import java.util.ArrayList;

public class ExtraMUtil $\{$

$/**$

$*$ Performs element$-$wise addition of two matrices of the same shape.

$*$ @param $1$: A double$[][]$ that represents a $2$D matrix with shape m$*$n

$*$ @param $2$: A double$[][]$ that represents a $2$D matrix with shape m$*$n

$*$ @return an ArrayList of double$[]$ that represents the result $2$D matrix with shape m$*$n$.$

$*/$

public static ArrayList matAddition$($double$[][]$ m$1,$ double$[][]$ m$2)\{$

$//$ Fill your code here for completing the matrix addition operation

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Performs naive matrix multiplication between two matrices of shape $[$k$][$l$]$ and $[$l$][$m$]$

$*$ @param $1$: An ArrayList of an ArrayList of Double that represents a $2$D matrix with shape k$*$p

$*$ @param $2$: An ArrayList of double$[]$ that represents a $2$D matrix with shape p$*$m

$*$ @return A double$[][]$ that represents the result $2$D matrix with shape k$*$m

$*/$

public static double$[][]$ matProduct$($ArrayList$>$ m$1,$ ArrayList m$2)\{$

$//$ Fill your code here for completing the matrix multiplication operation

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Performs element$-$wise multiplication between two matrices and sums the result.

$*$ @param $1$: A double$[][]$ that represents the first input matrix.

$*$ @param $2$: A double$[][]$ that represents the second input matrix.

$*$ @return a double$[][]$ that represents the result matrix.

$*/$

public static double$[][]$ matElemProduct$($double$[][]$ m$1,$ double$[][]$ m$2)\{$

$//$ Fill your code here for completing the Element$-$wise matrix multiplication operation

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Sum the elements in a given $2$D matrix

$*$ @param $1$: A double$[][]$ that represents the input $2$D matrix.

$*$ @return a double that equals the sum of the elements in the matrix.

$*/$

public static double matSum$($double$[][]$ m$)\{$

$//$ Fill your code here for completing the matrix sum operation

return $0$; $//$ You can remove this line of "return $0$;$"$

$\}$

$/**$

$*$ Returns the transpose of a given $2$D matrix with a shape of $[$m$][$n$].$

$*$ @param $1$: An ArrayList of ArrayList of Double that represents the input $2$D matrix.

$*$ @return a double$[][]$ that represents the result $2$D matrix with shape of n$*$m

$*/$

public static double$[][]$ matTranspose$($ArrayList$>$ m$)\{$

$//$ Fill your code here for completing the matrix transpose operation

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Returns a sub$-$matrix from a given $2$D matrix with the specified range of indices.

$*$ @param $1$: An int that indicates the start row index.

$*$ @param $2$: An int that indicates the end row index.

$*$ @param $3$: An int that indicates the start column index.

$*$ @param $4$: An int that indicates the end column index.

$*$ @param $5$: A double$[][]$ that represents the input $2$D matrix.

$*$ @return an ArrayList of double$[]$ that represents the sub$-$matrix with shape $($param$2-$ param$1+1)*($param$4-$ param$3+1)$

$*/$

public static ArrayList subMat$($int r$\_$s$,$ int r$\_$e$,$ int c$\_$s$,$ int c$\_$e$,$ double$[][]$ m$)\{$

$//$ Fill your code here for completing the sub$-$matrix extraction operation

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Flattens a $3$D matrix of shape m by n by p into a vector of size m$*$n$*$p

$*$ @param $1$: a double$[][][]$ that represents the input $3$D matrix.

$*$ @return a vector of size m$*$n$*$p

$*/$

public static double$[]$ matToVec$($double$[][][]$ m$)\{$

$//$ Fill your code here for completing the $3$D matrix flatten operation.

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Reorganizes a vector to the desired $3$D matrix of shape d by h by w$.$

$*$ the size of the input vector must equal to d$*$h$*$w$.$

$*$ @param $1$: A double$[]$ that represents the input vector.

$*$ @param $2$: An int that indicates the depth of the reshaped matrix.

$*$ @param $3$: An int that indicates the row size of the reshaped matrix.

$*$ @param $4$: An int that indicates the column size of the reshaped matrix.

$*$ @return a $3$D array of shape d by h by w

$*/$

public static double$[][][]$ vecToMat$($double$[]$ input, int d$,$ int h$,$ int w$)\{$

$//$ Fill your code here for completing the vector reshape operation

return null; $//$ You can remove this line of "return null;"

$\}$

$/**$

$*$ Pretty prints a double type vector with the specified number of significant figures.

$*$ @param $1$: the input vector.

$*/$

public static void vecPrint$($double$[]$ v$)\{$

for $($int j $=0$; j $<$ v$.$length; j$++)\{$

System.out.prin