Should I use a Class or a Structure, (Matrix Tool)

[tonyd5]

I made a Class for matrix operations, [MatrixObject]. I am mainly concerned with the inverse; I need to calculate many large matrix inverse's for this application.( size:~[R100xC100])

Right now the performance for computing the inverse is:

size:50x50 ---- time:~200ms
size:100x100 - time:~2.3s
size:200x200 - time:~29s
That sounds slow but its not, try beating that without purchasing libraries, its hard...

I can probably squeeze out a tiny bit more speed by cleaning the loops... But I'm wondering if turning this into a Structure would have major performance gains and makes sense ('would a smarter better looking programmer do this?').

The matrix code has the following charactistics:

• Large dynamic array member (for matrix values)
• Does not include any class members.
• will be used/declared within a method, copy's made will be minimal.
• speed of operation is important for the application

The speed of this inverse calculation is essential to the application but it contains a large dynamic array. The internet says large arrays are a no go for Structs... But are there circumstances where you would use a Struct anyway? Also, what happens if the Struct w/ methods is wrapped in Class?

My knowledge of stack and heap is to the extent of stuff said in youtube videos. I don't have a deep enough understanding to answer this question.

I would like to get some more info on exactly what can happen if a structure is too large. Does the complexity of the methods also affect stack usage? Do structures get compiled differently than classes do? (different assembly generated)

Here as example of the Code

As a Class (current version)

' Every thing inside a Class ----------------
Public Class MatrixObject1

    Private Structure Matrix4F_Array
        Dim A() As Matrix4x4
    End Structure

    Private m_ROW_Arrays() As Matrix4F_Array    '<-- array of [Matrix4x4] arrays 
    '
    '   m_ROW_Arrays(0)     .A(0)   .A(1)   .A(3)    ...
    '                       M11     M12     M13   
    '   m_ROW_Arrays(1)     .A(0)   .A(1)   .A(3)    ...
    '                       M21     M22     M23 
    '   m_ROW_Arrays(2)     .A(0)   .A(1)   .A(3)    ...
    '         :             M31     M32     M33 
    '         :

    Public Sub New()
        '...
    End Sub

    Public Shared Function Multiply(ByRef Mat1 As MatrixObject1, ByRef Mat2 As MatrixObject1) As MatrixObject1
        ' ....
    End Function

    Public Shared Function Inverse(ByRef i_Mat As MatrixObject1, ByRef success As Boolean) As MatrixObject1
        ' ....
    End Function

    ' * also includes propertys for size and shared operators: *,+,-
    '   and misc. functions.

End Class

As a Structure w/methods, and wrapper Class (for non essiential/slow methods); what i'm considering doing.

' Structure with only essential, tight functions
Public Structure MatrixStruct

    Private Structure Matrix4F_Array
        Dim A() As Matrix4x4
    End Structure

    Private m_ROW_Arrays() As Matrix4F_Array    '<-- array of [Matrix4x4] arrays 

    Public Shared Function Multiply(ByRef Mat1 As MatrixStruct, ByRef Mat2 As MatrixStruct) As MatrixStruct
        ' ....
    End Function

    Public Shared Function Inverse(ByRef i_Mat As MatrixStruct, ByRef success As Boolean) As MatrixStruct
        ' ....
    End Function

End Structure


' 
' Matrix Class that inlcudes [MatrixStruct] member
'   -Class Methods have error checks and other misc. stuff
Public Class MatrixObject2

    Private m_Struct As MatrixStruct

    Public Sub New()
        '...
    End Sub

    Public Shared Function Multiply(ByRef Mat1 As MatrixObject2, ByRef Mat2 As MatrixObject2) As MatrixObject2
        ' ....
        Dim ret As New MatrixObject2
        ret.m_Struct = MatrixStruct.Multiply(Mat1.m_Struct, Mat2.m_Struct)
        Return ret
    End Function

    '   :
    '   :
    '   :
    ' * also includes propertys for size and shared operators: *,+,-
    '   and misc. functions.
End Class

[Shaggy Hiker]

I don't think turning it into a structure would help any at all, and might end up costing too much. If you make it a structure, it is a value item, which means that if you were to pass it as an argument to a method, you'd be copying in the whole thing. For the larger matrices you are talking about, that could mean a significant chunk of memory being passed around. If you will NEVER pass it as an argument to anything, then you might see some trivial gain, but that's all.

[tonyd5]

Ok,
What if the Structure w/ methods is private within a wrapper Class... So that it is controlled and never unnecessarily copied.

Is that any different then just using a Class?

All the matrix operations (+,-,*) require scanning through a dynamic array(s), getting and setting values. I'm trying to prevent those arrays from being fragmented.

Also, saw a video that implied Structures methods generate different, more efficient assembly than Class methods, is that correct?

[PlausiblyDamp]

I suppose the easiest way would be to try both approaches and time them.

https://benchmarkdotnet.org/ is a great tool for benchmarking dotnet code.

[Shaggy Hiker]

There are differences between classes and structures, but largely at a level that won't matter much, as far as I am aware. For example, if you have a simple loop in a method, that loop will look the same whether in a class or a structure. How you get to the loop might be different, but the loop won't be, and the cost of the loop will out weigh the differences.

You ought to test it out, though. Create a simplified version (or not simplified) of both a class and a structure, then call the method over and over in a loop while timing it using a Stopwatch object. I have a test project that I use for that purpose. It has Test1 and Test2, which I call in the order Test1, Test2, Test2, Test1, then show the timing of each. By running those tests a few times, it is possible to see the cost and the variation within the runs. Inside the TextX methods, most timing requires a loop, because any one call can be too fast to time.

[tonyd5]

working on it...

[tonyd5]

Initial results indicate the Structure w/methods wrapped in a Class is many many times faster.
I need to verify this with more testing. I'll post the code and performance time when finished.

[jmcilhinney]

For the larger matrices you are talking about, that could mean a significant chunk of memory being passed around.

Structures are value types but arrays are classes and therefore reference types. Copying a structure that contains an array will not copy the array; only the reference to the array. If you then modify an element in that array in the copy, it will affect the original. If you assign a new array in the copy, that would not affect the original.

[Shaggy Hiker]

Structures are value types but arrays are classes and therefore reference types. Copying a structure that contains an array will not copy the array; only the reference to the array. If you then modify an element in that array in the copy, it will affect the original. If you assign a new array in the copy, that would not affect the original.

Right. I didn't read the code much at all. For some reason, I was thinking back to a time when a simple matrix (it could ONLY be simple) was built without using arrays. That would be totally unworkable for a matrix of the size described.

[Shaggy Hiker]

Initial results indicate the Structure w/methods wrapped in a Class is many many times faster.
I need to verify this with more testing. I'll post the code and performance time when finished.

That sounds suspicious. Fractionally different would be understandable. Something like this being many times faster sounds like you aren't comparing apples to apples.

