Final release

3fb222d0 · Pierre-Yves Barriat · 55947267 · 3fb222d0 · 3fb222d0 · 3fb222d0
--- a/.gitignore
+++ b/.gitignore
@@ -191,3 +191,5 @@ sympy-plots-for-*.tex/
 # Notebooks
 notebooks/*.ipynb_checkpoints
+notebooks/*dataxy
+notebooks/*gnuxy
--- a/notebooks/sandbox.ipynb
+++ b/notebooks/sandbox.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "10d0e3c5",
+   "metadata": {},
+   "source": [
+    "## Introduction to structured programming with Fortran\n",
+    "\n",
+    "### Why to learn Fortran ?\n",
+    "\n",
+    "* Because of the execution speed of a program\n",
+    "* Well suited for numerical computations : more than **45% of scientific applications** are in Fortran\n",
+    "\n",
+    "## Getting started\n",
+    "\n",
+    "### Hello World"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "00ec1776",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program hello_world\n",
+    "\n",
+    "  implicit none ! important\n",
+    "\n",
+    "  print *, \"Hello World!\"\n",
+    "\n",
+    "end program hello_world"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c4b788f0",
+   "metadata": {},
+   "source": [
+    "### Data Type Declarations and Assignments"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ffd3f0c3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program data_type\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real x, y\n",
+    "  integer i, j\n",
+    "  logical flag\n",
+    "  \n",
+    "  integer matrix(2,2) \n",
+    "  character(80) month\n",
+    "  character(len=80) months(12)\n",
+    "  \n",
+    "  character family*16\n",
+    "  \n",
+    "  real, dimension(12) :: small_array\n",
+    "  character(len=80), dimension(24) :: screen\n",
+    "  \n",
+    "  integer, parameter :: it = 100\n",
+    "  \n",
+    "  i = 1\n",
+    "  j = i+2\n",
+    "  x = 85.8\n",
+    "  y = 3.5*cos(x)\n",
+    "\n",
+    "  month=\"december\"\n",
+    "  \n",
+    "  months(:)=\"empty\"\n",
+    "  \n",
+    "  months(12)=month\n",
+    "  \n",
+    "  flag = .TRUE.\n",
+    "  \n",
+    "  family = \"GEORGE P. BURDELL\"\n",
+    "  print*,family(:6)\n",
+    "  print*,family(8:9)\n",
+    "  print*,family(11:)\n",
+    "  print*,family(:6)//FAMILY(10:)\n",
+    "  \n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "133046ed",
+   "metadata": {},
+   "source": [
+    "### Arithmetic Assignments\n",
+    "\n",
+    "The result of any integer divide is truncated to the integer value less than the correct decimal answer for the division. The result of this is that changing the order of operations can make a big difference in the answers.  Notice how parentheses force more expected results."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "13343800",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program arith\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real r2,r3,r4,r5,r6,ans1,ans2,ans3\n",
+    "  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4\n",
+    "  \n",
+    "  data r2/2./,r3/3./,r4/4.0/,r5/5.0/\n",
+    "  data i2,i3,i4,i5/2,3,4,5/\n",
+    "  \n",
+    "  ians1=i2*i3/i5\n",
+    "  ians2=i3/i5*i2\n",
+    "  ians3=i2*(i3/i5)\n",
+    "  ians4=(i3/i5)*i2\n",
+    "  print *, '2*3/5 =', ians1, ', 3/5*2 =',ians2,', 2*(3/5) =',ians3 ,', (3/5)*2 =',ians4\n",
+    "  \n",
+    "end program arith"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cabea667",
+   "metadata": {},
+   "source": [
+    "Real arithmetic behaves more uniformly:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e1de5730",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program arith\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real r2,r3,r4,r5,r6,ans1,ans2,ans3\n",
+    "  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4\n",
+    "  \n",
+    "  data r2/2./,r3/3./,r4/4.0/,r5/5.0/\n",
+    "  data i2,i3,i4,i5/2,3,4,5/\n",
+    "  \n",
+    "  ans1=r2*r3/r5\n",
+    "  ans2=r3/r5*r2\n",
+    "  ans3=(r3/r5)*r2\n",
+    "  print *, '2.0*3.0/5.0 =', ans1, ', 3.0/5.0*2.0 =',ans2,', (3.0/5.0)*2.0 =',ans3\n",
+    "      \n",
+    "end program arith      "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f18b85ec",
+   "metadata": {},
+   "source": [
+    "Watch how precedence of operations effects the following:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9a362858",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program arith\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real r2,r3,r4,r5,r6,ans1,ans2,ans3\n",
+    "  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4\n",
+    "  \n",
+    "  data r2/2./,r3/3./,r4/4.0/,r5/5.0/\n",
+    "  data i2,i3,i4,i5/2,3,4,5/\n",
+    "\n",
+    "  ians1=i2+i5*i3**i2\n",
+    "  ians2=i5*i3**i2+i2\n",
+    "  ians3=i3**i2*i5+i2\n",
+    "  print *, '2+5*3**2 =',ians1,', 5*3**2+2 =',ians2, ', 3**2*5+2 =',ians3\n",
+    "      \n",
+    "end program arith      "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5297b017",
+   "metadata": {},
+   "source": [
+    "You can mix real and integers, but watch what happens"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7d50669e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program arith\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real r2,r3,r4,r5,r6,ans1,ans2,ans3\n",
+    "  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4\n",
+    "  \n",
+    "  data r2/2./,r3/3./,r4/4.0/,r5/5.0/\n",
+    "  data i2,i3,i4,i5/2,3,4,5/\n",
+    "\n",
+    "  ans1=r5+i3/i2\n",
+    "  ans2=5.0+3/2\n",
+    "  print *, '5.0+3/2 =',ans1\n",
+    "  print *, '5.0+3/2 =',ans2\n",
+    "      \n",
+    "end program arith      "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "222cabbc",
+   "metadata": {},
+   "source": [
+    "Look at what happens when I put a real in either the numerator or denominator of the division term"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "78929c6e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program arith\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real r2,r3,r4,r5,r6,ans1,ans2,ans3\n",
+    "  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4\n",
+    "  \n",
+    "  data r2/2./,r3/3./,r4/4.0/,r5/5.0/\n",
+    "  data i2,i3,i4,i5/2,3,4,5/\n",
+    "\n",
+    "  ans1=r5+i3/r2\n",
+    "  ans2=r5+r3/i2\n",
+    "  print *, '5.0+3/2.0 =',ans1, ', 5.0+3.0/2 =', ans2\n",
+    "      \n",
+    "end program arith           "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a7d37bc2",
+   "metadata": {},
+   "source": [
