Eigen4AutoIt 5.3

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By RTFC

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About This File

Eigen4AutoIt Features:

free, fast matrix computing environment for Windows (runs under Wine on Linux and Mac)
built upon the robust Eigen code base (open-source), with many enhancements
simple, intuitive functions, with extensive online documentation
supports integer, single, and double precision, in real and complex matrices
Tutorials with scripts, plus Test scripts for each function section
easily exchange data between native binary files (.mat) and ASCII, Excel, and Xbase files, or AutoIt arrays
32-bit (x86-mode) and 64-bit (x64-mode) support
in x64-mode, matrices can be any size that fits into available virtual memory (>4GB), and can be shared between processes
over one thousand alias wrappers for flexibility and ease-of-use

The Eigen4AutoIt thread is here:

This computing environment allows you to do matrix I/O (memory & files), matrix arithmetic, transformation, reduction, and decomposition, solve systems of linear equations, and perform statistics. Most functions can act on integer, real, or complex matrices (or the latter's real/imaginary parts separately). Much of the actual complexity of using Eigen in its native C++ environment has been hidden for AutoIt users, through extensive bounds and error checks, an intuitive function-naming convention, a large help file, and detailed tutorials and test examples.

What's New in Version 5.3

Released May 9

Added (finally): Optional matrix file de/compression for integer and real matrices, using the open-source ZLib library (see www.zlib.net) as back end. Loading un/compressed matrices from file is transparent (no new functions are required), as is any operation affecting the matrix file header only. To store a specific matrix compressed on file, use new File I/O functions _Eigen_SaveMatrix_Compressed and _Eigen_SaveMatrix_Transposed_Compressed. Alternatively, set new operational flag $EIGEN_ALWAYSCOMPRESS prior to saving (see below). NB matrix variable type conversion on file (without loading into memory first) is not supported for compressed matrix files at this time (instead, load these into memory first and resave compressed). See also new example script EigenTest_29a/b_FileCompression.au3.
Added: The current matrix file storage mode (compressed/uncompressed, matrix vartype bit8 in the matrix file header) can be checked with new File I/O function _Eigen_IsCompressed, or with amended function _Eigen_ShowMatrixProfile_FromFile.
Added: global operational flag $EIGEN_ALWAYSCOMPRESS, controlled by Work Environment functions _Eigen_[Re]SetAlwaysCompressed, stored in Eigen4AutoIt.ini, and displayed by _Eigen_ShowEnvironmentVars. This flag controls whether calls to _Eigen_SaveMatrix[_Transposed] are automatically redirected to their compressed equivalent. This allows all existing E4A scripts to switch to compressed file storage without changing a single line of user code.
Added: _Eigen_GetMatrixHash_MD5 for retrieving a hex-string hash of the binary data in a matrix (excluding the file-only header); useful for checking matrix integrity and testing exact equality before and after operations that should leave the target matrix unchanged.
Added: Transformation function _Eigen_ClampValue (plus all matrix part variants), to replace all values within a defined range with a single constant.
Added: Transformation function _Eigen_Rescale (plus all matrix part variants), to replace a given linear range of values with a newly-defined range.
Added: CwiseUnaryOp* operators "rad2deg" (operator ID: 29) and "deg2rad" (operator ID: 30, to convert between radians and degrees.
Added: CwiseScalarOp* new bitwise operators (operator IDs10-17) for integer matrices: shift-left/right ("shl", "shr"), rotate-left/right int ("rol", "ror") , rotate-left/right byte ("rol8", "ror8") , and rotate-left/right word ("rol16", "ror16"); these operators are unavailable for ConditScalarOp*, but are accessible in CwiseScalarMasked* for selective application using a bitmask matrix.
Added: advanced Matrix Management function _Eigen_Remap_MatrixRows, to remap a contiguous sequence of cells in a (col)vector as a separate vector.

Changed: Eigen includes for dlls upgraded to stable release version 3.4.0.
Changed: Transformation functions _Eigen_Transpose_InPlace and _Eigen_Reverse_Cols no longer support complex part variants, due to an incompatibility with Eigen's revised template function. This is a script-breaking change.
Changed: functions _Eigen_FindAll variants no longer throw an error if nothing is found, matching _Eigen_Find in behaviour.
Changed: most dimensional checks have been relaxed from "exact" to "sufficient," in particular when parsing an existing matrix to store new results.