[tonyd5]

Structures are value types but arrays are classes and therefore reference types. Copying a structure that contains an array will not copy the array; only the reference to the array. If you then modify an element in that array in the copy, it will affect the original. If you assign a new array in the copy, that would not affect the original.

Yep, figured that out. Had to make copy methods... annoying.
I made structures with arrays members in another program I'm working on; Did NOT have this problem, arrays members were copied just fine...


My suspicion is because the array member is nested (array of array's), it copies byref... Because the value of each array item is a pointer to another array, the pointer value gets copied but still points to the same thing.

Public Structure MatrixStruct

    Private Structure Matrix4F_Array
        Dim A() As Matrix4x4
    End Structure

    Private m_ROW_Arrays() As Matrix4F_Array    '<-- array of [Matrix4x4] arrays 
    '
    '   m_ROW_Arrays(0)	     .A(0)	 .A(1)	    .A(3)    ...
    '                       (4x4)11	(4x4)12	   (4x4)13   
    '   m_ROW_Arrays(1)      .A(0)       .A(1)      .A(3)    ...
    '                       (4x4)21	(4x4)22	   (4x4)23 
    '   m_ROW_Arrays(2)      .A(0)       .A(1)      .A(3)    ...
    '         :             (4x4)31	(4x4)32	   (4x4)33 
    '         :


    '	:
    '	:
    '	:

End Structure

[Shaggy Hiker]

There is no method that can copy classes that is generic enough to use on everything and efficient enough that it is justified, so having people write copy methods, while annoying, is probably a good design decision. Some languages will take other routes, though, if they are willing to make a few sacrifices.

[tonyd5]

There is no method that can copy classes that is generic enough to use on everything and efficient enough that it is justified, so having people write copy methods, while annoying, is probably a good design decision. Some languages will take other routes, though, if they are willing to make a few sacrifices.

... I have made a universial clone function for anything. makes deep sea copys of all members(any type including objects) and can handle arrays of arrays of arrays....

Its monster, very slow. I only use it as a band aid when I don't want to think.

Public Module UtilitiesXXX




    '--- Clone object to get new instance with identical member values ------
    '
    '   returns a new instance of the object
    '
    Public Function clone(Of K)(copyObj As K) As K

        Dim newObj As K


        '--- for cloning arrays -----------------------------
        If copyObj.GetType.IsArray Then
            Dim arrObj As Object = copyObj

            Dim tArr As Array = Array.CreateInstance(arrObj(0).GetType, UBound(arrObj) + 1)

            '-- for all objects in array clone values -----
            For i As Integer = 0 To UBound(arrObj)

                tArr(i) = clone(arrObj(i))
            Next
            '----------------------------------------------

            newObj = CTypeDynamic(tArr, copyObj.GetType)

            Return newObj

        End If


        '--- for cloning non-arrays ------------------------
        newObj = get_new_instance_ofObject(newObj, copyObj)

        clone_members(newObj, copyObj)

        Return newObj

    End Function



    '--- returns new instance of Class or Value Type passed in
    Private Function get_new_instance_ofObject(Of K)(ByRef newVal As Object, ByVal of_obj As K) As K

        Dim ty As Type = of_obj.GetType


        If ty.IsArray Then _
            Throw New Exception("attmepting to create of a non array instance of an array object")


        If ty.IsClass Then _
            Return ty.GetConstructor(New System.Type() {}).Invoke(New K() {})


        If ty.IsValueType Then _
            Return CTypeDynamic(newVal, ty)


        Return Nothing
    End Function


    '--- sets field info value for Classes, Structs, and System types
    '---
    Private Sub SmartSetValue(Of K, T)(finfo As System.Reflection.FieldInfo,
                                       ByRef newObj As K,
                                       copyVal As T)

        Dim ty As Type = newObj.GetType

        '---- see if type is a standard system type ----
        Dim str As String = "System"
        Dim is_system_type As Boolean =
                ty.IsPrimitive Or
                Strings.Left(ty.Namespace, Len(str)) = str Or
                ty.IsEnum


        If is_system_type Then
            finfo.SetValue(newObj, copyVal)
            Exit Sub
        End If

        '----------------------------------------

        If ty.IsClass Then
            finfo.SetValue(newObj, copyVal)
            Exit Sub
        End If

        '----------------------------------------

        If ty.IsValueType Then
            Dim x As ValueType = CTypeDynamic(newObj, newObj.GetType)
            finfo.SetValue(x, copyVal)
            newObj = CTypeDynamic(x, newObj.GetType)
            Exit Sub
        End If



    End Sub




    '--- Clone object (1 member deep) to get new instance with identical member values ------
    '
    '   updates 'newObj' by ref

    '   returns True if @ no more seeded members
    '
    Private Sub clone_members(ByRef newObj_ As Object, ByVal baseObj As Object)


        Dim myObj As New Object            '<-- memeber feild as object
        Dim newObj As Object = newObj_

        Dim objType As Type                         '<-- type name for feild             
        Dim fInfo As System.Reflection.FieldInfo    '<-- feild info object


        Dim fInfo_arr() As System.Reflection.FieldInfo    '<-- feild info object
        Dim newfInfo_arr() As System.Reflection.FieldInfo



        objType = baseObj.GetType()
        fInfo_arr = objType.GetFields()



        For Each fInfo In fInfo_arr


            myObj = fInfo.GetValue(baseObj)                 '<-- get field object of "baseObj"



            '-- set null values case -----------------
            If IsNothing(myObj) Then
                SmartSetValue(fInfo, newObj_, myObj)
                Continue For
            End If
            '-----------------------------------------


            '-- get reference to 'newObj_' feild  -----
            '-- and Type of 'myObj'
            objType = myObj.GetType
            '-------------------------------------------


            '--- for standard system types case -------------------
            '------------------------------------------------------
            Dim str As String = "System"
            Dim is_system_type As Boolean =
                objType.IsPrimitive Or
                Strings.Left(objType.Namespace, Len(str)) = str Or
                objType.IsEnum

            If is_system_type Then
                SmartSetValue(fInfo, newObj_, myObj)
                Continue For
            End If
            '------------------------------------------------------
            '------------------------------------------------------


            '-- see if member feild is an array -------------------
            '-- if so recall 'clone_members' for all
            '-- objects in array
            If myObj.GetType.IsArray Then

                '-- make sure array is declared ----
                Try
                    Dim i = UBound(myObj)
                Catch ex As Exception
                    myObj = Nothing
                    SmartSetValue(fInfo, newObj_, myObj)
                    Continue For
                End Try
                '-----------------------------------

                '-- create an array instance for new values --
                objType = myObj(0).GetType
                Dim tArr As Array = Array.CreateInstance(objType, UBound(myObj) + 1)


                '-- for all objects in array clone values -----
                For i As Integer = 0 To UBound(myObj)

                    tArr(i) = clone(myObj(i))
                Next
                '----------------------------------------------
                SmartSetValue(fInfo, newObj_, tArr)
                Continue For

            End If
            '------------------------------------------------------
            '------------------------------------------------------




            '-- see if member feild has seeded values -----
            '-- if so recall 'clone_members' for object 
            newfInfo_arr = objType.GetFields()
            If newfInfo_arr.Length > 0 And Not (IsNothing(newfInfo_arr)) Then

                Dim currObj As New Object
                currObj = clone(myObj)

                SmartSetValue(fInfo, newObj_, currObj)
            End If
            '-----------------------------------------------


        Next

    End Sub



End Module

Current time performance
50x50: 5ms
100x100: 50ms
125x125: 90ms
150x150: 134ms
200x200: 290ms (but the result is incorrect, weird)

~100x faster.
Don't know for certain if this is 100% due to the Struct yet.