+    "Although Fortran normally works from left to right at a given level of precedence (does all multiply and divide from left to right before moving on to adds and subtracts). It works exponentiation from right to left when it hits 2 or more sequential exponentiation operations"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3c2da1a9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program arith\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real r2,r3,r4,r5,r6,ans1,ans2,ans3\n",
+    "  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4\n",
+    "  \n",
+    "  data r2/2./,r3/3./,r4/4.0/,r5/5.0/\n",
+    "  data i2,i3,i4,i5/2,3,4,5/\n",
+    "\n",
+    "  ians1= i5**i3**i2\n",
+    "  ians2= (i5**i3)**i2\n",
+    "  ians3= i5**(i3**i2)\n",
+    "  print *, '5**3**2 =',ians1, ', (5**3)**2 =',ians2,  ', 5**(3**2) =',ians3\n",
+    "      \n",
+    "end program arith           "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8387be7a",
+   "metadata": {},
+   "source": [
+    "When in doubt use parentheses to get the answer that you really want.\n",
+    "\n",
+    "### Assignments exercise"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14f6e7e2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program sphere  \n",
+    "\n",
+    "  implicit none\n",
+    "      \n",
+    "  real pi,radius,volume,area  \n",
+    "          \n",
+    "  radius = 1.0\n",
+    "  pi = 0.0\n",
+    "      \n",
+    "  write(*,*) 'The value of pi is ', pi\n",
+    "  write(*,*) \n",
+    "\n",
+    "  area = 0.0\n",
+    "  volume = 0.0\n",
+    "      \n",
+    "  write(*,*) 'For a radius ', radius \n",
+    "  write(*,*) 'the area of a sphere is ', area\n",
+    "  write(*,*) 'and the volume is ', volume\n",
+    "      \n",
+    "end "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a1702f7",
+   "metadata": {},
+   "source": [
+    "### Execution Control"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "41f9a8f0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "PROGRAM gcd\n",
+    "  ! Computes the greatest common divisor, Euclidean algorithm\n",
+    "  IMPLICIT NONE\n",
+    "  INTEGER :: m, n, t\n",
+    "  WRITE(*,*) \"Give positive integers m and n :\"\n",
+    "  m=5464\n",
+    "  n=484682\n",
+    "  WRITE(*,*) 'm:', m,' n:', n\n",
+    "  positive_check: IF (m > 0 .AND. n > 0) THEN\n",
+    "    main_algorithm: DO WHILE (n /= 0)\n",
+    "      t = MOD(m,n)\n",
+    "      m = n\n",
+    "      n = t\n",
+    "    END DO main_algorithm\n",
+    "    WRITE(*,*) \"Greatest common divisor: \",m\n",
+    "  ELSE\n",
+    "    WRITE(*,*) 'Negative value entered'\n",
+    "  END IF positive_check\n",
+    "END PROGRAM gcd"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cef2ad42",
+   "metadata": {},
+   "source": [
+    "### File-Directed Input and Output"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8fd042c4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program plot\n",
+    "\n",
+    "  ! Program to provide plots of Sin(x)\n",
+    "\n",
+    "  implicit none\n",
+    "  character label*150\n",
+    "  real x\n",
+    "  integer i\n",
+    "  character xlabel*32,ylabel*32,title*32\n",
+    "  real fx\n",
+    "  !\n",
+    "  ! label   -   Character string \n",
+    "  ! xlabel  -   Contains a label for the x-axis\n",
+    "  ! ylabel  -   Contains a label for the y-axis\n",
+    "  ! title   -   Contains a title for the plot\n",
+    "  !\n",
+    "  ! Drive a separate true graphics program (gnuplot)\n",
+    "  !\n",
+    "  ! First set up the command file for gnuplot\n",
+    "  !\n",
+    "  xlabel=\"'x'\"\n",
+    "  ylabel=\"'y'\"\n",
+    "  title=\"'sin(x)'\"\n",
+    "  open (112,file='03_gnuxy')\n",
+    "  !\n",
+    "  label='set xlabel '//xlabel\n",
+    "  write(112,*)label\n",
+    "  write(112,*)'set xrange [0:6]'\n",
+    "  label='set ylabel '//ylabel\n",
+    "  write(112,*)label\n",
+    "  write(112,*)'set yrange [-1.2:1.2]'\n",
+    "  label='plot \"03_dataxy\" using 1:2 title '//title\n",
+    "  label=trim(label)//' with lines lt rgb \"red\"'\n",
+    "  write(112,*) label\n",
+    "  write (112,*) 'pause -1'\n",
+    "  close(112)\n",
+    "  !\n",
+    "  !   Generate x-y pairs for the graph\n",
+    "  !\n",
+    "  open (112,file='03_dataxy')\n",
+    "  do i=0,60\n",
+    "    x=.1*i\n",
+    "    fx=sin(x)\n",
+    "    write(112,*) x,fx\n",
+    "  enddo\n",
+    "  close(112)\n",
+    "  !\n",
+    "end program"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "059d5e2a",
+   "metadata": {},
+   "source": [
+    "This code is going to create 2 files: \"03_dataxy\" and \"03_gnuxy\".\n",
+    "\n",
+    "The idea is to use a linux plotting tool called \"GNUplot\" to make a graph: the first file is the data for the graph, the second one is the gnuplot script using these data.\n",
+    "\n",
+    "```bash\n",
+    "gnuplot 03_gnuxy\n",
+    "```\n",
+    "\n",
+    "<img src=\"https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran/raw/master/assets/sin.png\">\n",
+    "\n",
+    "#### Format controlled IO"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a26b3cc5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program format\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real(4) A\n",
+    "  real(8) B\n",
+    "  integer I, KEY\n",
+    "\n",
+    "  A= 1500.*acos(0.)\n",
+    "  B= 4e3*dcos(16.5d0)\n",
+    "  KEY= 884\n",
+    "  \n",
+    "  write(*,*) A,B,KEY\n",
+    "  write(*,*)\n",
+    "  \n",
+    "  write(*,1000) A,B,KEY\n",
+    "  write(*,1001) (\"-\",I=1,38)\n",
+    "  \n",
+    "  1000 FORMAT(F18.10,E14.5,I6)\n",
+    "  1001 FORMAT(38A1)\n",
+    "      \n",
+    "end program format  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31f27416",
+   "metadata": {},
+   "source": [
+    "### Hands on learning: numerical analysis\n",
+    "\n",
+    "Apply the Newton's method to find the root(s) of a polynomial function.\n",
+    "\n",
+    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/6929060731e351c465426e37567abe5ee13d65d9\">"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "df362a1a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program newton\n",
+    "\n",
+    "  implicit none\n",
+    "\n",
+    "  ! Use a Newton iteration to solve a polynomial equation\n",
+    "\n",
+    "  integer :: i\n",
+    "\n",
+    "  write(*,*) 'Try to solve \"x**3+x-10=0\"'  \n",
+    "  write(*,*) 'What is your initial guess for the solution?'\n",
+    "\n",
+    "  do while( .TRUE. )\n",
+    "  \n",
+    "    write(*,*)\n",
+    "    exit\n",
+    "\n",
+    "  end do\n",
+    "\n",
+    "end program\n",
+    "\n",
