Your Task$$

Write the function assembleGlobalForceVector$()$ that takes five input arguments n$\_$load, force$\_$node, force$\_$val, n$\_$dof, eq$\_$num and returns one output p$\_$f:

Input arguments:

n$\_$load: the integer number of nonzero nodal forces.

force$\_$node: a $1-$D NumPy array of length $\_$n$\_$load containing the node numbers of the nodes that have nonzero forces on them.

force$\_$val: a $1-$D NumPy array of length $\_$n$\_$load containing the corresponding force values.

n$\_$dof: an integer representing the number of nodes with free displacement $($i$.$e$.$ the number of nodes without prescribed displacement$).$

eq$\_$num: a $1-$D NumPy array of length $\_$n$\_$node that determines how you should reorder your system of equations.

Output:

p$\_$f: a $1-$D NumPy array that stores corresponding force values in the order specified by eq$\_$num.

Remember:

Node numbers are $1-$indexed but NumPy arrays are $0-$indexed.

p$\_$f is an array of float values.

Algorithm to create the array p$\_$f:

p$\_$f stores the force values for all the nodes that do not have prescribed displacement. What should be the size of this array?

Initialize this array with zeros.

p$\_$f may include zero entries, corresponding to the nodes that do not have either prescribed force or displacement.

The non$-$zero entries of p$\_$f are initially stored in force$\_$val.

For each node where a force is applied $($node number in force$\_$node$),$ the corresponding equation number is identified from the eq$\_$num array.

The force value for that node $($value in force$\_$val$)$ is then assigned to the position in the force vector p$\_$f corresponding to this equation number. Note that this position is based on node numbers.

This process continues until all applied forces in force$\_$val are mapped to their respective positions in p$\_$f$.$