"Swap" - Bool/Position/Value : Array / Matrix / Var AutoswapLibrary "swap"
Side / Boundary Based All Types Swapper
- three automagical types for Arrays, Matrixes, and Variables
-- no signal : Long/ Short position autoswap
-- true / false : Boolean based side choice
-- Src / Thresh : if source is above or below the threshold
- two operating modes for variables, Holding mode only for arrays/matrixes
-- with two items, will automatically change between the two caveat is it does not delete table/box/line(fill VAR items automatically)
-- with three items, a neutral is available for NA input or neutral
- one function name for all of them. One import name that's easy to type/remember
-- make life easy for your conditional items.
side(source, thresh, _a, _b, _c)
side Change outputs based on position or a crossing level
Parameters:
source : (float) OPTIONAL value input
thresh : (float) OPTIONAL boundary line to cross
_a : (any) if Long/True/Above
_b : (any) if Short/False/Below
_c : (any) OPTIONAL NOT FOR MTX OR ARR... Neutral Item, if var/varip on a/b it will leave behind, ie, a table or box or line will not erase , if it's a varip you're sending in.
Returns: first, second, or third items based on input conditions
Please notify if bugs found.
Thanks.

# Matrix

[LIB] Array / Matrix DisplayLibrary "ArrayMatrixHUD"
Show Array or Matrix Elements In Table
For Arrays: Set the number of rows you want the data displayed in and it will generate a table, calculating the columns based on the size of the array being displayed.
For Matrix: It will automatically match the Rows and Columns to the values in the matrix.
Note: On the left, the table shows the index of the array/matrix value starting at 1. So, to call that value from inside the array, subtract 1 from the index value to the left. For matrices, keep in mind that the row and column are also starting at one when trying to call a value from the matrix. The numbering of the values on the left is for display purposes only.
viewArray(_arrayName, _pos, _txtSize, _tRows)
Array Element Display (Supports float, int, string, and bool)
Parameters:
_arrayName : ID of Array to be Displayed
_pos : Position for Table
_txtSize : Size of Table Cell Text
_tRows : Number of Rows to Display Data In (columns will be calculated accordingly)
Returns: A Display of Array Values in a Table
viewMatrix(_matrixName, _pos, _txtSize)
Matrix Element Display (Supports float, int, string, and bool)
Parameters:
_matrixName : ID of Matrix to be Displayed
_pos : Position for Table
_txtSize : Size of Table Cell Text
Returns: A Display of Matrix Values in a Table