+    "! ******************************************************************************************\n",
+    "\n",
+    "subroutine derivate()\n",
+    "\n",
+    "! Evaluate the function f(x)=x**3+x-10\n",
+    "! also return the derivative of the function\n",
+    "\n",
+    "\n",
+    "end subroutine\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "919d1d4f",
+   "metadata": {},
+   "source": [
+    "### COMMON Statement (F77)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4b517d6b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "      PROGRAM test_arg\n",
+    "\n",
+    "        implicit none\n",
+    "        integer a,b,c\n",
+    "\n",
+    "        common /arg/ a,b,c\n",
+    "\n",
+    "        a = 2\n",
+    "        c = 1\n",
+    "\n",
+    "        print *, 'Before the call:'\n",
+    "        print *, 'a = ',a,', b = ',b,', c = ',c\n",
+    "\n",
+    "        call sub\n",
+    "\n",
+    "        print *, 'After the call:'\n",
+    "        print *, 'a = ',a,', b = ',b,', c = ',c\n",
+    "\n",
+    "      END PROGRAM\n",
+    "\n",
+    "      SUBROUTINE sub\n",
+    "\n",
+    "        implicit none\n",
+    "\n",
+    "        integer a,b,c\n",
+    "        common /arg/ a,b,c\n",
+    "\n",
+    "        b = a + c\n",
+    "        c = c + 1\n",
+    "       \n",
+    "      END SUBROUTINE"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1e457015",
+   "metadata": {},
+   "source": [
+    "### MODULE Statement (F90)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "71f26006",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "MODULE arg\n",
+    " implicit none\n",
+    " integer :: a,b,c\n",
+    " real(8) :: x\n",
+    "END MODULE arg\n",
+    "\n",
+    "! * * * * * * * \n",
+    "\n",
+    "PROGRAM test_arg\n",
+    " USE arg\n",
+    " implicit none\n",
+    "\n",
+    " a = 2\n",
+    " c = 1\n",
+    "\n",
+    " write(*,*) 'Before the call:'\n",
+    " write(*,'(3(A5,I3))') ' a = ',a,', b = ',b,', c = ',c\n",
+    "\n",
+    " call sub\n",
+    "\n",
+    " write(*,*) 'After the call:'\n",
+    " write(*,'(3(A5,I3))') 'a = ',a,', b = ',b,', c = ',c\n",
+    "\n",
+    "END PROGRAM test_arg\n",
+    "\n",
+    "! * * * * * * * \n",
+    "\n",
+    "SUBROUTINE sub\n",
+    " USE arg, only : a,b,c    ! seuls a b et c sont utiles\n",
+    " implicit none\n",
+    "\n",
+    " b = a + c\n",
+    " c = c + 1\n",
+    "\n",
+    "END SUBROUTINE sub"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0900a54",
+   "metadata": {},
+   "source": [
+    "### NAMELIST (F90)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e3791d4f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "PROGRAM test_namelist\n",
+    "\n",
+    "  implicit none\n",
+    "\n",
+    "  real(8) lon_min, lon_max, lat_min, lat_max\n",
+    "\n",
+    "  NAMELIST/namlon/ lon_min, lon_max\n",
+    "  NAMELIST/namlat/ lat_min, lat_max\n",
+    "\n",
+    "  write(*,*) 'Before:'\n",
+    "  call print_res(lon_min, lon_max, lat_min, lat_max)\n",
+    "\n",
+    "  open(161,file='../src/07_namelist.def',status='old',form='formatted')\n",
+    "  read(161,NML=namlon)\n",
+    "\n",
+    "  write(*,*) 'Between:'\n",
+    "  call print_res(lon_min, lon_max, lat_min, lat_max)\n",
+    "\n",
+    "  read(161,NML=namlat)\n",
+    "  close (161)\n",
+    "\n",
+    "  write(*,*) 'After:'\n",
+    "  call print_res(lon_min, lon_max, lat_min, lat_max)\n",
+    "\n",
+    "END\n",
+    "\n",
+    "SUBROUTINE print_res(a,b,c,d)\n",
+    "  implicit none\n",
+    "  real(8), intent(in) :: a,b,c,d\n",
+    "  write(*,'(4(A12,F6.2))') '  lon_min = ',a,', lon_max = ',b, &\n",
+    "                          ', lat_min = ',c,', lat_max = ',d\n",
+    "  RETURN\n",
+    "END"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c0b0a801",
+   "metadata": {},
+   "source": [
+    "### Hands on learning: structure\n",
+    "\n",
+    "The aim of this exercise is to work with loops (for or while) in order to draw in a terminal a Christmas tree with its balls.\n",
+    "\n",
+    "The program must be carried out in Fortran 90. It will take as argument the height of the tree which is a variable of the problem:\n",
+    "\n",
+    "Height=7\n",
+    "```\n",
+    "      #\n",
+    "     ###\n",
+    "    #o###\n",
+    "   ##o####\n",
+    "  #o#####o#\n",
+    " ####o#####o\n",
+    "#####o#####o#\n",
+    "```\n",
+    "This parameter must be supplied at the command line when the program (for example './tree 10'). \n",
+    "\n",
+    "Balls must be positioned all 6 sharps."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "930eedf9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program ChristmasTree\n",
+    "\n",
+    "  implicit none\n",
+    "\n",
+    "\n",
+    "\n",
+    "end program"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6362d74e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Fortran",
+   "language": "Fortran",
+   "name": "fortran_spec"
+  },
+  "language_info": {
+   "file_extension": "f90",
+   "mimetype": "text/plain",
+   "name": "fortran"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
+%% Cell type:markdown id:10d0e3c5 tags:
+## Introduction to structured programming with Fortran
+### Why to learn Fortran ?
+* Because of the execution speed of a program
+* Well suited for numerical computations : more than **45% of scientific applications** are in Fortran
+## Getting started
+### Hello World
+%% Cell type:code id:00ec1776 tags:
+``` Fortran
+program hello_world
+  implicit none ! important
+  print *, "Hello World!"
+end program hello_world
+```
+%% Cell type:markdown id:c4b788f0 tags:
+### Data Type Declarations and Assignments
+%% Cell type:code id:ffd3f0c3 tags:
+``` Fortran
+program data_type
+  implicit none
+  real x, y
+  integer i, j
+  logical flag
+  integer matrix(2,2)
+  character(80) month
+  character(len=80) months(12)
+  character family*16
+  real, dimension(12) :: small_array
+  character(len=80), dimension(24) :: screen
+  integer, parameter :: it = 100
+  i = 1
+  j = i+2
+  x = 85.8
+  y = 3.5*cos(x)
+  month="december"
+  months(:)="empty"
+  months(12)=month
+  flag = .TRUE.
+  family = "GEORGE P. BURDELL"
+  print*,family(:6)
+  print*,family(8:9)
+  print*,family(11:)
+  print*,family(:6)//FAMILY(10:)
+end
+```
+%% Cell type:markdown id:133046ed tags:
+### Arithmetic Assignments
+The result of any integer divide is truncated to the integer value less than the correct decimal answer for the division. The result of this is that changing the order of operations can make a big difference in the answers.  Notice how parentheses force more expected results.
