Function TheWaveMatrix(ByVal theRange As Range, _
                       ByVal waves As Long, _
                       ByVal iterations As Integer, _
                       ByVal precision As Integer) As Variant()
    
    On Error GoTo ExitFunction
    Dim Er(0) As Variant: Er(0) = "Error"
    Dim i, j, k, items, mn, mx As Long: items = theRange.Rows.Count
    Dim arry() As Double: ReDim arry(1 To items): For i = 1 To items: arry(i) = theRange.Cells(i, 1): Next i
    Dim matrix() As Variant: ReDim matrix(1 To items, 1 To (waves + 2))
    Dim a, b, degree, sum_y, sum_xy, avg_x, avg_y, avg_xx, avg_xy As Double
    Dim amplitude_degree, amplitude_degree_precision As Double
    Dim frequency_degree, frequency_degree_precision As Double
    Dim degree_precision As Double: degree_precision = 1
    Dim optimal_found, optimal, last_optimal_state, arry_zeroed As Boolean
    Dim arry_up() As Double: ReDim arry_up(1 To items)
    Dim arry_down() As Double: ReDim arry_down(1 To items)
    Dim arry_average() As Double: ReDim arry_average(1 To items)
    Dim arry_sqr_sum, BMA_arry_sqr_sum, RMS_arry, RMS_BMA_arry As Double
    Dim frequency() As Long: ReDim frequency(1 To items)
    Dim diff_frequency() As Long: ReDim diff_frequency(1 To items - 1)
    Dim diff_diff_frequency() As Long: ReDim diff_diff_frequency(1 To items - 2)
    Dim frequency_set(1 To 3) As Long
    
    If (theRange.Columns.Count > 1) Then Er(0) = " Too Many Columns Selected": GoTo ExitFunction
    If (waves < 1) Then Er(0) = " # of Waves < 1": GoTo ExitFunction
    If (iterations < 1) Then Er(0) = " # of Iterations < 1": GoTo ExitFunction
    If (precision < 1) Or (precision > 8) Then Er(0) = " Precision = {1, 2, 3, 4, 5, 6, 7, 8}": GoTo ExitFunction
    
    For i = 1 To precision
        degree_precision = degree_precision / 10
    Next i
    
    sum_y = 0
    sum_xy = 0
    
    For i = 1 To items
        sum_y = sum_y + arry(i)
        sum_xy = sum_xy + i * arry(i)
    Next i
    
    avg_y = sum_y / items
    avg_xy = sum_xy / items
    
    avg_x = (items + 1) / 2
    avg_xx = (items + 1) * (2 * items + 1) / 6
    
    b = (avg_xy - avg_x * avg_y) / (avg_xx - avg_x * avg_x)
    a = avg_y - (b * avg_x)
    
    For i = 1 To items
        matrix(i, 1) = a + (b * i)
        arry(i) = arry(i) - matrix(i, 1)
    Next i
    
    arry_zeroed = False
    
    For k = 1 To waves
    
        sum_y = 0
        
        For i = 1 To items
            sum_y = sum_y + Abs(arry(i))
        Next i
    
        If (sum_y = 0) Then arry_zeroed = True
    
        If arry_zeroed Then
        
            For i = 1 To items
                matrix(i, k + 1) = arry(i)
            Next i
        
        Else
        
            amplitude_degree = 0
            amplitude_degree_precision = 1
            optimal_found = False
    
            For i = 1 To items
                arry_average(i) = arry(i)
            Next i
        
            For j = 1 To iterations
                arry_up(1) = arry_average(1)
            
                For i = 2 To items
                    arry_up(i) = (arry_up(i - 1) + Exp(amplitude_degree) * arry_average(i)) / (1 + Exp(amplitude_degree))
                Next i
            
                arry_down(items) = arry_average(items)
            
                For i = (items - 1) To 1 Step -1
                    arry_down(i) = (arry_down(i + 1) + Exp(amplitude_degree) * arry_average(i)) / (1 + Exp(amplitude_degree))
                Next i
            
                For i = 1 To items
                    arry_average(i) = (arry_up(i) + arry_down(i)) / 2
                Next i
            Next j
    
            arry_sqr_sum = 0
            BMA_arry_sqr_sum = 0
            RMS_arry = 0
            RMS_BMA_arry = 0
        
            For i = 1 To items
                arry_sqr_sum = arry_sqr_sum + arry(i) * arry(i)
                BMA_arry_sqr_sum = BMA_arry_sqr_sum + arry_average(i) * arry_average(i)
            Next i
        
            RMS_arry = Sqr(arry_sqr_sum / items)
            RMS_BMA_arry = Sqr(BMA_arry_sqr_sum / items)
        
            If ((RMS_arry / RMS_BMA_arry) > 2) Then
                optimal = True
            Else
                optimal = False
            End If
   
            last_optimal_state = optimal
        
            Do
                For i = 1 To items
                    arry_average(i) = arry(i)
                Next i
            