matrixautotableLibrary "matrixautotable"
Automatic Table from Matrixes with pseudo correction for na values and default color override for missing values. uses overloads in cases of cheap float only, with additional addon for strings next, then cell colors, then text colors, and tooltips last.. basic size and location are auto, include the template to speed this up...
TODO : make bools version
var string group_table = ' Table'
var int _tblssizedemo = input.int ( 10 )
string tableYpos = input.string ( 'middle' , '↕' , inline = 'place' , group = group_table, options= )
string tableXpos = input.string ( 'center' , '↔' , inline = 'place' , group = group_table, options= , tooltip='Position on the chart.')
int _textSize = input.int ( 1 , 'Table Text Size' , inline = 'place' , group = group_table)
var matrix _floatmatrix = matrix.new (_tblssizedemo, _tblssizedemo, 0 )
var matrix _stringmatrix = matrix.new (_tblssizedemo, _tblssizedemo, 'test' )
var matrix _bgcolormatrix = matrix.new (_tblssizedemo, _tblssizedemo, color.white )
var matrix _textcolormatrix = matrix.new (_tblssizedemo, _tblssizedemo, color.black )
var matrix _tooltipmatrix = matrix.new (_tblssizedemo, _tblssizedemo, 'tool' )
// basic table ready to go with the aboec matrixes (replace in your code)
// for demo purpose, random colors, random nums, random na vals
if barstate.islast
varip _xsize = matrix.rows (_floatmatrix) -1
varip _ysize = matrix.columns (_floatmatrix) -1
for _xis = 0 to _xsize -1 by 1
for _yis = 0 to _ysize -1 by 1
_randomr = int(math.random(50,250))
_randomg = int(math.random(50,250))
_randomb = int(math.random(50,250))
_randomt = int(math.random(10,90 ))
bgcolor = color.rgb(250 - _randomr, 250 - _randomg, 250 - _randomb, 100 - _randomt )
txtcolor = color.rgb(_randomr, _randomg, _randomb, _randomt )
matrix.set(_bgcolormatrix ,_yis,_xis, bgcolor )
matrix.set(_textcolormatrix ,_yis,_xis, txtcolor)
matrix.set(_floatmatrix ,_yis,_xis, _randomr)
// random na
_ymiss = math.floor(math.random(0, _yis))
_xmiss = math.floor(math.random(0, _xis))
matrix.set( _floatmatrix ,_ymiss, _xis, na)
matrix.set( _stringmatrix ,_ymiss, _xis, na)
matrix.set( _bgcolormatrix ,_ymiss, _xis, na)
matrix.set( _textcolormatrix ,_ymiss, _xis, na)
matrix.set( _tooltipmatrix ,_ymiss, _xis, na)
// import here
import kaigouthro/matrixautotable/1 as mtxtbl
// and render table..
mtxtbl.matrixtable(_floatmatrix, _stringmatrix, _bgcolormatrix, _textcolormatrix, _tooltipmatrix, _textSize ,tableYpos ,tableXpos)
matrixtable(_floatmatrix, _stringmatrix, _bgcolormatrix, _textcolormatrix, _tooltipmatrix, _textSize, tableYpos, tableXpos) matrixtable
Parameters:
_floatmatrix : float vals
_stringmatrix : string
_bgcolormatrix : color
_textcolormatrix : color
_tooltipmatrix : string
_textSize : int
tableYpos : string
tableXpos : string
matrixtable(_floatmatrix, _stringmatrix, _bgcolormatrix, _textcolormatrix, _textSize, tableYpos, tableXpos) matrixtable
Parameters:
_floatmatrix : float vals
_stringmatrix : string
_bgcolormatrix : color
_textcolormatrix : color
_textSize : int
tableYpos : string
tableXpos : string
matrixtable(_floatmatrix, _stringmatrix, _bgcolormatrix, _txtdefcol, _textSize, tableYpos, tableXpos) matrixtable
Parameters:
_floatmatrix : float vals
_stringmatrix : string
_bgcolormatrix : color
_txtdefcol : color
_textSize : int
tableYpos : string
tableXpos : string
matrixtable(_floatmatrix, _stringmatrix, _txtdefcol, _bgdefcol, _textSize, tableYpos, tableXpos) matrixtable
Parameters:
_floatmatrix : float vals
_stringmatrix : string
_txtdefcol : color
_bgdefcol : color
_textSize : int
tableYpos : string
tableXpos : string
matrixtable(_floatmatrix, _txtdefcol, _bgdefcol, _textSize, tableYpos, tableXpos) matrixtable
Parameters:
_floatmatrix : float vals
_txtdefcol : color
_bgdefcol : color
_textSize : int
tableYpos : string
tableXpos : string

Morningstar Equity Style Box HeatmapStyle boxes are a classification scheme created by Morningstar. They visually provide a graphical representation of investing categories for equity investments. A style box is a valuable tool for investors to use when determining asset allocation.
There are 9 categories:
Large Value, Large Blend, Large Growth
Medium Value, Medium Blend, Medium Growth
Small Value, Small Blend, Small Growth
The strength of the 9 categories are found by using 9 Vanguard ETF's that follow the respective CRSP index of their category.

SymMatrixTableSimple Example Table for Displaying Price, RSI, Volume of multiple Tickers on selected Timeframe
Displays Price, RSI and Volume of 3 Tickers and Timeframe selected by user input
Conditional Table Cell coloring
Price color green if > than previous candle close and red if < previous candle close
RSI color green if < 30 and red if > 70 (RSI14 by default)
Volume color green if above average volume and red if less than that (SMA20 volume by default)
Can turn on/off whole table, header columns, row indices, or select individual columns or rows to show/hide
// Example Mixed Type Matrix To Table //
access the simple example script by uncommenting the code at the end
Basically I wanted to have the headers and indices as strings and the rest of the matrix for the table body as floats, then conditional coloring on the table cells
And also the functionality to turn rows and columns on/off from table through checkboxes of user input
Before I was storing each of the values separately in arrays that didn't have a centralized way of controlling table structure
so now the structure is :
- string header array, string index array
- float matrix for table body
- color matrix with bool conditions for coloring table cells
- bool checkboxes for controlling table display

Reshape Table Matrix█ OVERVIEW
Simple method to reshape matrix to table.
Credits to Tradingview for new matrix update.

