How to translate this Math Formula in Haskell or Python? (Was translated in PHP)

Here you go.

I place this code into the public domain.

# Function to make an array of 'width' zeros
function makerow($width){
 $row=array();
 for($x=0;$x<$width;$x++){
   $row[$x]=0;
 }
 return $row;
}

# Function to make a width*height matrix
function makematrix($width,$height){
 $matrix=array();
 for($y=0;$y<$height;$y++){
  $matrix[$y]=array();
  for($x=0;$x<$width;$x++){
   $matrix[$y][$x]=0;
  }
 }
 return $matrix;
}

# Adds one matrix to another
function matrixadd(&$matrixdest,&$matrixsrc){
 for($i=0;$i<count($matrixdest);$i++){
  for($j=0;$j<count($matrixdest[$i]);$j++){
   $matrixdest[$i][$j]+=$matrixsrc[$i][$j];
  }
 }
}

# Multiplies a matrix by a scalar
function matrixmultiply(&$matrix,$scalar){
 for($i=0;$i<count($matrix);$i++){
  for($j=0;$j<count($matrix[$i]);$j++){
   $matrix[$i][$j]*=$scalar;
  }
 }
}

# Calculates the equity of each place. Rows indicate players;
# columns indicate places (0 is 1st place, 1 is second, and so on)
# The parameter 'places' is optional.  If not given, uses the 
# number of stacks.
function equitymatrix(&$stacks, $places=-1){
 if($places==-1){
  # replace places with the stack count
  $places=count($stacks);
 }
 if(count($stacks)<=1){
  return array(array(1));
 }  
 $totalStacks=0;
 for($i=0;$i<count($stacks);$i++){
  $totalStacks+=$stacks[$i];
 }
 # Optimize for case where there is only one place
 if($places==1){
  $matrix=makematrix(1,count($stacks));
  for($i=0;$i<count($stacks);$i++){
   $matrix[$i][0]=$stacks[$i]*1.0/$totalStacks;
  }
  return $matrix;
 }
 # Optimize for case where there are two places
 if($places==2){
  $matrix=makematrix(2,count($stacks));
  for($i=0;$i<count($stacks);$i++){
   $matrix[$i][0]=$stacks[$i]*1.0/$totalStacks;
  }
  for($i=0;$i<count($stacks);$i++){
   for($j=0;$j<count($stacks);$j++){
    if($i!=$j){
     $matrix[$i][1]+=$matrix[$j][0]*($stacks[$i]*1.0/($totalStacks-$stacks[$j]));
    }
   }
  }
  return $matrix;
 }
 # Calculate the probabilities of each player getting first place
 $probabilities=array();
 for($i=0;$i<count($stacks);$i++){
  $probabilities[$i]=$stacks[$i]*1.0/$totalStacks;
 }
 #echo(count($stacks)." ".$places."n");
 $subequities=array();
 for($i=0;$i<count($stacks);$i++){
  $substacks=array();
  # Assume that player i would be in first place
  # Create a new array with i's stack removed
  for($j=0;$j<count($stacks);$j++){
   if($j!=$i){
    array_push($substacks,$stacks[$j]);
   }
  }
  # Find the subequity of the remaining players
  $subequities[$i]=equitymatrix($substacks,
    min($places,count($substacks)));
  for($j=0;$j<count($subequities[$i]);$j++){
   array_unshift($subequities[$i][$j],0);
  }
  # Add player i back
  $newrow=makerow($places);
  $newrow[0]=1;
  array_splice($subequities[$i],$i,0,array($newrow));
 }
 $equities=makematrix($places,count($stacks));
 for($i=0;$i<count($stacks);$i++){
  # Multiply the probabilities
  matrixmultiply($subequities[$i],$probabilities[$i]);
  # Add the subequity
  matrixadd($equities,$subequities[$i]);
 }
 return $equities;
}

Example:

$mystacks=array(10,40,30,20);
print_r(equitymatrix($mystacks));

As to the use of matrices:

In PHP, a matrix can be represented as an array of arrays. You can see
that in the function makematrix, which returns an array of length height,
with each element being an array of width zeros. Your problem uses the following
matrix operations, both of which are simple:

• Adding two matrices (matrixadd). Here, just add the elements of one matrix to the
  corresponding elements of the other matrix.
• Multiplying a matrix by a single number (a scalar) (matrixmultiply) simply
  involves multiplying each element of the matrix by that number.