                For j = 1 To iterations
                    arry_up(1) = arry_average(1)
                
                    For i = 2 To items
                        arry_up(i) = (arry_up(i - 1) + Exp(amplitude_degree) * arry_average(i)) / (1 + Exp(amplitude_degree))
                    Next i
                
                    arry_down(items) = arry_average(items)
                
                    For i = (items - 1) To 1 Step -1
                        arry_down(i) = (arry_down(i + 1) + Exp(amplitude_degree) * arry_average(i)) / (1 + Exp(amplitude_degree))
                    Next i
                
                    For i = 1 To items
                        arry_average(i) = (arry_up(i) + arry_down(i)) / 2
                    Next i
                Next j
    
                arry_sqr_sum = 0
                BMA_arry_sqr_sum = 0
                RMS_arry = 0
                RMS_BMA_arry = 0
            
                For i = 1 To items
                    arry_sqr_sum = arry_sqr_sum + arry(i) * arry(i)
                    BMA_arry_sqr_sum = BMA_arry_sqr_sum + arry_average(i) * arry_average(i)
                Next i
            
                RMS_arry = Sqr(arry_sqr_sum / items)
                RMS_BMA_arry = Sqr(BMA_arry_sqr_sum / items)
            
                If ((RMS_arry / RMS_BMA_arry) > 2) Then
                    optimal = True
                Else
                    optimal = False
                End If
    
                If (Not optimal) And (Not last_optimal_state) Then
                    amplitude_degree = amplitude_degree - amplitude_degree_precision
                ElseIf (Not optimal) And (last_optimal_state) Then
                    amplitude_degree = amplitude_degree - amplitude_degree_precision
                    amplitude_degree_precision = amplitude_degree_precision / 10
                ElseIf (optimal) And (last_optimal_state) Then
                    amplitude_degree = amplitude_degree + amplitude_degree_precision
                ElseIf (optimal) And (Not last_optimal_state) Then
                    amplitude_degree = amplitude_degree + amplitude_degree_precision
                    amplitude_degree_precision = amplitude_degree_precision / 10
                End If
        
                If (optimal) And (amplitude_degree_precision <= degree_precision) Then optimal_found = True
                If (Abs(amplitude_degree) >= 100) Then optimal_found = True
        
                last_optimal_state = optimal
    
            Loop Until optimal_found
    
            frequency_degree = 0
            frequency_degree_precision = 1
            optimal_found = False
    
            For i = 1 To items
                arry_average(i) = arry(i)
            Next i
        
            For j = 1 To iterations
                arry_up(1) = arry_average(1)
            
                For i = 2 To items
                    arry_up(i) = (arry_up(i - 1) + Exp(frequency_degree) * arry_average(i)) / (1 + Exp(frequency_degree))
                Next i
            
                arry_down(items) = arry_average(items)
            
                For i = (items - 1) To 1 Step -1
                    arry_down(i) = (arry_down(i + 1) + Exp(frequency_degree) * arry_average(i)) / (1 + Exp(frequency_degree))
                Next i
            
                For i = 1 To items
                    arry_average(i) = (arry_up(i) + arry_down(i)) / 2
                Next i
            Next j
    
            frequency_set(1) = 0
            frequency_set(2) = 0
            frequency_set(3) = 0
        
            For i = 1 To items
                If (arry_average(i) > 0) Then
                    frequency(i) = 1
                Else
                    frequency(i) = 0
                End If
            Next i
    
            For i = 1 To items - 1
                If ((arry_average(i + 1) - arry_average(i)) > 0) Then
                    diff_frequency(i) = 1
                Else
                    diff_frequency(i) = 0
                End If
            Next i
    
            For i = 1 To items - 2
                If ((arry_average(i + 2) - 2 * arry_average(i + 1) + arry_average(i)) > 0) Then
                    diff_diff_frequency(i) = 1
                Else
                    diff_diff_frequency(i) = 0
                End If
            Next i
    
            For i = 1 To items - 1
                frequency_set(1) = frequency_set(1) + Abs(frequency(i + 1) - frequency(i))
            Next i
    
            For i = 1 To items - 2
                frequency_set(2) = frequency_set(2) + Abs(diff_frequency(i + 1) - diff_frequency(i))
            Next i
    
            For i = 1 To items - 3
                frequency_set(3) = frequency_set(3) + Abs(diff_diff_frequency(i + 1) - diff_diff_frequency(i))
            Next i
    
            mn = frequency_set(1)
            mx = frequency_set(1)
            If frequency_set(2) < mn Then mn = frequency_set(2)
            If frequency_set(2) > mx Then mx = frequency_set(2)
            If frequency_set(3) < mn Then mn = frequency_set(3)
            If frequency_set(3) > mx Then mx = frequency_set(3)
    