Fixed: functions _Eigen_CwiseLogicalOp_Diag/InPlace dll support for integer matrices was missing.
Fixed: functions _Eigen_CreateMatrix_Random_Integer wrapper support for integer matrices was disabled.
Fixed: functions _Eigen_FindAll subsidary variants did not provide the option of parsing an existing matrix to collect results (to enable control over the number of results returned).
Fixed: under x86, _Eigen_RemapCols remapped the entire matrix instead of the selected column range only.
Fixed: potential memory leak affecting call stack in _Eigen_SortUnique*, _Eigen_Copy_Acol_toAcol, and _Eigen_Copy_Arow_toArow.
Fixed: internal auxiliary function _HighMem_ReleaseAll allocation array bounds were not updated.

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  The Matrix v1.31.au3
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_WinAPI_DeleteObject($hHBitmap2) _GDIPlus_GraphicsDispose($hCanvas) _WinAPI_SelectObject($hDC_backbuffer, $hDC_obj) _WinAPI_DeleteDC($hDC_backbuffer) _WinAPI_DeleteObject($hHBitmap) _WinAPI_ReleaseDC($hGUI, $hDC) GUIDelete($hGUI) FMUSIC_StopSong($hMod) FSOUND_Close() MemoryDllClose($F_DLL) MemoryDllExit() DllClose($_MDKernel32Dll) EndFunc ;==>TheMatrix_v1 Func _Exit_About() $bExit = True EndFunc ;==>_Exit_About Func CalcFPS() ;display FPS $iShowFPS = $iFPS $iFPS = 0 EndFunc ;==>CalcFPS Func _WinAPI_BitmapCreateDIB($iWidth, $iHeight) Local $tBMI = DllStructCreate($tagBITMAPINFO) $tBMI.biSize = DllStructGetSize($tBMI) $tBMI.biWidth = $iWidth $tBMI.biHeight = -$iHeight $tBMI.biPlanes = 1 $tBMI.biBitCount = 32 $tBMI.biCompression = $BI_RGB Local $aResult = DllCall("gdi32.dll", "ptr", "CreateDIBSection", "hwnd", 0, "struct*", $tBMI, "uint", 0, "ptr*", 0, "ptr", 0, "uint", 0) Return $aResult[0] EndFunc ;Code below was generated by: 'File to Base64 String' Code Generator v1.20 Build 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'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' 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'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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= 'sNWZ5w1FgywLIm3UynDcHUl7T4v3FUIMjuedjvV1G6yfRMA9WY2Te0VSdC4We15DjQCi/1ad1qNTOiUJ3AbrpCUWpLVtSvajrcdQQNEafjJuXGiI4Dh/NPxZWURcpFpw329tXuAOHU9+rAsnVq4yrDAIT26CfF1r0Z9a+yPy8E5KTXtTGf3RluhkAuwGAQiypdimhBDqxnBDXIF0l1zZYgBqbCm6wmm+lNQ5JMnXl7mg1iDoiAoNVVJa2IHfiPXouLdA6nX/2KupFlJtG0yGSXgRHLcI+S48fg6gylKbhJpJTaTNhyFSZELqc0S8V46JW4WgCwZhLiQMMgmIDqD4aLuztH5cvLKeQTgiky6X77pk0+KzPcoDuYxYD3yboOSHzJFYkVAjlHGu4nNvbBI870jIt4VAALe/EtRLkKvpLccQQxQ1wXRelNoSUkHzpZedWWNPZHrUBAznyw9yBlK19uxEJeChXYq0ydYR6ZopbDhHOSJA9hTERD3Cn5iRiqN4WskdCRcOcr2GILiKcPDnFVa/C9O/LQZC4JgAuMTFA7V5MJQYSeIrxXyMGwuTbjUkQWfdIOlELJgZ6+1M4uHYH9uIkEIZhXhOYNSIcqmNU4hjbj/6LEv2HJNAVENaExMeOy8uOzikZa+nUAXfJ0LuAluwkYR22Zc7zX5I5doy3T9BWlBPMHBcuNJYCkdCCBYK6l6KRIkz+u1u9QTUzYCZIBIaaB+VMBQIQaSrQPlTuZdzPL4BGqS07c22qMcFzAtPvj0ex5/H408m3t6hwi9r8EN2bIJtRYui182BGaNhkhEPFvzTSgqv31FHupctCNXTehTqSBVEiduU9DakZ1fyiOZ48wOHKI+I87+H1BNqa10tPd8ZAzQkQnqbUjXL9kU404shQUZ7vk64Vfp3EcSbIEMSKZkW4+dlk1sFiB8LTUop+KA2s1AOp2fkbaFQkeHhjhrEdNui2ZAeEG3aJKckjLmcQbWrEF+EGY/lzHqY' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= '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' $BG_Image &= 'AABJRU5ErkJggg==' Local $bString = _WinAPI_Base64Decode($BG_Image) If @error Then Return SetError(1, 0, 0) $bString = Binary($bString) If $bSaveBinary Then Local Const $hFile = FileOpen($sSavePath & "\Neo_Matrix_800x500_cut_32c.png", 18) If @error Then Return SetError(2, 0, $bString) FileWrite($hFile, $bString) FileClose($hFile) EndIf Return $bString EndFunc ;==>_BG_Image You need The Matrix Sound.au3 which is in the Zip archive (see below) to run the code properly!
  