I'm still working on this. Adding print functions so I can actually see the Matrix while debugging and write to a CSV... I want it to be nice before posting it.

[Shaggy Hiker]

That universal clone won't work for EVERYTHING, it will work for certain things. For example, what happens if the array is an array of Object, where the actual items in the array are a variety of things, such as the first being an integer, the second being a string, and so forth. What type will arrObj(0).GetType return for such an array?

Another, more contrived, variation would be: What happens if the array is an array of classes that maintain a DB connection? What should the state of those connections be in the cloned array?

[PlausiblyDamp]

Don't know for certain if this is 100% due to the Struct yet.

I'm still working on this. Adding print functions so I can actually see the Matrix while debugging and write to a CSV... I want it to be nice before posting it.

Looking at this and your original post, I am not convinced that switching between a struct and a class would yield much of a performance difference. If there are speedups to be had they are probably more likely to be found in the implementation of the various methods that manipulate the matricies (Inverse etc.) or in the choice of data structure / access. Arrays and nested arrays can have performance issues depending on how they are accessed , there might be cleaner approaches compared to arrays of arrays perhaps.

[tonyd5]

Your suspiscions are correct, The Structure was NOT the cause of the major performance gain... The changing the Structure to a Class was only few % points slower...



What was change:

In the old version, in all the matrix operations (+,-,*) the size of the matrix's was checked. Like, before multipling these matrices check that the size's are vaild first... Real quick If statments in every operation method.

In the new version, A Structure w/ (+,-,*,..) methods was made. These methods did NOT have any if statements... Just assumed the matrices were of correct size and went right into scanning arrays and doing math.
The Structure was also conertrained to only do operations on (4x4) blocks (Matrix4x4)


So for the inverse method, which is hundreds of multiplications and adding & subtracting, hundreds of reduntant If statements were no longer executed...

I don't think the If checks were soaking up time but rather messing up the LUT or whatever... preventing next predictable memory location being ready to go in RAM.

The structure of arrays was NOT changed.

The matrix operations (+,-,*) were not changed significantly, other than removing reduntant If statements.

The biggest change was converting the seocond matrix into Column Major form when multipling, Which may or may not save time.

The inverse operation was not changed...

-----------------------

Whatever, below is the code and Demo. The only problem I encounted is that for matrices >150x150 the inverse because less accurate to invently invalid. Probably because a single does not have precission.
For example the array is 256x256... =2^16... A float (24b + 8exp), will only have 24b-16b=8b of precision for each value in matrix.


Demo of [MatrixObject] Class

Module MatrixObject_DEMO_MODULE

    Public Sub MatrixObject_demo()


        '~~~~~~~~   Properties: copy() , matrix_item(,) , row() , col()  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        '~~~~~
        '~~
        Dim x1 As New MatrixObject
        Dim Rsize As Integer
        Dim Csize As Integer
        Dim Rarr() As Single
        Dim Carr() As Single
        Dim valS As Single

        x1.matrix_item(row:=1, col:=1) = 11.0!
        x1.matrix_item(row:=1, col:=2) = 12.0!
        x1.matrix_item(row:=1, col:=3) = 13.0!

        Rsize = x1.RowSize
        Csize = x1.ColSize
        Rarr = x1.row(1)
        Carr = x1.col(3)

        x1.matrix_item(row:=2, col:=3) = 23.0!
        x1.matrix_item(row:=2, col:=4) = 24.0!
        x1.Print2Console()       '<-- prints to debug output when in debug mode


        For i As Integer = 1 To x1.RowSize
            Rarr = x1.row(i)
        Next

        For i As Integer = 1 To x1.ColSize
            Carr = x1.col(i)
        Next

        x1.row(1) = New Single() {11, 12, 13, 14, 15, 16}
        x1.row(2) = New Single() {21, 22, 23, 24, 25, 26}
        x1.row(3) = New Single() {31, 32, 33, 34, 35, 36}
        x1.row(4) = New Single() {41, 42, 43, 44, 45, 46}
        x1.col(7) = New Single() _
            {17,
            27,
            37,
            47}

        x1.Print2Console()

        Dim xCopy As MatrixObject = x1.copy
        xCopy *= 100
        xCopy.RowSize = 3
        '
        For i As Integer = 1 To xCopy.RowSize
            For j As Integer = 1 To xCopy.ColSize
                valS = xCopy.matrix_item(i, j)
            Next
        Next

        Console.WriteLine("xCopy")
        xCopy.Print2Console()
        '
        Console.WriteLine("x1")
        x1.Print2Console()


        '~~~~~~~~   Operators: + , - , *    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        '~~~~~
        '~~

        ' add, subtract, scaler multiple --------------------------
        Dim x2 As New MatrixObject
        Dim x3 As New MatrixObject
        Dim x4 As New MatrixObject
        Dim x5 As New MatrixObject
        Dim x6 As New MatrixObject
        Dim x7 As New MatrixObject
        '
        x2.row(1) = New Single() {10, 10, 10, 10, 10, 10}
        x2.row(2) = New Single() {20, 20, 20, 20, 20, 20}
        x2.row(3) = New Single() {30, 30, 30, 30, 30, 30}
        x2.row(4) = New Single() {40, 40, 40, 40, 40, 40}
        '
        x3.row(1) = New Single() {1, 2, 3, 4, 5, 6}
        x3.row(2) = New Single() {1, 2, 3, 4, 5, 6}
        x3.row(3) = New Single() {1, 2, 3, 4, 5, 6}
        x3.row(4) = New Single() {1, 2, 3, 4, 5, 6}

        x4 = x2 + x3
        Console.WriteLine("x4")
        x4.Print2Console()

        ' x5=x4 * 4
        x5 = x4.copy
        x5 = x5 + x4
        x5 += x4
        x5 = MatrixObject.Add(x5, x4)
        Console.WriteLine("x5")
        x5.Print2Console()

        ' x6=x4 * 4
        x6 = x4 * 1.0!
        x6 *= 2.0!
        x6 = MatrixObject.Multiply(x6, 2.0!)
        Console.WriteLine("x6")
        x6.Print2Console()

        x7 = x6 - x5
        x7 = MatrixObject.Subtract(x7, x5)
        x7 -= (x5 * (-1.0!))
        Console.WriteLine("x7")
        x7.Print2Console()