+%% Cell type:code id:13343800 tags:
+``` Fortran
+program arith
+  implicit none
+  real r2,r3,r4,r5,r6,ans1,ans2,ans3
+  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
+  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
+  data i2,i3,i4,i5/2,3,4,5/
+  ians1=i2*i3/i5
+  ians2=i3/i5*i2
+  ians3=i2*(i3/i5)
+  ians4=(i3/i5)*i2
+  print *, '2*3/5 =', ians1, ', 3/5*2 =',ians2,', 2*(3/5) =',ians3 ,', (3/5)*2 =',ians4
+end program arith
+```
+%% Cell type:markdown id:cabea667 tags:
+Real arithmetic behaves more uniformly:
+%% Cell type:code id:e1de5730 tags:
+``` Fortran
+program arith
+  implicit none
+  real r2,r3,r4,r5,r6,ans1,ans2,ans3
+  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
+  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
+  data i2,i3,i4,i5/2,3,4,5/
+  ans1=r2*r3/r5
+  ans2=r3/r5*r2
+  ans3=(r3/r5)*r2
+  print *, '2.0*3.0/5.0 =', ans1, ', 3.0/5.0*2.0 =',ans2,', (3.0/5.0)*2.0 =',ans3
+end program arith
+```
+%% Cell type:markdown id:f18b85ec tags:
+Watch how precedence of operations effects the following:
+%% Cell type:code id:9a362858 tags:
+``` Fortran
+program arith
+  implicit none
+  real r2,r3,r4,r5,r6,ans1,ans2,ans3
+  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
+  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
+  data i2,i3,i4,i5/2,3,4,5/
+  ians1=i2+i5*i3**i2
+  ians2=i5*i3**i2+i2
+  ians3=i3**i2*i5+i2
+  print *, '2+5*3**2 =',ians1,', 5*3**2+2 =',ians2, ', 3**2*5+2 =',ians3
+end program arith
+```
+%% Cell type:markdown id:5297b017 tags:
+You can mix real and integers, but watch what happens
+%% Cell type:code id:7d50669e tags:
+``` Fortran
+program arith
+  implicit none
+  real r2,r3,r4,r5,r6,ans1,ans2,ans3
+  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
+  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
+  data i2,i3,i4,i5/2,3,4,5/
+  ans1=r5+i3/i2
+  ans2=5.0+3/2
+  print *, '5.0+3/2 =',ans1
+  print *, '5.0+3/2 =',ans2
+end program arith
+```
+%% Cell type:markdown id:222cabbc tags:
+Look at what happens when I put a real in either the numerator or denominator of the division term
+%% Cell type:code id:78929c6e tags:
+``` Fortran
+program arith
+  implicit none
+  real r2,r3,r4,r5,r6,ans1,ans2,ans3
+  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
+  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
+  data i2,i3,i4,i5/2,3,4,5/
+  ans1=r5+i3/r2
+  ans2=r5+r3/i2
+  print *, '5.0+3/2.0 =',ans1, ', 5.0+3.0/2 =', ans2
+end program arith
+```
+%% Cell type:markdown id:a7d37bc2 tags:
+Although Fortran normally works from left to right at a given level of precedence (does all multiply and divide from left to right before moving on to adds and subtracts). It works exponentiation from right to left when it hits 2 or more sequential exponentiation operations
+%% Cell type:code id:3c2da1a9 tags:
+``` Fortran
+program arith
+  implicit none
+  real r2,r3,r4,r5,r6,ans1,ans2,ans3
+  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
+  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
+  data i2,i3,i4,i5/2,3,4,5/
+  ians1= i5**i3**i2
+  ians2= (i5**i3)**i2
+  ians3= i5**(i3**i2)
+  print *, '5**3**2 =',ians1, ', (5**3)**2 =',ians2,  ', 5**(3**2) =',ians3
+end program arith
+```
+%% Cell type:markdown id:8387be7a tags:
+When in doubt use parentheses to get the answer that you really want.
+### Assignments exercise
+%% Cell type:code id:14f6e7e2 tags:
+``` Fortran
+program sphere
+  implicit none
+  real pi,radius,volume,area
+  radius = 1.0
+  pi = 0.0
+  write(*,*) 'The value of pi is ', pi
+  write(*,*)
+  area = 0.0
+  volume = 0.0
+  write(*,*) 'For a radius ', radius
+  write(*,*) 'the area of a sphere is ', area
+  write(*,*) 'and the volume is ', volume
+end
+```
+%% Cell type:markdown id:9a1702f7 tags:
+### Execution Control
+%% Cell type:code id:41f9a8f0 tags:
+``` Fortran
+PROGRAM gcd
+  ! Computes the greatest common divisor, Euclidean algorithm
+  IMPLICIT NONE
+  INTEGER :: m, n, t
+  WRITE(*,*) "Give positive integers m and n :"
+  m=5464
+  n=484682
+  WRITE(*,*) 'm:', m,' n:', n
+  positive_check: IF (m > 0 .AND. n > 0) THEN
+    main_algorithm: DO WHILE (n /= 0)
+      t = MOD(m,n)
+      m = n
+      n = t
+    END DO main_algorithm
+    WRITE(*,*) "Greatest common divisor: ",m
+  ELSE
+    WRITE(*,*) 'Negative value entered'
+  END IF positive_check
+END PROGRAM gcd
+```
+%% Cell type:markdown id:cef2ad42 tags:
+### File-Directed Input and Output
+%% Cell type:code id:8fd042c4 tags:
+``` Fortran
+program plot
+  ! Program to provide plots of Sin(x)
+  implicit none
+  character label*150
+  real x
+  integer i
+  character xlabel*32,ylabel*32,title*32
+  real fx
+  !
+  ! label   -   Character string
+  ! xlabel  -   Contains a label for the x-axis
+  ! ylabel  -   Contains a label for the y-axis
+  ! title   -   Contains a title for the plot
+  !
+  ! Drive a separate true graphics program (gnuplot)
+  !
+  ! First set up the command file for gnuplot
+  !
+  xlabel="'x'"
+  ylabel="'y'"
+  title="'sin(x)'"
+  open (112,file='03_gnuxy')
+  !
+  label='set xlabel '//xlabel
+  write(112,*)label
+  write(112,*)'set xrange [0:6]'
+  label='set ylabel '//ylabel
+  write(112,*)label
+  write(112,*)'set yrange [-1.2:1.2]'
+  label='plot "03_dataxy" using 1:2 title '//title
+  label=trim(label)//' with lines lt rgb "red"'
+  write(112,*) label
+  write (112,*) 'pause -1'
+  close(112)
+  !
+  !   Generate x-y pairs for the graph
+  !
+  open (112,file='03_dataxy')
+  do i=0,60
+    x=.1*i
+    fx=sin(x)
+    write(112,*) x,fx
+  enddo
+  close(112)
+  !
+end program
+```
+%% Cell type:markdown id:059d5e2a tags:
+This code is going to create 2 files: "03_dataxy" and "03_gnuxy".
+The idea is to use a linux plotting tool called "GNUplot" to make a graph: the first file is the data for the graph, the second one is the gnuplot script using these data.
+```bash
+gnuplot 03_gnuxy
+```
+<img src="https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran/raw/master/assets/sin.png">
+#### Format controlled IO
+%% Cell type:code id:a26b3cc5 tags:
+``` Fortran
+program format
+  implicit none
+  real(4) A
+  real(8) B
+  integer I, KEY
+  A= 1500.*acos(0.)