US Stock Market Sectors Overview Table [By MUQWISHI]US Market Overview Table will identify the bullish and bearish sectors of a day by tracking the SPDR sectors funds.
It's possible to add a ticker symbol for correlation compared to each sector.
Overview Indicator

Discounted Price ProbabilityHere is an attempt to understand the probability of discounted price of a stock by comparing it to historical price and fundamental correlation. Have made use of some of the new features of pine in developing this script (Such as matrix and new features of tables such as cell merge and tooltip).
Script makes use of the library written on matrix matrix
🎲 Process
Probability is measured in two angles
🎯 Absolute : Measure the percentile of price and fundamentals with respect to all time high. The difference between the two is measure of probability of stock being undervalued.
🎯 Drawdown : Measure the percentile of distance from all time high for both price and fundamentals. The difference between the two is used for depicting the probability of stock being undervalued.
🎲 Components
In short, the definitions of stats presented are as below
🎲 Settings
Settings are pretty straightforward
🎲 How to look at these stats
To Start with
Are most of the fundamental values coloured in green? If yes, it means that they are near all time high in terms of percentile.
If drawdowns of fundamental values coloured in green? If yes, it means, the stock has not suffered much drawdowns of fundamentals from its peak.
Are the percentile values of drawdowns in green? If yes, it means, that drop in fundamentals are not high compared to its previous values.
If all the above are greener, then it means, company is in strong growth space.
Example: TSLA
Even though the financial ratios of TSLA are not in par with most of the fundamentally strong stocks, it is indeed growing steadily and at its near all time high.
Lets take another example of NKLA
Here the base columns regarding fundamentals are mostly red. This means, company has suffered setback with respect to their financials and the company is not where it used to be. But, if you see the differential probabilities, it says 92% of being undervalued?
Well, this is due to the fact that NKLA's fundamentals suffered most of the time and they are always below par when compared to price. Hence, such kind of cases may interpret the stocks as undervalued. Hence, even if the probability of being undervalued is more, it does not guarantee the quality of the stock. We need to be mindful overall financials of the company and how they fare with general standards.
Moving forward
To understand value of trending stock, use Absolute Probability (marked with P). Ex. GOOG, MSFT, BRK.B etc.
To understand value of stock which has been recently suffered huge price drop, look at drawdown based probability (marked with D). Ex. BABA, FB, PYPL, SQ, ROKU etc.
Some examples of high flyers:
Some for deep pullbacks:
And the meme stocks:

_matrixLibrary "_matrix"
Library helps visualize matrix as array of arrays and enables users to use array methods such as push, pop, shift, unshift etc along with cleanup activities on drawing objects wherever required
unshift(mtx, row) unshift array of lines to first row of the matrix
Parameters:
mtx : matrix of lines
row : array of lines to be inserted in row
Returns: resulting matrix of lines
unshift(mtx, row) unshift array of labels to first row of the matrix
Parameters:
mtx : matrix of labels
row : array of labels to be inserted in row
Returns: resulting matrix labels
unshift(mtx, row) unshift array of boxes to first row of the matrix
Parameters:
mtx : matrix of boxes
row : array of boxes to be inserted in row
Returns: resulting matrix of boxes
unshift(mtx, row) unshift array of linefill to first row of the matrix
Parameters:
mtx : matrix of linefill
row : array of linefill to be inserted in row
Returns: resulting matrix of linefill
unshift(mtx, row) unshift array of tables to first row of the matrix
Parameters:
mtx : matrix of tables
row : array of tables to be inserted in row
Returns: resulting matrix of tables
unshift(mtx, row) unshift array of int to first row of the matrix
Parameters:
mtx : matrix of int
row : array of int to be inserted in row
Returns: resulting matrix of int
unshift(mtx, row) unshift array of float to first row of the matrix
Parameters:
mtx : matrix of float
row : array of float to be inserted in row
Returns: resulting matrix of float
unshift(mtx, row) unshift array of bool to first row of the matrix
Parameters:
mtx : matrix of bool
row : array of bool to be inserted in row
Returns: resulting matrix of bool
unshift(mtx, row) unshift array of string to first row of the matrix
Parameters:
mtx : matrix of string
row : array of string to be inserted in row
Returns: resulting matrix of string
unshift(mtx, row) unshift array of color to first row of the matrix
Parameters:
mtx : matrix of colors
row : array of colors to be inserted in row
Returns: resulting matrix of colors
push(mtx, row) push array of lines to end of the matrix row
Parameters:
mtx : matrix of lines
row : array of lines to be inserted in row
Returns: resulting matrix of lines
push(mtx, row) push array of labels to end of the matrix row
Parameters:
mtx : matrix of labels
row : array of labels to be inserted in row
Returns: resulting matrix of labels
push(mtx, row) push array of boxes to end of the matrix row
Parameters:
mtx : matrix of boxes
row : array of boxes to be inserted in row
Returns: resulting matrix of boxes
push(mtx, row) push array of linefill to end of the matrix row
Parameters:
mtx : matrix of linefill
row : array of linefill to be inserted in row
Returns: resulting matrix of linefill
push(mtx, row) push array of tables to end of the matrix row
Parameters:
mtx : matrix of tables
row : array of tables to be inserted in row
Returns: resulting matrix of tables
push(mtx, row) push array of int to end of the matrix row
Parameters:
mtx : matrix of int
row : array of int to be inserted in row
Returns: resulting matrix of int
push(mtx, row) push array of float to end of the matrix row
Parameters:
mtx : matrix of float
row : array of float to be inserted in row
Returns: resulting matrix of float
push(mtx, row) push array of bool to end of the matrix row
Parameters:
mtx : matrix of bool
row : array of bool to be inserted in row
Returns: resulting matrix of bool
push(mtx, row) push array of string to end of the matrix row
Parameters:
mtx : matrix of string
row : array of string to be inserted in row
Returns: resulting matrix of string
push(mtx, row) push array of colors to end of the matrix row
Parameters:
mtx : matrix of colors
row : array of colors to be inserted in row
Returns: resulting matrix of colors
shift(mtx) shift removes first row from matrix of lines
Parameters:
mtx : matrix of lines from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of labels
Parameters:
mtx : matrix of labels from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of boxes
Parameters:
mtx : matrix of boxes from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of linefill
Parameters:
mtx : matrix of linefill from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of tables
Parameters:
mtx : matrix of tables from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of int
Parameters:
mtx : matrix of int from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of float
Parameters:
mtx : matrix of float from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of bool
Parameters:
mtx : matrix of bool from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of string
Parameters:
mtx : matrix of string from which the shift operation need to be performed
Returns: void
shift(mtx) shift removes first row from matrix of colors
Parameters:
mtx : matrix of colors from which the shift operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of lines
Parameters:
mtx : matrix of lines from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of labels
Parameters:
mtx : matrix of labels from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of boxes
Parameters:
mtx : matrix of boxes from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of linefill
Parameters:
mtx : matrix of linefill from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of tables
Parameters:
mtx : matrix of tables from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of int
Parameters:
mtx : matrix of int from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of float
Parameters:
mtx : matrix of float from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of bool
Parameters:
mtx : matrix of bool from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of string
Parameters:
mtx : matrix of string from which the pop operation need to be performed
Returns: void
pop(mtx) pop removes last row from matrix of colors
Parameters:
mtx : matrix of colors from which the pop operation need to be performed
Returns: void
clear(mtx) clear clears the matrix of lines
Parameters:
mtx : matrix of lines which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of labels
Parameters:
mtx : matrix of labels which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of boxes
Parameters:
mtx : matrix of boxes which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of linefill
Parameters:
mtx : matrix of linefill which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of tables
Parameters:
mtx : matrix of tables which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of int
Parameters:
mtx : matrix of int which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of float
Parameters:
mtx : matrix of float which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of bool
Parameters:
mtx : matrix of bool which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of string
Parameters:
mtx : matrix of string which needs to be cleared
Returns: void
clear(mtx) clear clears the matrix of colors
Parameters:
mtx : matrix of colors which needs to be cleared
Returns: void