        ' matrix multiply ---------------------------------------
        x2 = New MatrixObject
        x3 = New MatrixObject
        '
        x2.row(1) = New Single() {1, 2, 3}
        x3.col(1) = New Single() {1, 2, 3}
        x4 = x2 * x3
        Console.WriteLine("x4")
        x4.Print2Console()

        '----

        x2 = New MatrixObject
        x3 = New MatrixObject
        '
        x2.row(1) = New Single() {2, 2, 2, 2}
        x2.row(2) = New Single() {3, 3, 3, 3}
        '
        x3.col(1) = New Single() {1, 2, 3, 4}
        x3.col(2) = New Single() {1, 2, 3, 4}

        x4 = x2 * x3
        Console.WriteLine("x4")
        x4.Print2Console()

        '~~~~~~~~   Methods: Transpose(), Invert(), CSV_view()   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        '~~~~~
        '~~

        ' Transpose() --------------------------------------

        x1 = New MatrixObject
        x2 = New MatrixObject

        x1.row(1) = New Single() {11, 12, 13, 14, 15, 16}
        x1.row(2) = New Single() {21, 22, 23, 24, 25, 26}
        x1.row(3) = New Single() {31, 32, 33, 34, 35, 36}
        x1.row(4) = New Single() {41, 42, 43, 44, 45, 46}

        x2 = x1.Transpose
        Console.WriteLine("x1")
        x1.Print2Console()
        '
        Console.WriteLine("transpose")
        x2.Print2Console()

        ' Invert() -----------------------------------------

        Dim startSize As Integer = 40
        Dim endSize As Integer = 160
        Dim stepSize As Integer = 20

        Dim durrMS() As Single : ReDim durrMS(0)
        Dim matCNT() As Single : ReDim matCNT(0)
        Dim k As Integer = 0

        Dim Xmat As New MatrixObject
        Dim Ymat As New MatrixObject
        Dim Zmat As New MatrixObject

        For currSize As Integer = startSize To endSize Step stepSize

            'MatrixObject.m_dummy = 0

            Xmat.Size = currSize

            For i As Integer = 1 To currSize
                For j As Integer = 1 To currSize
                    Xmat.matrix_item(i, j) = CInt((Rnd()) * endSize)
                Next
            Next

            Dim timer As New System.Diagnostics.Stopwatch

            Dim success As Boolean

            timer.Start()
            Ymat = Xmat.Invert(success)
            timer.Stop()

            If success = False Then
                MsgBox("unable to find inverse")
            End If

            'Zmat = Ymat * Xmat
            'Console.WriteLine("XMAT")
            'Xmat.Print2Console("G2")
            'Console.WriteLine("YMAT")
            'Ymat.Print2Console("G2")
            'Console.WriteLine("ZMAT")
            'Zmat.Print2Console("G2")

            ReDim Preserve durrMS(k)
            ReDim Preserve matCNT(k)
            durrMS(k) = timer.ElapsedMilliseconds
            matCNT(k) = currSize
            k += 1

        Next

        Zmat = Ymat * Xmat
        Console.WriteLine("XMAT")
        Xmat.Print2Console("G2")
        Console.WriteLine("YMAT")
        Ymat.Print2Console("G2")
        Console.WriteLine("ZMAT")
        Zmat.Print2Console("G2")

        ' create CSV of Inverse*MAT, should equal Identity matrix
        Zmat.ToCSV(filename:="newCSV")

        ' create CSV of performance results
        Dim prfrmnceMAT As New MatrixObject
        prfrmnceMAT.col(1) = matCNT
        prfrmnceMAT.col(2) = durrMS
        prfrmnceMAT.ToCSV(filename:="MatrixDemo_InvertPerformance")

    End Sub

End Module

[tonyd5]

Could not fit everything in 1 post....

Code for Structure & Class

Imports System.Numerics


Imports System.Runtime.InteropServices


' Structure with only essential, tight functions
Public Structure MatrixStruct

    Public Structure Matrix4F_Array
        Dim A() As Matrix4x4
    End Structure

    Private m_ROW_Arrays() As Matrix4F_Array    '<-- array of [Matrix4x4] arrays 

    Private p_BR_size As Integer
    Private p_BC_size As Integer


    Public Sub setSize(RowBlck_sz As Integer, ColBlck_sz As Integer)

        If Me.p_BR_size < 1 Then
            ReDim Me.m_ROW_Arrays(0)
            ReDim Me.m_ROW_Arrays(0).A(0)
        End If

        Dim chg_row As Boolean = False
        Dim chg_col As Boolean = False

        If Me.p_BR_size <> RowBlck_sz Then
            chg_row = True
            If Me.p_BR_size < RowBlck_sz Then
                chg_col = True
            End If
        End If
        '
        If Me.p_BC_size <> ColBlck_sz Then
            chg_col = True
        End If


        If chg_row Then
            Me.p_BR_size = RowBlck_sz
            ReDim Preserve Me.m_ROW_Arrays(Me.p_BR_size - 1)
        End If

        If chg_col Then
            Me.p_BC_size = ColBlck_sz
            For i As Integer = 0 To Me.p_BR_size - 1
                ReDim Preserve Me.m_ROW_Arrays(i).A(Me.p_BC_size - 1)
            Next
        End If

    End Sub


    Public Function RowBlockSize() As Integer
        Return Me.p_BR_size
    End Function

    Public Function ColBlockSize() As Integer
        Return Me.p_BC_size
    End Function


    Public Property MatBlock(rowb As Integer, colb As Integer) As Matrix4x4
        Get
            Return Me.m_ROW_Arrays(rowb - 1).A(colb - 1)
        End Get
        Set(value As Matrix4x4)
            Me.m_ROW_Arrays(rowb - 1).A(colb - 1) = value
        End Set
    End Property


    Public Function copy() As MatrixStruct
        Dim o_res = New MatrixStruct
        o_res.setSize(Me.p_BR_size, Me.p_BC_size)

        For i As Integer = 0 To Me.p_BR_size - 1
            o_res.m_ROW_Arrays(i).A = Me.m_ROW_Arrays(i).A.Clone
        Next
        Return o_res
    End Function


    Private Property row_BLOCKS(i As Integer) As Matrix4x4()
        Get
            Return Me.m_ROW_Arrays(i - 1).A
        End Get
        Set(value As Matrix4x4())
            Me.m_ROW_Arrays(i - 1).A = value
        End Set
    End Property



    Private Property col_BLOCKS(i As Integer) As Matrix4x4()
        Get
            Dim ret() As Matrix4x4 : ReDim ret(p_BR_size - 1)
            For j As Integer = 0 To (p_BR_size - 1)
                ret(j) = Me.m_ROW_Arrays(j).A(i - 1)
            Next
            Return ret
        End Get
        Set(value As Matrix4x4())
            For j As Integer = 0 To (p_BR_size - 1)
                Me.m_ROW_Arrays(j).A(i - 1) = value(j)
            Next
        End Set
    End Property