+  B= 4e3*dcos(16.5d0)
+  KEY= 884
+  write(*,*) A,B,KEY
+  write(*,*)
+  write(*,1000) A,B,KEY
+  write(*,1001) ("-",I=1,38)
+  1000 FORMAT(F18.10,E14.5,I6)
+  1001 FORMAT(38A1)
+end program format
+```
+%% Cell type:markdown id:31f27416 tags:
+### Hands on learning: numerical analysis
+Apply the Newton's method to find the root(s) of a polynomial function.
+<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6929060731e351c465426e37567abe5ee13d65d9">
+%% Cell type:code id:df362a1a tags:
+``` Fortran
+program newton
+  implicit none
+  ! Use a Newton iteration to solve a polynomial equation
+  integer :: i
+  write(*,*) 'Try to solve "x**3+x-10=0"'
+  write(*,*) 'What is your initial guess for the solution?'
+  do while( .TRUE. )
+    write(*,*)
+    exit
+  end do
+end program
+! ******************************************************************************************
+subroutine derivate()
+! Evaluate the function f(x)=x**3+x-10
+! also return the derivative of the function
+end subroutine
+```
+%% Cell type:markdown id:919d1d4f tags:
+### COMMON Statement (F77)
+%% Cell type:code id:4b517d6b tags:
+``` Fortran
+      PROGRAM test_arg
+        implicit none
+        integer a,b,c
+        common /arg/ a,b,c
+        a = 2
+        c = 1
+        print *, 'Before the call:'
+        print *, 'a = ',a,', b = ',b,', c = ',c
+        call sub
+        print *, 'After the call:'
+        print *, 'a = ',a,', b = ',b,', c = ',c
+      END PROGRAM
+      SUBROUTINE sub
+        implicit none
+        integer a,b,c
+        common /arg/ a,b,c
+        b = a + c
+        c = c + 1
+      END SUBROUTINE
+```
+%% Cell type:markdown id:1e457015 tags:
+### MODULE Statement (F90)
+%% Cell type:code id:71f26006 tags:
+``` Fortran
+MODULE arg
+ implicit none
+ integer :: a,b,c
+ real(8) :: x
+END MODULE arg
+! * * * * * * *
+PROGRAM test_arg
+ USE arg
+ implicit none
+ a = 2
+ c = 1
+ write(*,*) 'Before the call:'
+ write(*,'(3(A5,I3))') ' a = ',a,', b = ',b,', c = ',c
+ call sub
+ write(*,*) 'After the call:'
+ write(*,'(3(A5,I3))') 'a = ',a,', b = ',b,', c = ',c
+END PROGRAM test_arg
+! * * * * * * *
+SUBROUTINE sub
+ USE arg, only : a,b,c    ! seuls a b et c sont utiles
+ implicit none
+ b = a + c
+ c = c + 1
+END SUBROUTINE sub
+```
+%% Cell type:markdown id:a0900a54 tags:
+### NAMELIST (F90)
+%% Cell type:code id:e3791d4f tags:
+``` Fortran
+PROGRAM test_namelist
+  implicit none
+  real(8) lon_min, lon_max, lat_min, lat_max
+  NAMELIST/namlon/ lon_min, lon_max
+  NAMELIST/namlat/ lat_min, lat_max
+  write(*,*) 'Before:'
+  call print_res(lon_min, lon_max, lat_min, lat_max)
+  open(161,file='../src/07_namelist.def',status='old',form='formatted')
+  read(161,NML=namlon)
+  write(*,*) 'Between:'
+  call print_res(lon_min, lon_max, lat_min, lat_max)
+  read(161,NML=namlat)
+  close (161)
+  write(*,*) 'After:'
+  call print_res(lon_min, lon_max, lat_min, lat_max)
+END
+SUBROUTINE print_res(a,b,c,d)
+  implicit none
+  real(8), intent(in) :: a,b,c,d
+  write(*,'(4(A12,F6.2))') '  lon_min = ',a,', lon_max = ',b, &
+                          ', lat_min = ',c,', lat_max = ',d
+  RETURN
+END
+```
+%% Cell type:markdown id:c0b0a801 tags:
+### Hands on learning: structure
+The aim of this exercise is to work with loops (for or while) in order to draw in a terminal a Christmas tree with its balls.
+The program must be carried out in Fortran 90. It will take as argument the height of the tree which is a variable of the problem:
+Height=7
+```
+      #
+     ###
+    #o###
+   ##o####
+  #o#####o#
+ ####o#####o
+#####o#####o#
+```
+This parameter must be supplied at the command line when the program (for example './tree 10').
+Balls must be positioned all 6 sharps.
+%% Cell type:code id:930eedf9 tags:
+``` Fortran
+program ChristmasTree
+  implicit none
+end program
+```
+%% Cell type:code id:6362d74e tags:
+``` Fortran
+```
--- a/notebooks/training_fortran.ipynb
+++ b/notebooks/training_fortran.ipynb
@@ -12,9 +12,9 @@
    "* Because of the execution speed of a program\n",
    "* Well suited for numerical computations : more than **45% of scientific applications** are in Fortran\n",
    "\n",
-    "### Getting started\n",
+    "## Getting started\n",
    "\n",
-    "#### Hello World"
+    "### Hello World"
   ]
  },
  {
@@ -38,7 +38,7 @@
   "id": "c4b788f0",
   "metadata": {},
   "source": [
-    "#### Data Type Declarations and Assignments"
+    "### Data Type Declarations and Assignments"
   ]
  },
  {
@@ -94,7 +94,7 @@
   "id": "133046ed",
   "metadata": {},
   "source": [
-    "#### Arithmetic Assignments\n",
+    "### Arithmetic Assignments\n",
    "\n",
    "The result of any integer divide is truncated to the integer value less than the correct decimal answer for the division. The result of this is that changing the order of operations can make a big difference in the answers.  Notice how parentheses force more expected results."