FunctionMatrixSolveLibrary "FunctionMatrixSolve"
Matrix Equation solution for Ax = B, finds the value of x.
solve(A, B) Solves Matrix Equation for Ax = B, finds value for x.
Parameters:
A : matrix, Square matrix with data values.
B : matrix, One column matrix with data values.
Returns: matrix with X, x = A^-1 b, assuming A is square and has full rank
introcs.cs.princeton.edu

FunctionPatternDecompositionLibrary "FunctionPatternDecomposition"
Methods for decomposing price into common grid/matrix patterns.
series_to_array(source, length) Helper for converting series to array.
Parameters:
source : float, data series.
length : int, size.
Returns: float array.
smooth_data_2d(data, rate) Smooth data sample into 2d points.
Parameters:
data : float array, source data.
rate : float, default=0.25, the rate of smoothness to apply.
Returns: tuple with 2 float arrays.
thin_points(data_x, data_y, rate) Thin the number of points.
Parameters:
data_x : float array, points x value.
data_y : float array, points y value.
rate : float, default=2.0, minimum threshold rate of sample stdev to accept points.
Returns: tuple with 2 float arrays.
extract_point_direction(data_x, data_y) Extract the direction each point faces.
Parameters:
data_x : float array, points x value.
data_y : float array, points y value.
Returns: float array.
find_corners(data_x, data_y, rate) ...
Parameters:
data_x : float array, points x value.
data_y : float array, points y value.
rate : float, minimum threshold rate of data y stdev.
Returns: tuple with 2 float arrays.
grid_coordinates(data_x, data_y, m_size) transforms points data to a constrained sized matrix format.
Parameters:
data_x : float array, points x value.
data_y : float array, points y value.
m_size : int, default=10, size of the matrix.
Returns: flat 2d pseudo matrix.

ArrayMultipleDimensionPrototypeLibrary "ArrayMultipleDimensionPrototype"
A prototype library for Multiple Dimensional array methods
index_md_to_1d()
new_float(dimensions, initial_size) Creates a variable size multiple dimension array.
Parameters:
dimensions : int array, dimensions of array.
initial_size : float, default=na, initial value of the array.
Returns: float array
dimensions(id, value) set value of a element in a multiple dimensions array.
Parameters:
id : float array, multiple dimensions array.
value : float, new value.
Returns: float.
get(id) get value of a multiple dimensions array.
Parameters:
id : float array, multiple dimensions array.
Returns: float.
set(id) set value of a element in a multiple dimensions array.
Parameters:
id : float array, multiple dimensions array.
Returns: float.

{Gunzo} Animated Pixel Art - ASCII ArtAnimated Pixel Art - ASCII Art is not only an easy-to-use platform to create and visualize pixel animations. This script can also be used with the Nyan Cat visualization as a companion tool for all traders to know when the price is changing on the chart.
OVERVIEW :
In the first place, this tool has been created to celebrate the new design of the Trading View platform. The new monogram logo and the previous cloud logo can be displayed as pixel art within this script.
To test the limits of the pine script language, I tried to improve this simple pixel art script to be able to display complex pixel animations with good performance (max allowed 100 milliseconds per bar). That's how the Nyan Cat companion was created. Nyan Cat is moving every time the data on the chart is refreshed, so the animation time may differ depending on your environment. Only the pixels that changed between two animations are repainted on each loop so that the performance is significantly improved and allowing so to create bigger pixel art designs.
HOW IT WORKS :
The pixels are displayed on the chart using a huge table variable. Each cell of the table can be used to display one pixel of the initial matrix. New designs can easily be implemented as the pixel matrix is stored as a simple text variable.
The pixel matrix is composed of hexadecimal characters (0123456789ABCDEF). Each hexadecimal character correspond to a color in the 16 color palette.
SETTINGS :
Matrix Visual : Name of the pixel art matrix to be displayed
Matrix Colors : Palette to be used for painting the pixels. 16 color palette for colorful matrix or phosphor colors for retro aspect on simple pixel art.
Type of art : Pixel art paint square pixels on chart and ASCII art paints hexadecimal characters on a chart.
Pixel Grid color : Color used between each pixel, by default it is transparent.
Pixel Width : Change the aspect ratio of the matrix. Useful to fine-tune the size of the pixels according to your screen size and the script size.
Pixel Height : Change the aspect ratio of the matrix. Useful to fine-tune the size of the pixels according to your screen size and the script size.
ASCII Background Character : Character that will be replaced with no color

Test - Gramian Angular FieldExperimental:
The Gramian Angular Field is usually used in machine learning for machine vision, it allows the encoding of data as a visual queue / matrix.

