Appendix 1 - Exercises¶

Variables and data types¶

1-1 Which of the following names can be used as Fortran variable names?

number_of_stars

fortran_is_a_nice_language_to_use

2001_a_space_odyssey

more$_money

1-2 Declare the following variables in Fortran: 2 scalar integers a, and b, 3 floating point scalars c, d and e, 2 character strings infile and outfile and a logical variable f.

1-3 Declare a floating point variable a that can represent values between 10$^{-150}$ and 10$^{150}$ with 14 significatn numbers.

1-4 What is printed by the following program?

program precision

    implicit none

    integer, parameter :: ap = &
    selected_real_kind(15,300)

    real(ap) :: a, b

    a = 1.234567890123456
    b = 1.234567890123456_ap

    if (a==b) then
        write(*,*) 'Values are equal.'
    else
        write(*,*) 'Values are different.'
    endif

    stop

end program precision

Arrays and matrices¶

2-1 Declare a $[3 \times 3]$ floating point array, $\mathbf{Ke}$, and an 3 element integer array, $\mathbf{f}$.

2-2 Declare an integer array, $\mathbf{idx}$, with the indices [0, 1, 2, 3, 4, 5, 6, 7]

2-3 Give the following assignments:

Floating point array, A, is assigned the value 5.0 at (2,3).
Integer matrix, C, is assigned the value 0 at row 2.

2-4 Write a program declaring a floating point matrix, I, with the dimensions [10×10] and initialise it with the identity matrix.

2-5 Declare an allocatable 2-dimensional floating point array and a 1-dimensional floating point vector. Also show programstatements how memory for these variables are allocated and deallocated.

2-6 Create a subroutine, identity, initialising a arbitrary twodimensionl to the identity matrix. Write a program illustrating the use of the subroutine.

2-7 Create a program that:

Defines an array to have 100 elements;
assigns to the elements the values 1,2,3, …, 100;
reads two integer values in the range 1 to 100;
reverses the order of the elements of the array in the range specified by the two values.

2-8 Given the array declaration

real, dimension(50,20) :: a

write array sections representing

the first row of a;
the last column of a;
every second element in each row and column;
as for (iii) in reverse order in both dimensions;

2-9 Complete excercise 2.8 using array syntax instead of do constructs.

2-10 Create a derived data type for a particle in a particle system. The particle should have the following attributes:

position
velocity
mass

Create an allocatable array with 1000 particles. Initialise all particles with the position (0,0,0) and a random velocity and a mass of 1.0.

Conditional statements¶

3-1 Give the following if-statements:

If the value of the variable, i, is greater than 100 print ’i is greater than 100!’
If the value of the logical variable, extra_filling, is true print ’Extra filling is ordered.’, otherwise print ’No extra filling.’.

3-2 Give a case-statment for the variable, a, printing ’a is 1’ when a is 1, ’a is between 2 and 20’ for values between 1 and 20 and prints ’a is not between 1 and 20’ for all other values.

Repetitive statements¶

4-1 Write a program consisting of a do-statement 1 to 20 with the control variable, i. For values, i, between 1 till 5, the value of i is printed, otherwise ’i > 5’ is printed. The loop is to be terminated when i equals 15.

Built-in functions¶

5-1 Give the following expressions in Fortran:

$\frac{1}{\sqrt{2}}$
$e^{x} \sin ^{2} x$
$\sqrt{a^{2} +b^{2}}$
$\left| x-y\right|$

5-2 Give the following matrix and vector expressions in Fortran. Also give appropriate array declarations:

$\mathbf{AB}$
$\mathbf{A^{T} A}$
$\mathbf{ABC}$
$\mathbf{a\cdot b}$

5-3 Show expressions in Fortran calculating maximum, mininmum, sum and product of the elements of an array.

Program units and subroutines¶

6-1 Implement a function returning the value of the the following expression:

$e^{x} \sin ^{2} x$

6-2 A subroutine receives as an argument an array of values, x, and the number of elements in x, n. If the mean and variance of the values in x are estimated by

\[mean = \frac{1}{n}\sum_{i=1}^{n}x(i)\]

and

\[variance = \frac{1}{n-1}\sum_{i=1}^{n}(x(i)-mean)^2\]

Write a subroutine which returns these calculated values as arguments. The subroutine check for invalid values of n (<=1). Write a main program that illustrates the use of this subroutine.

6-3 Create a module, statistics, containing the functions in 6-2. Change the program in 6-2 to use this module. The module is placed in a separate file, and the main program in main.f90.

Input and output¶

7-1 Write a program which reads a value, x, and calculates and prints the corresponding value x/(1.+x). The case x=-1 shoud produce an error message and be followed by an attempt to read a new value of x.

7-2 Write a program listing $f(x)=\sin x$ from $-1.0$ to $1.0$ inintervals of $0.1$. The output from the program should have the following format:

         111111111122222222223
123456789012345678901234567890
 x      f(x)
-1.000 -0.841
-0.900 -0.783
-0.800 -0.717
-0.700 -0.644
-0.600 -0.565
-0.500 -0.479
-0.400 -0.389
-0.300 -0.296
-0.200 -0.199
-0.100 -0.100
 0.000  0.000
 0.100  0.100
 0.200  0.199
 0.300  0.296
 0.400  0.389
 0.500  0.479
 0.600  0.565
 0.700  0.644
 0.800  0.717
 0.900  0.783
 1.000  0.841

7-3 Write a program calculating the total length of a piecewise linear curve. The curve is defined in a textfile line.dat.

The file has the following structure:

{number of points n in the file}
{x-coordinate point 1} {y-coordinate point 1}
{x-coordinate point 2} {y-coordinate point 2}
.
.
{x-coordinate point n} {y-coordinate point n}

The program must not contain any limitations regarding the number of points in the number of points in the curve read from the file.

String manipulation¶

8-1 Declare 3 strings, c1, c2 and c3 containing the words ’Fortran’, ’is’ och ’fun’. Merge these into a new string, c4, making a complete sentence.

8-2 Write a function converting a string into a floating point value. Write a program illustrating the use of the function. |

Object-oriented programming¶

9-1 Implement a derived datatype for a vector and use operator overloading to implement common vector operations such as adding, subtracting and multiplication (cross-product).