   ]
@@ -296,7 +296,7 @@
   "source": [
    "When in doubt use parentheses to get the answer that you really want.\n",
    "\n",
-    "#### Assignments exercise"
+    "### Assignments exercise"
   ]
  },
  {
@@ -310,20 +310,20 @@
    "\n",
    "  implicit none\n",
    "      \n",
-    "      real pi,radius,volume,area  \n",
+    "  real pi,radius,volume,area  \n",
    "          \n",
-    "      radius = 1.0\n",
+    "  radius = 1.0\n",
-    "      pi = 0.0\n",
+    "  pi = 0.0\n",
    "      \n",
-    "      write(*,*) 'The value of pi is ', pi\n",
+    "  write(*,*) 'The value of pi is ', pi\n",
-    "      write(*,*) \n",
+    "  write(*,*) \n",
    "\n",
-    "      area = 0.0\n",
+    "  area = 0.0\n",
-    "      volume = 0.0\n",
+    "  volume = 0.0\n",
    "      \n",
-    "      write(*,*) 'For a radius ', radius \n",
+    "  write(*,*) 'For a radius ', radius \n",
-    "      write(*,*) 'the area of a sphere is ', area\n",
+    "  write(*,*) 'the area of a sphere is ', area\n",
-    "      write(*,*) 'and the volume is ', volume\n",
+    "  write(*,*) 'and the volume is ', volume\n",
    "      \n",
    "end "
   ]
@@ -333,7 +333,7 @@
   "id": "9a1702f7",
   "metadata": {},
   "source": [
-    "#### Execution Control"
+    "### Execution Control"
   ]
  },
  {
@@ -369,7 +369,7 @@
   "id": "cef2ad42",
   "metadata": {},
   "source": [
-    "#### File-Directed Input and Output"
+    "### File-Directed Input and Output"
   ]
  },
  {
@@ -431,7 +431,7 @@
  },
  {
   "cell_type": "markdown",
-   "id": "31f27416",
+   "id": "059d5e2a",
   "metadata": {},
   "source": [
    "This code is going to create 2 files: \"03_dataxy\" and \"03_gnuxy\".\n",
@@ -442,25 +442,60 @@
    "gnuplot 03_gnuxy\n",
    "```\n",
    "\n",
-    "<img src=\"https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran/raw/master/assets/sin.png\">"
+    "<img src=\"https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran/raw/master/assets/sin.png\">\n",
+    "\n",
+    "#### Format controlled IO"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a26b3cc5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program format\n",
+    "\n",
+    "  implicit none\n",
+    "  \n",
+    "  real(4) A\n",
+    "  real(8) B\n",
+    "  integer I, KEY\n",
+    "\n",
+    "  A= 1500.*acos(0.)\n",
+    "  B= 4e3*dcos(16.5d0)\n",
+    "  KEY= 884\n",
+    "  \n",
+    "  write(*,*) A,B,KEY\n",
+    "  write(*,*)\n",
+    "  \n",
+    "  write(*,1000) A,B,KEY\n",
+    "  write(*,1001) (\"-\",I=1,38)\n",
+    "  \n",
+    "  1000 FORMAT(F18.10,E14.5,I6)\n",
+    "  1001 FORMAT(38A1)\n",
+    "      \n",
+    "end program format  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31f27416",
+   "metadata": {},
+   "source": [
+    "### Hands on learning: numerical analysis\n",
+    "\n",
+    "Apply the Newton's method to find the root(s) of a polynomial function.\n",
+    "\n",
+    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/6929060731e351c465426e37567abe5ee13d65d9\">"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
   "id": "df362a1a",
   "metadata": {},
-   "outputs": [
+   "outputs": [],
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      " Try to solve \"x**3+x-10=0\"\n",
-      " What is your initial guess for the solution?\n",
-      "\n"
-     ]
-    }
-   ],
   "source": [
    "program newton\n",
    "\n",
@@ -470,7 +505,7 @@
    "\n",
    "  integer :: i\n",
    "\n",
-    "  write(*,*) 'Try to solve \"x**3+x-10=0\"'\n",
+    "  write(*,*) 'Try to solve \"x**3+x-10=0\"'  \n",
    "  write(*,*) 'What is your initial guess for the solution?'\n",
    "\n",
    "  do while( .TRUE. )\n",
@@ -493,23 +528,20 @@
    "end subroutine\n"
   ]
  },
+  {
+   "cell_type": "markdown",
+   "id": "919d1d4f",
+   "metadata": {},
+   "source": [
+    "### COMMON Statement (F77)"
+   ]
+  },
  {
   "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
   "id": "4b517d6b",
   "metadata": {},
-   "outputs": [
+   "outputs": [],
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      " Before the call:\n",
-      " a =            2 , b =            0 , c =            1\n",
-      " After the call:\n",
-      " a =            2 , b =            3 , c =            2\n"
-     ]
-    }
-   ],
   "source": [
    "      PROGRAM test_arg\n",
    "\n",
@@ -544,23 +576,20 @@
    "      END SUBROUTINE"
   ]
  },
+  {
+   "cell_type": "markdown",
+   "id": "1e457015",
+   "metadata": {},
+   "source": [
+    "### MODULE Statement (F90)"
+   ]
+  },
  {
   "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
   "id": "71f26006",
   "metadata": {},
-   "outputs": [
+   "outputs": [],
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      " Before the call:\n",
-      " a =   2, b =  0, c =  1\n",
-      " After the call:\n",
-      " a =   2, b =  3, c =  2\n"
-     ]
-    }
-   ],
   "source": [
    "MODULE arg\n",
    " implicit none\n",
@@ -599,25 +628,20 @@
    "END SUBROUTINE sub"
   ]
  },
+  {
+   "cell_type": "markdown",
+   "id": "a0900a54",
+   "metadata": {},
+   "source": [
+    "### NAMELIST (F90)"
+   ]
+  },
  {
   "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
   "id": "e3791d4f",
   "metadata": {},
-   "outputs": [
+   "outputs": [],
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      " Before:\n",
-      "  lon_min =   0.00, lon_max =  -0.00, lat_min =   0.00, lat_max =  -0.00\n",
-      " Between:\n",
-      "  lon_min =   0.00, lon_max = 360.00, lat_min =   0.00, lat_max =  -0.00\n",
-      " After:\n",
-      "  lon_min =   0.00, lon_max = 360.00, lat_min = -90.00, lat_max =  90.00\n"
-     ]
-    }
-   ],
   "source": [
    "PROGRAM test_namelist\n",
    "\n",
@@ -654,10 +678,52 @@
    "END"
   ]
  },
+  {
+   "cell_type": "markdown",
+   "id": "c0b0a801",
+   "metadata": {},
+   "source": [
+    "### Hands on learning: structure\n",
+    "\n",
+    "The aim of this exercise is to work with loops (for or while) in order to draw in a terminal a Christmas tree with its balls.\n",
+    "\n",
+    "The program must be carried out in Fortran 90. It will take as argument the height of the tree which is a variable of the problem:\n",
+    "\n",
+    "Height=7\n",
+    "```\n",
+    "      #\n",
+    "     ###\n",
+    "    #o###\n",
+    "   ##o####\n",
+    "  #o#####o#\n",
+    " ####o#####o\n",
+    "#####o#####o#\n",
+    "```\n",
+    "This parameter must be supplied at the command line when the program (for example './tree 10'). \n",
+    "\n",
+    "Balls must be positioned all 6 sharps."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "930eedf9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "program ChristmasTree\n",
+    "\n",
+    "  implicit none\n",
+    "\n",
+    "\n",
+    "\n",
+    "end program"
+   ]
+  },
  {
   "cell_type": "code",
   "execution_count": null,
-   "id": "27748335",
+   "id": "6362d74e",
   "metadata": {},
   "outputs": [],
   "source": []

 %% Cell type:markdown id:10d0e3c5 tags:
 ## Introduction to structured programming with Fortran
 ### Why to learn Fortran ?
 * Because of the execution speed of a program
 * Well suited for numerical computations : more than **45% of scientific applications** are in Fortran
-### Getting started
+## Getting started
-#### Hello World
+### Hello World
 %% Cell type:code id:00ec1776 tags:
 ``` Fortran
 program hello_world
  implicit none ! important
  print *, "Hello World!"
 end program hello_world
 ```
 %% Cell type:markdown id:c4b788f0 tags:
-#### Data Type Declarations and Assignments
+### Data Type Declarations and Assignments
 %% Cell type:code id:ffd3f0c3 tags:
 ``` Fortran
 program data_type
  implicit none
  real x, y
  integer i, j
  logical flag
  integer matrix(2,2)
  character(80) month
  character(len=80) months(12)
  character family*16
  real, dimension(12) :: small_array
  character(len=80), dimension(24) :: screen
  integer, parameter :: it = 100
  i = 1
  j = i+2
  x = 85.8
  y = 3.5*cos(x)
  month="december"
  months(:)="empty"
  months(12)=month
  flag = .TRUE.
  family = "GEORGE P. BURDELL"
  print*,family(:6)
  print*,family(8:9)
  print*,family(11:)
  print*,family(:6)//FAMILY(10:)
 end
 ```
 %% Cell type:markdown id:133046ed tags:
-#### Arithmetic Assignments
+### Arithmetic Assignments
 The result of any integer divide is truncated to the integer value less than the correct decimal answer for the division. The result of this is that changing the order of operations can make a big difference in the answers.  Notice how parentheses force more expected results.