    ' Public Operator Methods ===========================================

    Public Shared Function Multiply(ByRef Mat1 As MatrixStruct, ByRef Mat2 As MatrixStruct) As MatrixStruct

        Dim row_len As Integer = Mat1.p_BR_size - 1
        Dim col_len As Integer = Mat2.p_BC_size - 1
        Dim len2 As Integer = Mat1.p_BC_size

        Dim o_RES As New MatrixStruct
        ReDim o_RES.m_ROW_Arrays(row_len)
        For i As Integer = 0 To row_len
            ReDim o_RES.m_ROW_Arrays(i).A(col_len)
        Next
        '
        o_RES.p_BR_size = row_len + 1
        o_RES.p_BC_size = col_len + 1

        Dim col_MAJOR As New MatrixStruct
        ReDim col_MAJOR.m_ROW_Arrays(col_len)
        For i As Integer = 1 To (col_len + 1)
            col_MAJOR.row_BLOCKS(i) = Mat2.col_BLOCKS(i)
        Next


        Dim r As Integer = 0
        For Each row_ARRAY As Matrix4F_Array In Mat1.m_ROW_Arrays
            Dim c As Integer = 0
            For Each col_ARRAY As Matrix4F_Array In col_MAJOR.m_ROW_Arrays

                o_RES.m_ROW_Arrays(r).A(c) = MatrixStruct.DOTproduct(row_ARRAY.A, col_ARRAY.A, len2)
                c += 1
            Next
            r += 1
        Next
        Return o_RES
    End Function


    Public Shared Function MultiplyScaler(ByRef Mat1 As MatrixStruct, ByRef S As Single) As MatrixStruct

        Dim o_RES As MatrixStruct = Mat1.copy

        Dim r As Integer = 0
        For Each row_ARRAY As Matrix4F_Array In o_RES.m_ROW_Arrays
            Dim c As Integer = 0
            For Each col_MAT As Matrix4x4 In row_ARRAY.A
                o_RES.m_ROW_Arrays(r).A(c) = Matrix4x4.Multiply(col_MAT, S)
                c += 1
            Next
            r += 1
        Next
        Return o_RES
    End Function


    Public Shared Function Add(ByRef Mat1 As MatrixStruct, ByRef Mat2 As MatrixStruct) As MatrixStruct
        Dim o_RES As MatrixStruct = Mat1.copy
        For i As Integer = 0 To o_RES.p_BR_size - 1
            o_RES.m_ROW_Arrays(i).A = MatrixStruct.ADDvector(Mat1.m_ROW_Arrays(i).A, Mat2.m_ROW_Arrays(i).A, o_RES.p_BC_size)
        Next
        Return o_RES
    End Function

    Public Shared Function Subtract(ByRef Mat1 As MatrixStruct, ByRef Mat2 As MatrixStruct) As MatrixStruct
        Dim o_RES As MatrixStruct = Mat1.copy
        For i As Integer = 0 To o_RES.p_BR_size - 1
            o_RES.m_ROW_Arrays(i).A = MatrixStruct.SUBTRACTvector(Mat1.m_ROW_Arrays(i).A, Mat2.m_ROW_Arrays(i).A, o_RES.p_BC_size)
        Next
        Return o_RES
    End Function



    Public Shared Sub Inverse(ByRef i_Mat As MatrixStruct, ByRef invA As MatrixStruct, ByRef success As Boolean)

        Dim N_blocks As Integer = i_Mat.p_BR_size
        Dim B As MatrixStruct
        Dim C As MatrixStruct
        Dim D As MatrixStruct

        Dim x1 As MatrixStruct
        Dim x2 As MatrixStruct
        Dim x3 As MatrixStruct
        Dim x4 As MatrixStruct

        ReDim invA.m_ROW_Arrays(0)
        ReDim invA.m_ROW_Arrays(0).A(0)
        invA.p_BR_size = 1
        invA.p_BC_size = 1

        success = Matrix4x4.Invert(i_Mat.m_ROW_Arrays(0).A(0), invA.m_ROW_Arrays(0).A(0))
        If success = False Then Exit Sub


        For i As Integer = 2 To N_blocks

            B = MatrixStruct.get_sub_BLOCKS(i_Mat, 1, i, i - 1, i)
            C = MatrixStruct.get_sub_BLOCKS(i_Mat, i, 1, i, i - 1)
            D = MatrixStruct.get_sub_BLOCKS(i_Mat, i, i, i, i)

            x4 = MatrixStruct.Multiply(invA, B)
            x4 = MatrixStruct.Multiply(C, x4)
            x4 = MatrixStruct.Subtract(D, x4)
            success = Matrix4x4.Invert(x4.m_ROW_Arrays(0).A(0), x4.m_ROW_Arrays(0).A(0))
            If success = False Then Exit Sub

            '----------------------------------------

            x1 = MatrixStruct.Multiply(x4, C)
            x1 = MatrixStruct.Multiply(x1, invA)
            x1 = MatrixStruct.Multiply(B, x1)
            x1 = MatrixStruct.Multiply(invA, x1)
            x1 = MatrixStruct.Add(invA, x1)

            '----------------------------------------

            x2 = MatrixStruct.Multiply(B, x4)
            x2 = MatrixStruct.Multiply(invA, x2)
            x2 = MatrixStruct.MultiplyScaler(x2, -1.0!)

            '----------------------------------------

            x3 = MatrixStruct.MultiplyScaler(x4, -1.0!)
            x3 = MatrixStruct.Multiply(x3, C)
            x3 = MatrixStruct.Multiply(x3, invA)

            '----------------------------------------

            invA = x1
            invA.p_BR_size = x1.p_BR_size + 1
            invA.p_BC_size = x1.p_BC_size + 1

            ReDim Preserve invA.m_ROW_Arrays(invA.p_BR_size - 1)
            invA.m_ROW_Arrays(invA.p_BR_size - 1) = x3.m_ROW_Arrays(0)

            For j As Integer = 0 To (invA.p_BR_size - 2)
                ReDim Preserve invA.m_ROW_Arrays(j).A(invA.p_BC_size - 1)
                invA.m_ROW_Arrays(j).A(invA.p_BC_size - 1) = x2.m_ROW_Arrays(j).A(0)
            Next

            ReDim Preserve invA.m_ROW_Arrays(invA.p_BR_size - 1).A(invA.p_BC_size - 1)
            invA.m_ROW_Arrays(invA.p_BR_size - 1).A(invA.p_BC_size - 1) = x4.m_ROW_Arrays(0).A(0)

            '    _     _   __
            '   |       | |  |
            '   |   X1  | |x2|
            '   |_     _| |__|
            '    _     _   __
            '   |_  x3 _| |x4|
            '
        Next

    End Sub

    '=== private methods used by operators ================================

    Private Shared Function DOTproduct(ByRef x1() As Matrix4x4, ByRef x2() As Matrix4x4, ByRef len As Integer) As Matrix4x4
        Dim res As New Matrix4x4
        For i As Integer = 0 To len - 1
            res = Matrix4x4.Add(res, Matrix4x4.Multiply(x1(i), x2(i)))
        Next
        Return res
    End Function


