  1.e-6  100
-3 1 2 4
-3 3
-1 1
-n, prec,nmax
-A
-b
-x

src/gauss_seidel.f

-      module gauss_seidel
-        implicit none
-        private
-        public :: solve_system
-
-        interface solve_system
-          procedure solve_system_double, solve_system_real
-        endinterface
-      contains
-
-        subroutine solve_system_double(A, b, x)
-          implicit none
-          integer :: An(2), n(1), i, j
-          double precision :: A(:,:), b(:), x(:), tmp
-          n = shape(b)
-
-          do i=1,n(1)
-            tmp = 0
-            do j=1,n(1)
-              if (j /= i) then
-                tmp = tmp + A(i,j) * x(j)
-              endif
-            enddo
-            x(i) = (b(i) - tmp) / A(i, i)
-          enddo
-
-        end subroutine solve_system_double
-
-        subroutine solve_system_real(A, b, x)
-          implicit none
-          integer :: n(1), i, j
-          real :: A(:,:), b(:), x(:), tmp
-          n = shape(b)
-
-          do i=1,n(1)
-            tmp = 0
-            do j=1,n(1)
-              if (j /= i) then
-                tmp = tmp + A(i,j) * x(j)
-              endif
-            enddo
-            x(i) = (b(i) - tmp) / A(i, i)
-          enddo
-
-        end subroutine solve_system_real
-      end module
\ No newline at end of file

src/gauss_seidel.m

-%A = [1 2 3 4 5 ; 5 1 2 3 4 ; 4 5 1 2 3 ; 3 4 5 1 2 ; 2 3 4 5 1];
-%Abis = [1 -1 -200 0 ; 0 1 100 -100 ; 0 1 101 -101 ; 0 0 0 100];
-%b = [1 ; 1 ; 3 ; 4 ; 2];
-%bbis = [1 ; 1 ; 2 ; 4];
-%x = [0 ; 0 ; 0 ; 0 ; 0];
-%xbis = [0 ; 0 ; 0 ; 0];
-
-
-tol = 1e-10; 
-cont = 0;
-delta = 10; 
-
-A = [3 1;2 4];
-b = [3;3];
-x = [1;1];
-
-n = size(b);
-
-while delta > tol  & cont < 200
-  ref = x;
-  for i = 1:n(1)
-    tmp = 0;
-    for j = 1:n(1)
-      if j != i
-        tmp = tmp + A(i,j)*x(j);
-      end
-      x(i) = (b(i) - tmp) / A(i,i);
-    end
-  end
-  delta = norm(ref - x);
-  cont = cont + 1;
-end
-
-fprintf('%f\n%f\n%f\n%f\n en %d boucles',x, cont);
\ No newline at end of file

src/main.f

-      program main
-      use gauss_seidel
-      implicit none
-      integer i, n,nmax
-      real, allocatable :: A(:,:), b(:), x(:)
-      real :: prec,res
-  
-      read (*,*) n, prec,nmax
-      allocate(A(n,n))
-      allocate(b(n))
-      allocate(x(n))
-
-      read (*,*) A
-      read (*,*) b
-      read (*,*) x
-
-      do i=1,nmax
-        call solve_system(A, b, x)
-        res = norm2(matmul(A, x) - b)
-        write(*,*) i, res
-        if ( res < prec) then
-          exit
-        endif
-      enddo
-      
-      end

tril.f90

-function tril(M, nmax, n)
-    integer :: nmax, n
-    real M(nmax,nmax), tril(nmax, nmax)
-    tril = 0
-    do i=1,n
-        do j=1,i
-            tril(i,j) = M(i,j)
-        end do
-    end do
-end function tril
\ No newline at end of file

triu.f90

-function triu(M, nmax, n)
-    integer :: nmax, n
-    real M(nmax,nmax), triu(nmax, nmax)
-    triu = 0
-    do i=1,n
-        do j=i,n
-            triu(i,j) = M(i,j)
-        end do
-    end do
-end function triu
\ No newline at end of file