 %% Cell type:code id:13343800 tags:
 ``` Fortran
 program arith
  implicit none
  real r2,r3,r4,r5,r6,ans1,ans2,ans3
  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
  data i2,i3,i4,i5/2,3,4,5/
  ians1=i2*i3/i5
  ians2=i3/i5*i2
  ians3=i2*(i3/i5)
  ians4=(i3/i5)*i2
  print *, '2*3/5 =', ians1, ', 3/5*2 =',ians2,', 2*(3/5) =',ians3 ,', (3/5)*2 =',ians4
 end program arith
 ```
 %% Cell type:markdown id:cabea667 tags:
 Real arithmetic behaves more uniformly:
 %% Cell type:code id:e1de5730 tags:
 ``` Fortran
 program arith
  implicit none
  real r2,r3,r4,r5,r6,ans1,ans2,ans3
  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
  data i2,i3,i4,i5/2,3,4,5/
  ans1=r2*r3/r5
  ans2=r3/r5*r2
  ans3=(r3/r5)*r2
  print *, '2.0*3.0/5.0 =', ans1, ', 3.0/5.0*2.0 =',ans2,', (3.0/5.0)*2.0 =',ans3
 end program arith
 ```
 %% Cell type:markdown id:f18b85ec tags:
 Watch how precedence of operations effects the following:
 %% Cell type:code id:9a362858 tags:
 ``` Fortran
 program arith
  implicit none
  real r2,r3,r4,r5,r6,ans1,ans2,ans3
  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
  data i2,i3,i4,i5/2,3,4,5/
  ians1=i2+i5*i3**i2
  ians2=i5*i3**i2+i2
  ians3=i3**i2*i5+i2
  print *, '2+5*3**2 =',ians1,', 5*3**2+2 =',ians2, ', 3**2*5+2 =',ians3
 end program arith
 ```
 %% Cell type:markdown id:5297b017 tags:
 You can mix real and integers, but watch what happens
 %% Cell type:code id:7d50669e tags:
 ``` Fortran
 program arith
  implicit none
  real r2,r3,r4,r5,r6,ans1,ans2,ans3
  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
  data i2,i3,i4,i5/2,3,4,5/
  ans1=r5+i3/i2
  ans2=5.0+3/2
  print *, '5.0+3/2 =',ans1
  print *, '5.0+3/2 =',ans2
 end program arith
 ```
 %% Cell type:markdown id:222cabbc tags:
 Look at what happens when I put a real in either the numerator or denominator of the division term
 %% Cell type:code id:78929c6e tags:
 ``` Fortran
 program arith
  implicit none
  real r2,r3,r4,r5,r6,ans1,ans2,ans3
  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
  data i2,i3,i4,i5/2,3,4,5/
  ans1=r5+i3/r2
  ans2=r5+r3/i2
  print *, '5.0+3/2.0 =',ans1, ', 5.0+3.0/2 =', ans2
 end program arith
 ```
 %% Cell type:markdown id:a7d37bc2 tags:
 Although Fortran normally works from left to right at a given level of precedence (does all multiply and divide from left to right before moving on to adds and subtracts). It works exponentiation from right to left when it hits 2 or more sequential exponentiation operations
 %% Cell type:code id:3c2da1a9 tags:
 ``` Fortran
 program arith
  implicit none
  real r2,r3,r4,r5,r6,ans1,ans2,ans3
  integer i2,i3,i4,i5,i6,ians1,ians2,ians3,ians4
  data r2/2./,r3/3./,r4/4.0/,r5/5.0/
  data i2,i3,i4,i5/2,3,4,5/
  ians1= i5**i3**i2
  ians2= (i5**i3)**i2
  ians3= i5**(i3**i2)
  print *, '5**3**2 =',ians1, ', (5**3)**2 =',ians2,  ', 5**(3**2) =',ians3
 end program arith
 ```
 %% Cell type:markdown id:8387be7a tags:
 When in doubt use parentheses to get the answer that you really want.
-#### Assignments exercise
+### Assignments exercise
 %% Cell type:code id:14f6e7e2 tags:
 ``` Fortran
 program sphere
  implicit none
-      real pi,radius,volume,area
+  real pi,radius,volume,area
-      radius = 1.0
+  radius = 1.0
-      pi = 0.0
+  pi = 0.0
-      write(*,*) 'The value of pi is ', pi
+  write(*,*) 'The value of pi is ', pi
-      write(*,*)
+  write(*,*)
-      area = 0.0
+  area = 0.0
-      volume = 0.0
+  volume = 0.0
-      write(*,*) 'For a radius ', radius
+  write(*,*) 'For a radius ', radius
-      write(*,*) 'the area of a sphere is ', area
+  write(*,*) 'the area of a sphere is ', area
-      write(*,*) 'and the volume is ', volume
+  write(*,*) 'and the volume is ', volume
 end
 ```
 %% Cell type:markdown id:9a1702f7 tags:
-#### Execution Control
+### Execution Control
 %% Cell type:code id:41f9a8f0 tags:
 ``` Fortran
 PROGRAM gcd
  ! Computes the greatest common divisor, Euclidean algorithm
  IMPLICIT NONE
  INTEGER :: m, n, t
  WRITE(*,*) "Give positive integers m and n :"
  m=5464
  n=484682
  WRITE(*,*) 'm:', m,' n:', n
  positive_check: IF (m > 0 .AND. n > 0) THEN
    main_algorithm: DO WHILE (n /= 0)
      t = MOD(m,n)
      m = n
      n = t
    END DO main_algorithm
    WRITE(*,*) "Greatest common divisor: ",m
  ELSE
    WRITE(*,*) 'Negative value entered'
  END IF positive_check
 END PROGRAM gcd
 ```
 %% Cell type:markdown id:cef2ad42 tags:
-#### File-Directed Input and Output
+### File-Directed Input and Output
 %% Cell type:code id:8fd042c4 tags:
 ``` Fortran
 program plot
  ! Program to provide plots of Sin(x)
  implicit none
  character label*150
  real x
  integer i
  character xlabel*32,ylabel*32,title*32
  real fx
  !
  ! label   -   Character string
  ! xlabel  -   Contains a label for the x-axis
  ! ylabel  -   Contains a label for the y-axis
  ! title   -   Contains a title for the plot
  !