            If ((mx - mn) > 3) Then
                optimal = False
            Else
                optimal = True
            End If
    
            last_optimal_state = optimal
        
            Do
        
                For i = 1 To items
                    arry_average(i) = arry(i)
                Next i
            
                For j = 1 To iterations
                    arry_up(1) = arry_average(1)
                
                    For i = 2 To items
                        arry_up(i) = (arry_up(i - 1) + Exp(frequency_degree) * arry_average(i)) / (1 + Exp(frequency_degree))
                    Next i
                
                    arry_down(items) = arry_average(items)
                
                    For i = (items - 1) To 1 Step -1
                        arry_down(i) = (arry_down(i + 1) + Exp(frequency_degree) * arry_average(i)) / (1 + Exp(frequency_degree))
                    Next i
                
                    For i = 1 To items
                        arry_average(i) = (arry_up(i) + arry_down(i)) / 2
                    Next i
                Next j
    
                frequency_set(1) = 0
                frequency_set(2) = 0
                frequency_set(3) = 0
            
                For i = 1 To items
                    If (arry_average(i) > 0) Then
                        frequency(i) = 1
                    Else
                        frequency(i) = 0
                    End If
                Next i
    
                For i = 1 To items - 1
                    If ((arry_average(i + 1) - arry_average(i)) > 0) Then
                        diff_frequency(i) = 1
                    Else
                        diff_frequency(i) = 0
                    End If
                Next i
    
                For i = 1 To items - 2
                    If ((arry_average(i + 2) - 2 * arry_average(i + 1) + arry_average(i)) > 0) Then
                        diff_diff_frequency(i) = 1
                    Else
                        diff_diff_frequency(i) = 0
                    End If
                Next i
    
                For i = 1 To items - 1
                    frequency_set(1) = frequency_set(1) + Abs(frequency(i + 1) - frequency(i))
                Next i
    
                For i = 1 To items - 2
                    frequency_set(2) = frequency_set(2) + Abs(diff_frequency(i + 1) - diff_frequency(i))
                Next i
    
                For i = 1 To items - 3
                    frequency_set(3) = frequency_set(3) + Abs(diff_diff_frequency(i + 1) - diff_diff_frequency(i))
                Next i
    
                mn = frequency_set(1)
                mx = frequency_set(1)
                If frequency_set(2) < mn Then mn = frequency_set(2)
                If frequency_set(2) > mx Then mx = frequency_set(2)
                If frequency_set(3) < mn Then mn = frequency_set(3)
                If frequency_set(3) > mx Then mx = frequency_set(3)
    
                If ((mx - mn) > 3) Then
                    optimal = False
                Else
                    optimal = True
                End If
            
                If (Not optimal) And (Not last_optimal_state) Then
                    frequency_degree = frequency_degree - frequency_degree_precision
                ElseIf (Not optimal) And (last_optimal_state) Then
                    frequency_degree = frequency_degree - frequency_degree_precision
                    frequency_degree_precision = frequency_degree_precision / 10
                ElseIf (optimal) And (Not last_optimal_state) Then
                    frequency_degree = frequency_degree + frequency_degree_precision
                    frequency_degree_precision = frequency_degree_precision / 10
                ElseIf (optimal) And (last_optimal_state) Then
                    frequency_degree = frequency_degree + frequency_degree_precision
                End If
            
                If (optimal) And (frequency_degree_precision <= degree_precision) Then optimal_found = True
                If (Abs(frequency_degree) >= 100) Then optimal_found = True
        
                last_optimal_state = optimal
        
            Loop Until optimal_found
    
            degree = (amplitude_degree + frequency_degree) / 2
    
            For i = 1 To items
                arry_average(i) = arry(i)
            Next i
        
            For j = 1 To iterations
                arry_up(1) = arry_average(1)
            
                For i = 2 To items
                    arry_up(i) = (arry_up(i - 1) + Exp(degree) * arry_average(i)) / (1 + Exp(degree))
                Next i
            
                arry_down(items) = arry_average(items)
            
                For i = (items - 1) To 1 Step -1
                    arry_down(i) = (arry_down(i + 1) + Exp(degree) * arry_average(i)) / (1 + Exp(degree))
                Next i
            
                For i = 1 To items
                    arry_average(i) = (arry_up(i) + arry_down(i)) / 2
                Next i
            Next j
    
            For i = 1 To items
                matrix(i, k + 1) = arry_average(i)
                arry(i) = arry(i) - matrix(i, k + 1)
            Next i
        
        End If
    
    Next k
    
    For i = 1 To items
        matrix(i, waves + 2) = arry(i)
    Next i
    
    TheWaveMatrix = matrix()
    
    Exit Function
    
ExitFunction:

    If Er(0) = "Error" Then Er(0) = " Error - " & err.Number & ", " & err.Description

    TheWaveMatrix = Er()
    
End Function