add matrix methods

addons/easy_charts/utilities/classes/structures/matrix.gd

@@ -16,6 +16,10 @@ func update_row(row : Array, index : int) -> void:
 	assert(rows() > index, "the row size must match matrix row size")
 	values[index] = row
 
+func remove_row(index: int) -> void:
+	assert(rows() > index, "the row size must match matrix row size")
+	values.remove(index)
+
 func insert_column(column : Array, index : int = values[0].size()) -> void:
 	if columns() != 0:
 		assert(column.size() == rows(), "the column size must match matrix column size")
@@ -27,6 +31,11 @@ func update_column(column : Array, index : int) -> void:
 	for row_idx in column.size():
 		values[row_idx][index] = column[row_idx]
 
+func remove_column(index: int) -> void:
+	assert(columns() > index, "the column index must be at least equals to the rows count")
+	for row in get_rows():
+		row.remove(index)
+
 func resize(rows: int, columns: int) -> void:
 	for row in range(rows):
 		var row_column: Array = []
@@ -45,6 +54,12 @@ func rows() -> int:
 func columns() -> int:
 	return values[0].size() if rows() != 0 else 0
 
+func value(row: int, column: int) -> float:
+	return values[row][column]
+
+func set_value(value: float, row: int, column: int) -> void:
+	values[row][column] = value
+
 func get_column(column : int) -> Array:
 	assert(column < columns(), "index of the column requested (%s) exceedes matrix columns (%s)"%[column, columns()])
 	var column_array : Array = []
@@ -67,9 +82,64 @@ func get_rows(from : int = 0, to : int = rows()-1) -> Array:
 	return values.slice(from, to)
 #    return MatrixGenerator.from_array(values)    
 
-func empty() -> bool:
+func is_empty() -> bool:
 	return rows() == 0 and columns() == 0
 
+
+func is_square() -> bool:
+	return columns() == rows()
+
+
+func is_diagonal() -> bool:
+	if not is_square():
+		return false
+	
+	for i in rows():
+		for j in columns():
+			if i != j and values[i][j] != 0:
+				return false
+	
+	return true
+
+
+func is_upper_triangular() -> bool:
+	if not is_square():
+		return false
+	
+	for i in rows():
+		for j in columns():
+			if i > j and values[i][j] != 0:
+				return false
+	
+	return true
+
+
+func is_lower_triangular() -> bool:
+	if not is_square():
+		return false
+	
+	for i in rows():
+		for j in columns():
+			if i < j and values[i][j] != 0:
+				return false
+	
+	return true
+
+
+func is_triangular() -> bool:
+	return is_upper_triangular() or is_lower_triangular()
+
+
+func is_identity() -> bool:
+	if not is_diagonal():
+		return false
+	
+	for i in rows():
+		if values[i][i] != 1:
+			return false
+	
+	return true
+
 func _to_string() -> String:
 	var last_string_len : int
 	for row in values:
@@ -83,6 +153,11 @@ func _to_string() -> String:
 		string+="\n"
 	return string
 
+# ----
+func set(position: String, value) -> void:
+	var t_pos: Array = position.split(",")
+	values[t_pos[0]][t_pos[1]] = value
+
 # --------------
 func _get(_property : String):
 	# ":" --> Columns 

addons/easy_charts/utilities/classes/structures/matrix_generator.gd

@@ -2,6 +2,15 @@ tool
 extends Reference
 class_name MatrixGenerator
 
+static func zeros(rows: int, columns: int) -> Matrix:
+	var zeros: Array = []
+	var t_rows: Array = []
+	t_rows.resize(columns)
+	t_rows.fill(0.0)
+	for row in rows:
+		zeros.append(t_rows.duplicate())
+	return Matrix.new(zeros)
+
 # Generates a Matrix with random values between [from; to] with a given @size (rows, columns)
 static func random_float_range(from : float, to : float, size : Vector2, _seed : int = 1234) -> Matrix:
 	seed(_seed)
@@ -33,6 +42,55 @@ static func sub_matrix(_matrix : Matrix, from : PoolIntArray, to : PoolIntArray)
 static func duplicate(_matrix : Matrix) -> Matrix:
 	return Matrix.new(_matrix.to_array().duplicate())
 
+# Calculate the determinant of a matrix
+static func determinant(matrix: Matrix) -> float:
+	assert(matrix.is_square(), "Expected square matrix")
+	
+	var determinant: float = 0.0
+	
+	if matrix.rows() == 2 :
+		determinant = (matrix.value(0, 0) * matrix.value(1, 1)) - (matrix.value(0, 1) * matrix.value(1, 0))
+	elif matrix.is_diagonal() or matrix.is_triangular() :
+		for i in matrix.rows():
+			determinant *= matrix.value(i, i)
+	elif matrix.is_identity() :
+		determinant = 1.0
+	else:
+		# Laplace expansion
+		var multiplier: float = -1.0
+		var submatrix: Matrix = sub_matrix(matrix, [1, 0], [matrix.rows(), matrix.columns()])
+		for j in matrix.columns() :
+			var cofactor: Matrix = copy(submatrix)
+			cofactor.remove_column(j)
+			multiplier *= -1.0
+			determinant += multiplier * matrix.value(0, j) * determinant(cofactor)
+	
+	return determinant
+
+
+# Calculate the inverse of a Matrix
+static func inverse(matrix: Matrix) -> Matrix:
+	var inverse: Matrix
+	
+	# Minors and Cofactors
+	var minors_cofactors: Matrix = zeros(matrix.rows(), matrix.columns())
+	var multiplier: float = -1.0
+	
+	for i in minors_cofactors.rows():
+		for j in minors_cofactors.columns():
+			var t_minor: Matrix = copy(matrix)
+			t_minor.remove_row(i)
+			t_minor.remove_column(j)
+			multiplier *= -1.0
+			minors_cofactors.set_value(multiplier * determinant(t_minor), i, j)
+	
+	var transpose: Matrix = transpose(minors_cofactors)
+	var determinant: float = determinant(matrix)
+	
+	inverse = multiply_float(transpose, 1 / determinant)
+	
+	return inverse
+
 # Transpose a given Matrix
 static func transpose(_matrix : Matrix) -> Matrix:
 	var array : Array = []
@@ -93,6 +151,10 @@ static func multiply_float(_matrix1 : Matrix, _float : float) -> Matrix:
 			array[x][y]*=_float
 	return Matrix.new(array)
 
+
+static func copy(matrix: Matrix) -> Matrix:
+	return Matrix.new(matrix.values.duplicate(true))
+
 # ------------------------------------------------------------
 static func get_letter_index(index : int) -> String:
 	return "A B C D E F G H I J K L M N O P Q R S T U V W X Y Z".split(" ")[index]