  ! Drive a separate true graphics program (gnuplot)
  !
  ! First set up the command file for gnuplot
  !
  xlabel="'x'"
  ylabel="'y'"
  title="'sin(x)'"
  open (112,file='03_gnuxy')
  !
  label='set xlabel '//xlabel
  write(112,*)label
  write(112,*)'set xrange [0:6]'
  label='set ylabel '//ylabel
  write(112,*)label
  write(112,*)'set yrange [-1.2:1.2]'
  label='plot "03_dataxy" using 1:2 title '//title
  label=trim(label)//' with lines lt rgb "red"'
  write(112,*) label
  write (112,*) 'pause -1'
  close(112)
  !
  !   Generate x-y pairs for the graph
  !
  open (112,file='03_dataxy')
  do i=0,60
    x=.1*i
    fx=sin(x)
    write(112,*) x,fx
  enddo
  close(112)
  !
 end program
 ```
-%% Cell type:markdown id:31f27416 tags:
+%% Cell type:markdown id:059d5e2a tags:
 This code is going to create 2 files: "03_dataxy" and "03_gnuxy".
 The idea is to use a linux plotting tool called "GNUplot" to make a graph: the first file is the data for the graph, the second one is the gnuplot script using these data.
 ```bash
 gnuplot 03_gnuxy
 ```
 <img src="https://gogs.elic.ucl.ac.be/pbarriat/learning-fortran/raw/master/assets/sin.png">
+#### Format controlled IO
+%% Cell type:code id:a26b3cc5 tags:
+``` Fortran
+program format
+  implicit none
+  real(4) A
+  real(8) B
+  integer I, KEY
+  A= 1500.*acos(0.)
+  B= 4e3*dcos(16.5d0)
+  KEY= 884
+  write(*,*) A,B,KEY
+  write(*,*)
+  write(*,1000) A,B,KEY
+  write(*,1001) ("-",I=1,38)
+  1000 FORMAT(F18.10,E14.5,I6)
+  1001 FORMAT(38A1)
+end program format
+```
+%% Cell type:markdown id:31f27416 tags:
+### Hands on learning: numerical analysis
+Apply the Newton's method to find the root(s) of a polynomial function.
+<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6929060731e351c465426e37567abe5ee13d65d9">
 %% Cell type:code id:df362a1a tags:
 ``` Fortran
 program newton
  implicit none
  ! Use a Newton iteration to solve a polynomial equation
  integer :: i
  write(*,*) 'Try to solve "x**3+x-10=0"'
  write(*,*) 'What is your initial guess for the solution?'
  do while( .TRUE. )
    write(*,*)
    exit
  end do
 end program
 ! ******************************************************************************************
 subroutine derivate()
 ! Evaluate the function f(x)=x**3+x-10
 ! also return the derivative of the function
 end subroutine
 ```
-%% Output
+%% Cell type:markdown id:919d1d4f tags:
-     Try to solve "x**3+x-10=0"
+### COMMON Statement (F77)
-     What is your initial guess for the solution?
 %% Cell type:code id:4b517d6b tags:
 ``` Fortran
      PROGRAM test_arg
        implicit none
        integer a,b,c
        common /arg/ a,b,c
        a = 2
        c = 1
        print *, 'Before the call:'
        print *, 'a = ',a,', b = ',b,', c = ',c
        call sub
        print *, 'After the call:'
        print *, 'a = ',a,', b = ',b,', c = ',c
      END PROGRAM
      SUBROUTINE sub
        implicit none
        integer a,b,c
        common /arg/ a,b,c
        b = a + c
        c = c + 1
      END SUBROUTINE
 ```
-%% Output
+%% Cell type:markdown id:1e457015 tags:
-     Before the call:
+### MODULE Statement (F90)
-     a =            2 , b =            0 , c =            1
-     After the call:
-     a =            2 , b =            3 , c =            2
 %% Cell type:code id:71f26006 tags:
 ``` Fortran
 MODULE arg
 implicit none
 integer :: a,b,c
 real(8) :: x
 END MODULE arg
 ! * * * * * * *
 PROGRAM test_arg
 USE arg
 implicit none
 a = 2
 c = 1
 write(*,*) 'Before the call:'
 write(*,'(3(A5,I3))') ' a = ',a,', b = ',b,', c = ',c
 call sub
 write(*,*) 'After the call:'
 write(*,'(3(A5,I3))') 'a = ',a,', b = ',b,', c = ',c
 END PROGRAM test_arg
 ! * * * * * * *
 SUBROUTINE sub
 USE arg, only : a,b,c    ! seuls a b et c sont utiles
 implicit none
 b = a + c
 c = c + 1
 END SUBROUTINE sub
 ```
-%% Output
+%% Cell type:markdown id:a0900a54 tags:
-     Before the call:
+### NAMELIST (F90)
-     a =   2, b =  0, c =  1
-     After the call:
-     a =   2, b =  3, c =  2
 %% Cell type:code id:e3791d4f tags:
 ``` Fortran
 PROGRAM test_namelist
  implicit none
  real(8) lon_min, lon_max, lat_min, lat_max
  NAMELIST/namlon/ lon_min, lon_max
  NAMELIST/namlat/ lat_min, lat_max
  write(*,*) 'Before:'
  call print_res(lon_min, lon_max, lat_min, lat_max)
  open(161,file='../src/07_namelist.def',status='old',form='formatted')
  read(161,NML=namlon)
  write(*,*) 'Between:'
  call print_res(lon_min, lon_max, lat_min, lat_max)
  read(161,NML=namlat)
  close (161)
  write(*,*) 'After:'
  call print_res(lon_min, lon_max, lat_min, lat_max)
 END
 SUBROUTINE print_res(a,b,c,d)
  implicit none
  real(8), intent(in) :: a,b,c,d
  write(*,'(4(A12,F6.2))') '  lon_min = ',a,', lon_max = ',b, &
                          ', lat_min = ',c,', lat_max = ',d
  RETURN
 END
 ```
-%% Output
+%% Cell type:markdown id:c0b0a801 tags:
+### Hands on learning: structure
+The aim of this exercise is to work with loops (for or while) in order to draw in a terminal a Christmas tree with its balls.
+The program must be carried out in Fortran 90. It will take as argument the height of the tree which is a variable of the problem:
+Height=7
+```
+      #
+     ###
+    #o###
+   ##o####
+  #o#####o#
+ ####o#####o
+#####o#####o#
+```
+This parameter must be supplied at the command line when the program (for example './tree 10').
+Balls must be positioned all 6 sharps.
+%% Cell type:code id:930eedf9 tags:
-     Before:
+``` Fortran
-      lon_min =   0.00, lon_max =  -0.00, lat_min =   0.00, lat_max =  -0.00
+program ChristmasTree
-     Between:
-      lon_min =   0.00, lon_max = 360.00, lat_min =   0.00, lat_max =  -0.00
+  implicit none
-     After:
-      lon_min =   0.00, lon_max = 360.00, lat_min = -90.00, lat_max =  90.00
+end program
+```
-%% Cell type:code id:27748335 tags:
+%% Cell type:code id:6362d74e tags:
 ``` Fortran
 ```