  Download: The Matrix v1.31 (incl. sound), without sound The Matrix v1.30
  
  Can you decipher the code?
- Eigen4AutoIt - Matrix computing with Eigen
  By RTFC
  
  The Eigen C++ template library is a great environment for matrix computing; it is fast, reliable, extensive, and well-documented. It is also completely free, and does not rely on any external dependencies. Unfortunately for AutoIt users, the term “template library” implies that any functions you call are only instantiated upon compilation (in C++). That means there's nothing to hook into.
  To make Eigen ’s most important functionality directly accessible from within AutoIt scripts (version 3.3.12+, download it here), I developed the Eigen4AutoIt environment. It runs on Windows and under Wine also on Linux and Mac (Ubuntu, Debian, Fedora, and MacOS supported by WineHQ), and SUSE, Slackware, and FreeBSD supported by the distros).
  >Download the latest version
  
  It consists of:
  1) Eigen4AutoIt.au3
  an AutoIt library of wrapper functions that contain extensive bounds checks, matrix management, file I/O, type conversion, and precision control, and two-way data exchange with files and native AutoIt arrays;
  2) Eigen-wrapper dlls (EigenDense.dll, EigenDense_x64.dll)
  re-maps matrices created in AutoIt as Eigen Matrix objects, then calls Eigen’s powerful core functions; in the spirit of open-source, the full C++ source code I wrote is included in the bundle (see subdirectory "source"). The basic functions consist of a single Eigen call; decompositions and statistics are more involved. 3) Additional materials:
  the user-interactive, animated Function Selector and MatrixViewer tools the MatrixFileConverter to read/write E4A matrices from/to .csv ASCII, Excel, and Xbase files. three libraries of scientific and mathematical constants online Help, with example code for every function Large (.chm) Help file (for offline access) Quickstart Manual (11-page pdf, updated) Test suite Tutorials from Basics to Advanced Please note:
  none of this is part of Eigen's own distribution you only need this bundle; you do not need to install Eigen. How it works:
  No matrix content is ever transferred, only memory pointers, meaning computations in AutoIt are virtually as fast as in Eigen’s native environment, with the added advantage of not having to be compiled first. The drawback is that Eigen's native ad-hoc expression templates (and their internal optimisations) cannot be exploited here; you have to construct your operations with the basic building blocks. These provide matrix creation, I/O, cellwise operations, reduction, multiplication, transformation, decomposition (LU, Householder, Choleski, and Jacobi SVD; these include general linear solvers) and a small statistics module by yours truly.
  
  IMPORTANT: Posting Rules for this thread:
  
  1) Do not post or PM me any matrix-, maths-, or Eigen-related questions. Eigen has its own User Forum for that (or try math.stackExchange.com). I am not your maths guru! If you post such questions, I will either ignore your post or remind you of this rule.
  