Directional Matrix [LuxAlgo]Returns a dashboard showing the direction taken by 4 overlay indicators, SMA (simple moving average), TMA (triangular moving average), WMA (weighted moving average), and REG (linear regression), all using different length periods.
The user can select the minimum and maximum length of these indicators and introduce an increment.
1. Settings
Maximum Length: The end value of sequences of the indicator periods to analyze
Minimum Length: The starting value of sequences of the indicator periods to analyze
Step: Determines the spacing between each indicator periods values
Src: Data source for each of the 4 indicators
1.1 Style settings
Normalized Change Mode: Allows the user to access a different interpretation of the indicator by showing the normalized first differences of each indicator in the dashboard instead of their sign
Dashboard Location: Location of the dashboard on the chart
Dashboard Size: Size of the dashboard on the chart
Text/Frame Color: Determines the color of the frame grid as well as the text color
Bullish Cell Color: Determines the color of cell associated with a rising indicator direction
Bearish Cell Color: Determines the color of cell associated with a decreasing indicator direction
Cell Transparency: Transparency of each cell
2. Usage
Each of the indicators included in the dashboard aim to give an estimate of the underlying trend in the price. Knowing which direction they are taking can help us have a broader view regarding the direction of shorter/longer-term trends. We will later see that this is not the only kind of information that we can get from this indicator.
Rising indicators are represented by blue cells (or the color selected in the Bullish Cell Color setting) while decreasing indicators are represented by red cells (or the color selected in the Bearish Cell Color setting).
The percentage of bullish cells is given in the top-left cell of the dashboard.
2.1 Normalized change mode
Enabling the Normalized Change mode will display the normalized changes returned by the indicators over different length periods. This metric is within a range (0,1), with 1 indicating the highest change over the selected length periods, while 0 indicates the lowest one.
When enabling this mode the color of the cells makes use of a gradient with a color palette ranging from the color selected in the Bearish Cell setting to the color selected in the Bullish Cell setting.
2.1 Other Usage
The direction taken by certain indicators can give more information than one would think. Indeed, the sign of the change of one indicator can often be given by different indicators.
A positive change in a simple moving average indicates that the price is greater than the price p bars ago, where p is the period of the simple moving average.
A positive change in a triangular moving average indicates that a simple moving average of period p is above a simple moving average of period p × 2 , where p is the period of the triangular moving average (note that we assume here that the TMA is given by cascading two SMAs of period p ).
A positive change in a weighted moving average indicates that the price is above a simple moving average of period p+1 , where p is the period of the WMA.
Finally, a positive change in a linear regression indicates that a weighted moving average is above a simple moving average of period p , where p is the period of the linear regression.

Correlation MatrixReturns a 4x4 correlation matrix between various user-selected symbols. Users can change the window of the correlation with the setting length .
Correlation matrices can be useful to see the linear relationship between various symbols, this is an important tool for diversification.