    Private Shared Function ADDvector(ByRef x1() As Matrix4x4, ByRef x2() As Matrix4x4, ByRef len As Integer) As Matrix4x4()
        Dim res() As Matrix4x4 : ReDim res(len - 1)
        For i As Integer = 0 To len - 1
            res(i) = Matrix4x4.Add(x1(i), x2(i))
        Next
        Return res
    End Function

    Private Shared Function SUBTRACTvector(ByRef x1() As Matrix4x4, ByRef x2() As Matrix4x4, ByRef len As Integer) As Matrix4x4()
        Dim res() As Matrix4x4 : ReDim res(len - 1)
        For i As Integer = 0 To len - 1
            res(i) = Matrix4x4.Subtract(x1(i), x2(i))
        Next
        Return res
    End Function



    Private Shared Function get_sub_BLOCKS(ByRef i_MAT As MatrixStruct,
                                           ByRef i_row_block1 As Integer, ByRef i_col_block1 As Integer,
                                           ByRef i_row_block2 As Integer, ByRef i_col_block2 As Integer) As MatrixStruct

        Dim row_len As Integer = i_row_block2 - i_row_block1
        Dim col_len As Integer = i_col_block2 - i_col_block1

        Dim o_RES As New MatrixStruct
        ReDim o_RES.m_ROW_Arrays(row_len)
        For i As Integer = 0 To row_len
            ReDim o_RES.m_ROW_Arrays(i).A(col_len)
        Next
        o_RES.p_BR_size = row_len + 1
        o_RES.p_BC_size = col_len + 1

        Dim r As Integer = 0
        For i As Integer = (i_row_block1 - 1) To (i_row_block2 - 1)

            Dim c As Integer = 0
            For j As Integer = (i_col_block1 - 1) To (i_col_block2 - 1)

                o_RES.m_ROW_Arrays(r).A(c) = i_MAT.m_ROW_Arrays(i).A(j)
                c += 1
            Next
            r += 1
        Next

        Return o_RES
    End Function


End Structure

[tonyd5]

Wrapper Class..

' Matrix wrapper Class, uses MatrixStruct
' has methods and properties that allow matrix to be easily edited and viewed by user
Public Class MatrixObject

    Private m_Struct As MatrixStruct

    Private p_R_size As Integer
    Private p_C_size As Integer

    Public Sub New()
        Me.m_Struct = New MatrixStruct
        Me.m_Struct.setSize(0, 0)
        '
        Me.p_R_size = 0
        Me.p_C_size = 0
    End Sub


    Public Function copy() As MatrixObject
        Dim ret As New MatrixObject

        ret.m_Struct = Me.m_Struct.copy
        '
        ret.p_R_size = Me.p_R_size
        ret.p_C_size = Me.p_C_size
        Return ret
    End Function



    Public Property RowSize() As Integer
        Get
            Return Me.p_R_size
        End Get
        Set(value As Integer)

            Me.p_R_size = value
            Dim a As Integer
            Dim v As Integer
            MatrixObject.index2_block(value, a, v)
            Me.m_Struct.setSize(a, Me.m_Struct.ColBlockSize)

            For j As Integer = 1 To (Me.m_Struct.ColBlockSize)
                MatrixObject.keep_rows(v, Me.m_Struct.MatBlock(a, j))
            Next

        End Set
    End Property


    Public Property ColSize() As Integer
        Get
            Return Me.p_C_size
        End Get
        Set(value As Integer)

            Me.p_C_size = value

            Dim a As Integer
            Dim v As Integer
            MatrixObject.index2_block(value, a, v)
            Me.m_Struct.setSize(Me.m_Struct.RowBlockSize, a)

            For j As Integer = 1 To (Me.m_Struct.RowBlockSize)
                MatrixObject.keep_cols(v, Me.m_Struct.MatBlock(j, a))
            Next

        End Set
    End Property


    Public Property Size() As Integer
        Get
            If Me.RowSize <> Me.ColSize Then
                Return -1
            Else
                Return Me.RowSize
            End If
        End Get
        Set(value As Integer)
            Me.RowSize = value
            Me.ColSize = value
        End Set
    End Property



    Private Property prv_matrix_item(row As Integer, col As Integer) As Single
        Get
            Dim rowB As Integer
            Dim colB As Integer
            Dim rowV As Integer
            Dim colV As Integer

            MatrixObject.index2_block(row, rowB, rowV)
            MatrixObject.index2_block(col, colB, colV)

            Dim ret As Single
            MatrixObject.Matrix4x4_value_IO(MAT4x4_IO.GET_, rowV, colV, Me.m_Struct.MatBlock(rowB, colB), ret)
            Return ret

        End Get
        Set(value As Single)

            Dim rowB As Integer
            Dim colB As Integer
            Dim rowV As Integer
            Dim colV As Integer

            MatrixObject.index2_block(row, rowB, rowV)
            MatrixObject.index2_block(col, colB, colV)

            MatrixObject.Matrix4x4_value_IO(MAT4x4_IO.SET_, rowV, colV, Me.m_Struct.MatBlock(rowB, colB), value)
        End Set
    End Property



    Public Property matrix_item(row As Integer, col As Integer) As Single
        Get

            If row > Me.RowSize Then Return 0
            If col > Me.ColSize Then Return 0

            Return Me.prv_matrix_item(row, col)
        End Get
        Set(value As Single)

            If Me.RowSize < row Then Me.RowSize = row
            If Me.ColSize < col Then Me.ColSize = col

            Me.prv_matrix_item(row, col) = value
        End Set
    End Property




    Public Property row(i As Integer) As Single()
        Get
            Dim array As Single()
            If i < 1 Then Return array
            If Me.RowSize < i Then Return array
            If Me.ColSize < 1 Then Return array

            ReDim array(Me.ColSize - 1)
            For j As Integer = 1 To Me.ColSize
                array(j - 1) = Me.prv_matrix_item(i, j)
            Next
            Return array
        End Get
        Set(value As Single())

            If i < 1 Then Exit Property
            If Me.RowSize < i Then Me.RowSize = i
            If Me.ColSize < value.Length Then Me.ColSize = value.Length

            For j As Integer = 1 To value.Length
                Me.prv_matrix_item(i, j) = value(j - 1)
            Next
        End Set
    End Property


    Public Property col(i As Integer) As Single()
        Get
            Dim array As Single()
            If i < 1 Then Return array
            If Me.ColSize < i Then Return array
            If Me.RowSize < 1 Then Return array

            ReDim array(Me.RowSize - 1)
            For j As Integer = 1 To Me.RowSize
                array(j - 1) = Me.prv_matrix_item(j, i)
            Next
            Return array
        End Get
        Set(value As Single())

            If i < 1 Then Exit Property
            If Me.ColSize < i Then Me.ColSize = i
            If Me.RowSize < value.Length Then Me.RowSize = value.Length