  2) Do not post or PM me your data sets and/or non-working Eigen4AutoIt scripts; I will not analyse your data or fix your scripts for you! There are many reasons why a linear algebra procedure might fail to produce the answer you expect. You are wielding great mathematical power here, so exploit the fantastic internet resources at your fingertips and learn how to use it. To get you started, I've listed a few video tutorials and other helpful materials in the header remarks of Eigen4AutoIt.au3. Also check out the test scripts, the Tutorials, and the Help file.
  
  3) I do warmly welcome all of the following:
  remarks, advice, suggestions for improvements, encouragement, cash; bug reports re. the Eigen4AutoIt interface (individual functions that don't work the way they should) and/or the associated dll code (ditto); your own working Eigen4AutoIt templates of general use that you'd like to see implemented in a future release. Regarding that last item, have a look at my PCA tutorial. After the step-by-step stage, I summarise the entire procedure in a "mini script" of Eigen4AutoIt calls. Then I introduce the two internal PCA functions I developed, which replace that script with two simple calls. You can do the same thing, and submit your own functional Eigen4AutoIt script in this thread. If I consider it of general use and can implement it, it may become a new Eigen4AutoIt function in the next release (with source acknowledgement, of course). This means that you'd get a precompiled dll version of your script that will likely run faster and be simpler to call. Thereby this thread would become an Eigen4AutoIt Example Scripts mini forum. It's just a thought.
  
  >Download the latest version (uncompressed size: 38.4 MB)
  
  How to Install
  You need AutoIt version 3.3.12 or later. Simply run the installer, navigate to the tutorial subdirectory, open the first tutorial ("Basics") in Scite, and start it. This shows basic matrix I/O and mode switching (single versus double precision). If that runs, you're in business.
  NB to leverage the full power of x64 features, you'll also need to have the full Scite4AutoIt3 package installed. For more info, see sections "Bitness" and "Shared Memory" in the Help, main topic: "Work Environment" page.
- A BitMask-based Sudoku Solver
  By RTFC
  
  The Short Version:
  This set of well-annotated example scripts shows how to solve sudoku puzzles with simple, powerful bitmask functions applied on a massive scale, demonstrating both common solving techniques and highly-optimised brute-force.
  All you need is:
  to like sudoku's basic logic primary school maths to download & install this bundle (v1.2; 25 July 2020) and this #include file (v5.1+) the CrossFilter GUI
- Capatcha AutoIt using Vector
  By Ascer
  
  1. Description
  Anti-bot system to avoid spam. Vector graphic style generates 4 random numbers from 0-9 and create a picture. 2. Requirements
  .NET Framework 1.1 - 4.5 (on this version Microsoft destroy old rules) 3. Possibilities.
  
  4. Downloads.
  Source package Capatcha.rar
- WIA.Vector resize image
  By Ascer
  
  Hello,
  Do you have any idea to resize Vector graphic using some maths trick?
  It's example to create Vector image 10x10px and write A
  Local $a10x10 = [ _ 1,1,1,1,1,1,1,1,1,1, _ 1,1,1,0,0,0,0,1,1,1, _ 1,1,0,0,1,1,0,0,1,1, _ 1,1,0,1,1,1,1,0,1,1, _ 1,1,0,1,1,1,1,0,1,1, _ 1,1,0,0,0,0,0,0,1,1, _ 1,1,0,1,1,1,1,0,1,1, _ 1,1,0,1,1,1,1,0,1,1, _ 1,0,0,0,1,1,0,0,0,1, _ 1,1,1,1,1,1,1,1,1,1 _ ] Local $oVector = ObjCreate("WIA.Vector.1") If Not IsObj($oVector) Then ConsoleWrite("+++ Error " & @error & " durning create a Vector.object." & @CRLF) Exit EndIf Local $iBlue = 0xFF0000FF ; ARGB color Local $iWhite = 0xFFFFFFFF ; adding pixels to vector For $i = 0 To UBound($a10x10) - 1 Local $iPixel = $a10x10[$i] Local $iColor = $iBlue If $iPixel = 0 Then $iColor = $iWhite $oVector.Add($iColor) Next ; create a img 10x10 px Local $oImg = $oVector.ImageFile(10, 10) ; path to file Local $sPath = @ScriptDir & "\Vector.bmp" ; delete previous file if exits. FileDelete($sPath) ; save img to script direction. $oImg.SaveFile($sPath) ; show result, you have to use 800% size to see effects. ShellExecute("Vector.bmp")

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