STEM-Fortran

A collection of Fortran modules and routines for math, science and engineering calculations.

Table of Contents

• Array Module
• Vector Module
• Calculus Module
• Functions Module
• Plot Module
• Stats Module
• Geo Module

Array Module

A collection of sub-routines and functions for operating with and on arrays. The sub-routines and functions are listed below.

• linspace(x, xMin, xMax, xLength) This subroutine will create a linearly spaced array. x is the array, xMin is the start value, xMax is the end value and xLength is the length of the array.

Vector Module

A collection of types, sub-routines and functions for operating with and on vectors. The types, sub-routines and functions are listed below.

• vec2d is the type that defines a 2d vector, it is defined as follows.

        type vec2d
            real(8) :: x, y
        end type vec2d

• vec3d is the type that defines a 3d vector, it is defined as follows.

        type vec3d
            real(8) :: x, y, z
        end type vec3d

• dotProduct2d(vec1, vec2) This function will return the dot product of two, 2-dimensional vectors. It takes the arguments vec1 and vec2, these are both of the type vec2d.
• dotProduct3d(vec1, vec2) This function will return the dot product of two, 3-dimensional vectors. It takes the arguments vec1 and vec2, these are both of the type vec3d.
• dotProductNd(vec1, vec2) This function will return the dot product of two, n-dimensional vectors. It takes the arguments vec1 and vec2, these are both arrays.
• crossProduct(vec1, vec2) This function will return the cross product of two vectors as the type of vec3d. It taks the arguments of vec1 and vec2, these are both of the type of vec3d.
• crossProductArray(vec1, vec2) This function will return the cross product of two vectors as an array. It takes the arguments of vec1 and vec2, these are both arrays.
• vecAdd2d(vec1, vec2) This function will return the addition of two 2-dimensional vectors. It takes the arguments of vec1 and vec2, these are both of the type vec2d.
• vecAdd3d(vec1, vec2) This function will return the addition of two 3-dimensional vectors. It takes the arguments of vec1 and vec2, these are both of the type vec3d.
• vecAddArray This function will return the additon of two n-dimensional vectors. It takes the arguments of vec1 and vec2, these are both arrays.

Calculus Module

A collection of sub-routines and functions for calculus based operations. The sub-routines and functions are listed below.

• trapezoidalIntegrate(x, y) This function will return the integral using the trapezoidal method. It takes the arguments x and y that are in the form of arrays.
• simpsonIntegrate(x, y) This function will return the integral using Simpson's method. It takes the arguments x and y that are in the form of arrays.
• trapezoid_integrate(f, a, b, n) This function will return the integral using the trapezoidal method. It takes the arguments, f the function to be integrated, a and b the bounds and n for the number of sub intervals.
• simpson_integrate(f, a, b, n) This function will return the integral using Simpson's method. It takes the arguments, f the function to be integrated, a and b the bounds and n for the number of sub intervals.

Functions Module

A module where users define their own mathematical functions.

Plot Module

A collection of sub-routines and functions for plotting operations. The sub-routines and functions are listed below.

• plot2d(x, y) This sub-routine will save a file named data.dat to the working directory, so that it can be plotted in gnuplot or other visualisation software. It accepts to arguments x and y, these are both arrays of the same length.

Stats Module

A collection of sub-routines and functions for statistical operations. The sub-routines and functions are lised below.

• mean(x) This function will return the mean value of an input array x
• median(x) This function will return the median value of an input array x. Note that currently the sorting method is extremley inefficient.
• normalDistrubtions(x, sigma, mu) This function will return a normal distribution. It takes arguments x an input array to operate on, sigma the standard deviation of the normal distribution and mu the mean of the normal distribution.

Geo Module

A collection of sub-routines and functions for geographical operations. The sub-routines and functions are listed below.

• pointInCircle(px, py, cx, cy, r) This function will return a boolean value, true or false, for if the point lies within the circle, this function assumes standard rectangular coordinates and is not recommended to be used for spheres or ellipsoids. It takes the arguments px and py for the x and y coordinates of the point, cx and cy for the coordinates of the circle centre and r for the radius of the circle.
• pointInCircleHaversine(px, py, cx, cy, r) This function will return a boolean value, true or false, for if a point lies within a circle. This function utilises the haversine method to find the distance and thus is suitable for use on spheres. It takes the arguments of px and py for the x and y coordinates of the point, cx and cy for the coordinates of the circle centre and r for the radius of the circle.
• pointInCircleVincenty(px, py, cx, cy, r) This function will return a boolean value, true or false, for if a point lies within a circle. This function utilises the vincenty method to find the distance and thus is suitable for use on ellipsoids. It takes the arguments of px and py for the x and y coordinates of the point, cx and cy for the coordinates of the circle centre and r for the radius of the circle.
• haversineDistance(lon1, lat1, lon2, lat2) This function will return the distance between two points on the surface of the earth, assuming it is a sphere. It takes the arguments, lon1 and lat1 for the coordinates of the first point and lon2 and lat2 for the coordinates of the second point.
• haversineDistanceArray(lon, lat) This function will return the distance between successive points in an array, using the above haversineDistance function.
• vincentyDistance(lon1, lat1, lon2, lat2) This function will return the distance between two points on the surface of the earth, assuming it is the WGS-84 ellipsoid. It takes the arguments, lon1 and lat1 for the coordinates of the first point and lon2 and lat2 for the coordinates of the second point.
• vincentyDistanceArray(lon, lat) This function will return the distance between successive points in an array, using the above vincentyDistance function.