            For j As Integer = 1 To value.Length
                Me.prv_matrix_item(j, i) = value(j - 1)
            Next

        End Set
    End Property



    Public Shared Function Multiply(ByRef i_MatObj1 As MatrixObject, ByRef i_MatObj2 As MatrixObject) As MatrixObject

        If i_MatObj1.RowSize < 1 Then Return New MatrixObject
        If i_MatObj2.RowSize < 1 Then Return New MatrixObject
        If i_MatObj1.ColSize < 1 Then Return New MatrixObject
        If i_MatObj2.ColSize < 1 Then Return New MatrixObject
        If i_MatObj1.ColSize <> i_MatObj2.RowSize Then Return New MatrixObject

        Dim o_res As New MatrixObject
        o_res.m_Struct = MatrixStruct.Multiply(i_MatObj1.m_Struct, i_MatObj2.m_Struct)

        o_res.RowSize = i_MatObj1.RowSize
        o_res.ColSize = i_MatObj2.ColSize
        Return o_res
    End Function



    Public Shared Function Multiply(ByRef i_MatObj As MatrixObject, ByRef C As Single) As MatrixObject

        If i_MatObj.RowSize < 1 Then Return New MatrixObject
        If i_MatObj.ColSize < 1 Then Return New MatrixObject

        Dim o_res As New MatrixObject
        o_res.m_Struct = MatrixStruct.MultiplyScaler(i_MatObj.m_Struct, C)

        o_res.RowSize = i_MatObj.RowSize
        o_res.ColSize = i_MatObj.ColSize
        Return o_res
    End Function


    Public Shared Function Add(ByRef i_MatObj1 As MatrixObject, ByRef i_MatObj2 As MatrixObject) As MatrixObject

        If i_MatObj1.RowSize < 1 Then Return New MatrixObject
        If i_MatObj1.ColSize < 1 Then Return New MatrixObject
        If i_MatObj1.RowSize <> i_MatObj2.RowSize Then Return New MatrixObject
        If i_MatObj1.ColSize <> i_MatObj2.ColSize Then Return New MatrixObject

        Dim o_res As New MatrixObject
        o_res.m_Struct = MatrixStruct.Add(i_MatObj1.m_Struct, i_MatObj2.m_Struct)

        o_res.RowSize = i_MatObj1.RowSize
        o_res.ColSize = i_MatObj1.ColSize
        Return o_res
    End Function


    Public Shared Function Subtract(ByRef i_MatObj1 As MatrixObject, ByRef i_MatObj2 As MatrixObject) As MatrixObject

        If i_MatObj1.RowSize < 1 Then Return New MatrixObject
        If i_MatObj1.ColSize < 1 Then Return New MatrixObject
        If i_MatObj1.RowSize <> i_MatObj2.RowSize Then Return New MatrixObject
        If i_MatObj1.ColSize <> i_MatObj2.ColSize Then Return New MatrixObject

        Dim o_res As New MatrixObject
        o_res.m_Struct = MatrixStruct.Subtract(i_MatObj1.m_Struct, i_MatObj2.m_Struct)

        o_res.RowSize = i_MatObj1.RowSize
        o_res.ColSize = i_MatObj1.ColSize
        Return o_res
    End Function


    Public Shared Operator *(A1 As MatrixObject, A2 As MatrixObject) As MatrixObject
        Return MatrixObject.Multiply(A1, A2)
    End Operator


    Public Shared Operator *(A1 As MatrixObject, x As Single) As MatrixObject
        Return MatrixObject.Multiply(A1, x)
    End Operator


    Public Shared Operator +(A1 As MatrixObject, A2 As MatrixObject) As MatrixObject
        Return MatrixObject.Add(A1, A2)
    End Operator



    Public Shared Operator -(A1 As MatrixObject, A2 As MatrixObject) As MatrixObject
        Return MatrixObject.Subtract(A1, A2)
    End Operator



    Public Shared Function Invert(ByRef i_MAT As MatrixObject, ByRef o_res As MatrixObject) As Boolean

        If i_MAT.RowSize < 1 Then o_res = New MatrixObject : Return False
        If i_MAT.RowSize <> i_MAT.ColSize Then o_res = New MatrixObject : Return False

        Dim org_size As Integer = i_MAT.Size

        i_MAT.Size = i_MAT.m_Struct.RowBlockSize * 4%

        ' make extra row/cols identity
        For j As Integer = (org_size + 1) To i_MAT.Size
            i_MAT.matrix_item(j, j) = 1
        Next

        o_res = New MatrixObject
        Dim success As Boolean

        MatrixStruct.Inverse(i_MAT.m_Struct, o_res.m_Struct, success)

        i_MAT.Size = org_size
        If success Then o_res.Size = org_size

        Return success
    End Function


    Public Function Invert(ByRef success As Boolean) As MatrixObject
        Dim o_res As MatrixObject
        success = MatrixObject.Invert(Me, o_res)
        Return o_res
    End Function


    '' --https://www.youtube.com/watch?v=vGowBXcur1k
    ''
    Public Function Transpose() As MatrixObject

        Dim newObj As New MatrixObject

        newObj.m_Struct.setSize(Me.m_Struct.ColBlockSize, Me.m_Struct.RowBlockSize)

        For i As Integer = 1 To Me.m_Struct.RowBlockSize
            For j As Integer = 1 To Me.m_Struct.ColBlockSize
                newObj.m_Struct.MatBlock(j, i) = Matrix4x4.Transpose(Me.m_Struct.MatBlock(i, j))
            Next
        Next

        newObj.RowSize = Me.ColSize
        newObj.ColSize = Me.RowSize
        Return newObj

    End Function




    Private Shared Sub index2_block(ByRef i_index As Integer, ByRef o_array4x4 As Integer, ByRef o_vector4x4 As Integer)

        If i_index < 1 Then o_array4x4 = 0 : o_vector4x4 = 0 : Exit Sub

        Dim n As Integer = (i_index - 1) \ 4%
        o_array4x4 = n + 1
        o_vector4x4 = i_index - (n) * 4%

    End Sub


    Private Shared Sub keep_rows(ByRef i_row As Integer, ByRef io_MAT As Matrix4x4)
        If i_row = 4 Then Exit Sub
        If i_row = 0 Then io_MAT = New Matrix4x4
        io_MAT = Matrix4x4.Multiply(c_Identity(i_row), io_MAT)
    End Sub

    Private Shared Sub keep_cols(ByRef i_col As Integer, ByRef io_MAT As Matrix4x4)
        If i_col = 4 Then Exit Sub
        If i_col = 0 Then io_MAT = New Matrix4x4
        io_MAT = Matrix4x4.Multiply(io_MAT, c_Identity(i_col))
    End Sub