Matrix Library (Linear Algebra, incl Multiple Linear Regression)What's this all about?
Ever since 1D arrays were added to Pine Script, many wonderful new opportunities have opened up. There has been a few implementations of matrices and matrix math (most notably by TradingView-user tbiktag in his recent Moving Regression script: ). However, so far, no comprehensive libraries for matrix math and linear algebra has been developed. This script aims to change that.
I'm not math expert, but I like learning new things, so I took it upon myself to relearn linear algebra these past few months, and create a matrix math library for Pine Script. The goal with the library was to make a comprehensive collection of functions that can be used to perform as many of the standard operations on matrices as possible, and to implement functions to solve systems of linear equations. The library implements matrices using arrays, and many standard functions to manipulate these matrices have been added as well.
The main purpose of the library is to give users the ability to solve systems of linear equations (useful for Multiple Linear Regression with K number of independent variables for example), but it can also be used to simulate 2D arrays for any purpose.
So how do I use this thing?
Personally, what I do with my private Pine Script libraries is I keep them stored as text-files in a Libraries folder, and I copy and paste them into my code when I need them. This library is quite large, so I have made sure to use brackets in comments to easily hide any part of the code. This helps with big libraries like this one.
The parts of this script that you need to copy are labeled "MathLib", "ArrayLib", and "MatrixLib". The matrix library is dependent on the functions from these other two libraries, but they are stripped down to only include the functions used by the MatrixLib library.
When you have the code in your script (pasted somewhere below the "study()" call), you can create a matrix by calling one of the constructor functions. All functions in this library start with "matrix_", and all constructors start with either "create" or "copy". I suggest you read through the code though. The functions have very descriptive names, and a short description of what each function does is included in a header comment directly above it. The functions generally come in the following order:
Constructors: These are used to create matrices (empy with no rows or columns, set shape filled with 0s, from a time series or an array, and so on).
Getters and setters: These are used to get data from a matrix (like the value of an element or a full row or column).
Matrix manipulations: These functions manipulate the matrix in some way (for example, functions to append columns or rows to a matrix).
Matrix operations: These are the matrix operations. They include things like basic math operations for two indices, to transposing a matrix.
Decompositions and solvers: Next up are functions to solve systems of linear equations. These include LU and QR decomposition and solvers, and functions for calculating the pseudo-inverse or inverse of a matrix.
Multiple Linear Regression: Lastly, we find an implementation of a multiple linear regression, including all the standard statistics one can expect to find in most statistical software packages.
Are there any working examples of how to use the library?
Yes, at the very end of the script, there is an example that plots the predictions from a multiple linear regression with two independent (explanatory) X variables, regressing the chart data (the Y variable) on these X variables. You can look at this code to see a real-world example of how to use the code in this library.
Are there any limitations?
There are no hard limiations, but the matrices uses arrays, so the number of elements can never exceed the number of elements supported by Pine Script (minus 2, since two elements are used internally by the library to store row and column count). Some of the operations do use a lot of resources though, and as a result, some things can not be done without timing out. This can vary from time to time as well, as this is primarily dependent on the available resources from the Pine Script servers. For instance, the multiple linear regression cannot be used with a lookback window above 10 or 12 most of the time, if the statistics are reported. If no statistics are reported (and therefore not calculated), the lookback window can usually be extended to around 60-80 bars before the servers time out the execution.
Hopefully the dev-team at TradingView sees this script and find ways to implement this functionality diretly into Pine Script, as that would speed up many of the operations and make things like MLR (multiple linear regression) possible on a bigger lookback window.
Some parting words
This library has taken a few months to write, and I have taken all the steps I can think of to test it for bugs. Some may have slipped through anyway, so please let me know if you find any, and I'll try my best to fix them when I have time to do so. This library is intended to help the community. Therefore, I am releasing the library as open source, in the hopes that people may improving on it, or using it in their own work. If you do make something cool with this, or if you find ways to improve the code, please let me know in the comments.

