$2)$ Assemble the global response arrays

The second part of your task is to create a assembleGlobalArrays$()$ that assembles the global displacement $$Uur and force $$Pur vectors:

$[]\{\}=\{\}=[$KppKpfKfpKff$]\{$UpUf$\}=\{$PpPf$\}$KurUur$=$Pur

where the global arrays follow the node ascending ordering, i$.$e$.,=[1,2,3,...,\_]$Uur$=[$u$1,$u$2,$u$3,...,$un$\_$node$]$ and $$ui is the displacement of node $$i$.$

Write the function assembleGlobalArrays$()$ that takes six input arguments u$\_$p$,$ p$\_$f$,$ u$\_$f$,$ p$\_$p$,$ n$\_$node, eq$\_$num and returns two outputs u$\_$ur$,$ p$\_$ur:

Input arguments:

u$\_$p: a $1-$D NumPy array that stores the known prescribed displacement values $$Up$.$

p$\_$f: a $1-$D NumPy array that stores the known force values $$Pf$.$

u$\_$f: a $1-$D NumPy array that stores the displacement values of the free nodes $$Uf$.$

p$\_$p: a $1-$D NumPy array that stores the reaction forces on the prescribed nodes $$Pp$.$

n$\_$node: an integer that represents the number of nodes.

eq$\_$num: a $1-$D NumPy array that determines how you should reorder your system of equations, used for the Assemble module.

Outputs:

u$\_$ur: a $1-$D NumPy array that stores the displacement values of all nodes $$Uur in the original order $($also called the unreduced global displacement vector$).$

p$\_$ur: a $1-$D NumPy array that stores the force values applied on all nodes $$Pur in the original order $($also called the unreduced global force vector$).$

Algorithm to create the arrays p$\_$ur and u$\_$ur:

initialize the arrays u$\_$ur and p$\_$ur with zeros.

what should be the type of these arrays?

what is the shape of these arrays?

for each entry of u$\_$ur$,$ find the corresponding equation number $($eq$\_$num$).$

the value and sign of the equation number will tell you if the contributions are coming from u$\_$f or u$\_$p$.$

the same algorithm works to build p$\_$ur

Remember:

Be aware that the node and equation numbers are $1-$indexed but NumPy arrays are $0-$indexed.