    Private Shared ReadOnly c_Identity() As Matrix4x4 = New Matrix4x4() {
        New Matrix4x4 With {.M11 = 1, .M22 = 1, .M33 = 1, .M44 = 1},
        New Matrix4x4 With {.M11 = 1, .M22 = 0, .M33 = 0, .M44 = 0},
        New Matrix4x4 With {.M11 = 1, .M22 = 1, .M33 = 0, .M44 = 0},
        New Matrix4x4 With {.M11 = 1, .M22 = 1, .M33 = 1, .M44 = 0},
        New Matrix4x4 With {.M11 = 1, .M22 = 1, .M33 = 1, .M44 = 1}}




    Private Shared Sub Matrix4x4_value_IO(ByRef i_GetSet As MAT4x4_IO,
                                          ByRef i_row As Integer, ByRef i_col As Integer,
                                          ByRef io_MAT As Matrix4x4, ByRef io_val As Single)

        Select Case i_row

            '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            Case 1
                Select Case i_col
                    Case 1
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M11 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M11 : Exit Sub
                        End Select
                    Case 2
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M12 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M12 : Exit Sub
                        End Select
                    Case 3
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M13 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M13 : Exit Sub
                        End Select
                    Case 4
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M14 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M14 : Exit Sub
                        End Select
                End Select
                '------------------------------------

            '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            Case 2
                Select Case i_col
                    Case 1
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M21 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M21 : Exit Sub
                        End Select
                    Case 2
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M22 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M22 : Exit Sub
                        End Select
                    Case 3
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M23 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M23 : Exit Sub
                        End Select
                    Case 4
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M24 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M24 : Exit Sub
                        End Select
                End Select
                '------------------------------------

                '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            Case 3
                Select Case i_col
                    Case 1
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M31 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M31 : Exit Sub
                        End Select
                    Case 2
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M32 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M32 : Exit Sub
                        End Select
                    Case 3
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M33 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M33 : Exit Sub
                        End Select
                    Case 4
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M34 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M34 : Exit Sub
                        End Select
                End Select
                '------------------------------------

            '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            Case 4
                Select Case i_col
                    Case 1
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M41 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M41 : Exit Sub
                        End Select
                    Case 2
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M42 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M42 : Exit Sub
                        End Select
                    Case 3
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M43 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M43 : Exit Sub
                        End Select
                    Case 4
                        Select Case i_GetSet
                            Case MAT4x4_IO.SET_ : io_MAT.M44 = io_val : Exit Sub
                            Case MAT4x4_IO.GET_ : io_val = io_MAT.M44 : Exit Sub
                        End Select
                End Select
                '------------------------------------

        End Select

    End Sub

    Private Enum MAT4x4_IO
        NA = 0
        SET_ = 1
        GET_ = 2
    End Enum


    ' Matrix View/String Convert methods ==================================================

    Public Shared Narrowing Operator CType(ByVal MatObj As MatrixObject) As String
        Return MatObj.ToString("G3")
    End Operator


    Public Sub Print2Console(Optional format As String = "G")
        Static k As Integer = 0
        If k = 0 Then
            k = 1
            Win32.AllocConsole()
        End If
        Console.WriteLine(Me.ToString(format))
    End Sub



    Public Overloads Function ToString(Optional format As String = "") As String

        Dim maxlen As Integer = Me.MaxStringLength(format)

        Dim val As Single
        Dim str As String
        Dim len As Integer

        Dim ret_str As String = ""
        For i As Integer = 1 To Me.RowSize
            For j As Integer = 1 To Me.ColSize

                val = Me.matrix_item(i, j)
                str = val.ToString(format)

                len = str.Length
                Do While len < maxlen
                    str &= " "
                    len += 1
                Loop

                ret_str &= str & vbTab
            Next
            ret_str &= vbCrLf
        Next
        Return ret_str
    End Function


    Public Sub ToCSV(Optional filename As String = "", Optional fullpath As String = "", Optional format As String = "")

        If fullpath = "" Then
            If filename = "" Then filename = "matrix_view"
            fullpath = AppDomain.CurrentDomain.BaseDirectory & filename & ".csv"
        End If


        Dim str As String = Me.ToString(format)
        str = Strings.Replace(str, vbTab, " ")

        Do While InStr(str, "  ") <> 0
            str = Strings.Replace(str, "  ", " ")
        Loop
        str = Strings.Replace(str, " " & vbCrLf, vbCrLf)
        str = Strings.Replace(str, " ", ",")

        Dim str_rows() As String = Strings.Split(str, vbCrLf)

        Dim csv_str As String

        csv_str = ""
        csv_str &= ",,col" & vbCrLf
        csv_str &= ",row"

        For i As Integer = 1 To Me.ColSize
            csv_str &= "," & CStr(i)
        Next
        csv_str &= vbCrLf

        For i As Integer = 1 To Me.RowSize
            csv_str &= "," & CStr(i) & "," & str_rows(i - 1) & vbCrLf
        Next



        Dim sw As System.IO.StreamWriter

        fullpath = Strings.Replace(fullpath, ".csv", "")
        Dim fullpath2 As String = fullpath
        Dim j As Integer = 0
        Do
            Try
                sw = New System.IO.StreamWriter(fullpath2 & ".csv")
                Exit Do
            Catch ex As Exception
                j += 1
                fullpath2 &= fullpath & CStr(j)
            End Try
        Loop While (1)
        fullpath2 &= ".csv"

        sw.WriteLine(csv_str)
        sw.Close()
        Process.Start(fullpath2)

    End Sub



    Private Function MaxStringLength(format As String) As Integer

        Dim val As Single
        Dim str As String
        Dim len As Integer
        Dim N_len As Integer

        N_len = 0
        For i As Integer = 1 To Me.RowSize
            For j As Integer = 1 To Me.ColSize

                val = Me.matrix_item(i, j)
                str = val.ToString(format)

                len = str.Length
                If N_len < len Then N_len = len
            Next
        Next

        Return N_len
    End Function

End Class

Public Class Win32
    <DllImport("kernel32.dll")> Public Shared Function AllocConsole() As Boolean
    End Function

    <DllImport("kernel32.dll")> Public Shared Function FreeConsole() As Boolean
    End Function
End Class

[tonyd5]

That universal clone won't work for EVERYTHING, it will work for certain things. For example, what happens if the array is an array of Object, where the actual items in the array are a variety of things, such as the first being an integer, the second being a string, and so forth. What type will arrObj(0).GetType return for such an array?

Another, more contrived, variation would be: What happens if the array is an array of classes that maintain a DB connection? What should the state of those connections be in the cloned array?

It'll work for the first 2 examples. Every item in the array calls 'Clone' again... its recursive.
Every member in a object calls Clone again... keeps going and going until it gets to the valuetype.

[Shaggy Hiker]

Right, and it WILL clone most everything, but not absolutely everything. I think there's a faster method to accomplish the same thing, but whether or not it is simpler is certainly debatable. I haven't tried it, just seen it, and I may not be remembering it right, but I think the idea was to binary serialize to a memory stream, then restore to a new location. I think that's slightly wrong, as the binary serialization sounds a bit off, but it was something like that.