Polynomial Regression Bands + Channel [DW]This is an experimental study designed to calculate polynomial regression for any order polynomial that TV is able to support.
This study aims to educate users on polynomial curve fitting, and the derivation process of Least Squares Moving Averages (LSMAs).
I also designed this study with the intent of showcasing some of the capabilities and potential applications of TV's fantastic new array functions.
Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as a polynomial of nth degree (order).
For clarification, linear regression can also be described as a first order polynomial regression. The process of deriving linear, quadratic, cubic, and higher order polynomial relationships is all the same.
In addition, although deriving a polynomial regression equation results in a nonlinear output, the process of solving for polynomials by least squares is actually a special case of multiple linear regression.
So, just like in multiple linear regression, polynomial regression can be solved in essentially the same way through a system of linear equations.
In this study, you are first given the option to smooth the input data using the 2 pole Super Smoother Filter from John Ehlers.
I chose this specific filter because I find it provides superior smoothing with low lag and fairly clean cutoff. You can, of course, implement your own filter functions to see how they compare if you feel like experimenting.
Filtering noise prior to regression calculation can be useful for providing a more stable estimation since least squares regression can be rather sensitive to noise.
This is especially true on lower sampling lengths and higher degree polynomials since the regression output becomes more "overfit" to the sample data.
Next, data arrays are populated for the x-axis and y-axis values. These are the main datasets utilized in the rest of the calculations.
To keep the calculations more numerically stable for higher periods and orders, the x array is filled with integers 1 through the sampling period rather than using current bar numbers.
This process can be thought of as shifting the origin of the x-axis as new data emerges.
This keeps the axis values significantly lower than the 10k+ bar values, thus maintaining more numerical stability at higher orders and sample lengths.
The data arrays are then used to create a pseudo 2D matrix of x power sums, and a vector of x power*y sums.
These matrices are a representation the system of equations that need to be solved in order to find the regression coefficients.
Below, you'll see some examples of the pattern of equations used to solve for our coefficients represented in augmented matrix form.
For example, the augmented matrix for the system equations required to solve a second order (quadratic) polynomial regression by least squares is formed like this:
(∑x^0 ∑x^1 ∑x^2 | ∑(x^0)y)
(∑x^1 ∑x^2 ∑x^3 | ∑(x^1)y)
(∑x^2 ∑x^3 ∑x^4 | ∑(x^2)y)
The augmented matrix for the third order (cubic) system is formed like this:
(∑x^0 ∑x^1 ∑x^2 ∑x^3 | ∑(x^0)y)
(∑x^1 ∑x^2 ∑x^3 ∑x^4 | ∑(x^1)y)
(∑x^2 ∑x^3 ∑x^4 ∑x^5 | ∑(x^2)y)
(∑x^3 ∑x^4 ∑x^5 ∑x^6 | ∑(x^3)y)
This pattern continues for any n ordered polynomial regression, in which the coefficient matrix is a n + 1 wide square matrix with the last term being ∑x^2n, and the last term of the result vector being ∑(x^n)y.
Thanks to this pattern, it's rather convenient to solve the for our regression coefficients of any nth degree polynomial by a number of different methods.
In this script, I utilize a process known as LU Decomposition to solve for the regression coefficients.
Lower-upper (LU) Decomposition is a neat form of matrix manipulation that expresses a 2D matrix as the product of lower and upper triangular matrices.
This decomposition method is incredibly handy for solving systems of equations, calculating determinants, and inverting matrices.
For a linear system Ax=b, where A is our coefficient matrix, x is our vector of unknowns, and b is our vector of results, LU Decomposition turns our system into LUx=b.
We can then factor this into two separate matrix equations and solve the system using these two simple steps:
1. Solve Ly=b for y, where y is a new vector of unknowns that satisfies the equation, using forward substitution.
2. Solve Ux=y for x using backward substitution. This gives us the values of our original unknowns - in this case, the coefficients for our regression equation.
After solving for the regression coefficients, the values are then plugged into our regression equation:
Y = a0 + a1*x + a1*x^2 + ... + an*x^n, where a() is the ()th coefficient in ascending order and n is the polynomial degree.
From here, an array of curve values for the period based on the current equation is populated, and standard deviation is added to and subtracted from the equation to calculate the channel high and low levels.
The calculated curve values can also be shifted to the left or right using the "Regression Offset" input
Changing the offset parameter will move the curve left for negative values, and right for positive values.
This offset parameter shifts the curve points within our window while using the same equation, allowing you to use offset datapoints on the regression curve to calculate the LSMA and bands.
The curve and channel's appearance is optionally approximated using Pine's v4 line tools to draw segments.
Since there is a limitation on how many lines can be displayed per script, each curve consists of 10 segments with lengths determined by a user defined step size. In total, there are 30 lines displayed at once when active.
By default, the step size is 10, meaning each segment is 10 bars long. This is because the default sampling period is 100, so this step size will show the approximate curve for the entire period.
When adjusting your sampling period, be sure to adjust your step size accordingly when curve drawing is active if you want to see the full approximate curve for the period.
Note that when you have a larger step size, you will see more seemingly "sharp" turning points on the polynomial curve, especially on higher degree polynomials.
The polynomial functions that are calculated are continuous and differentiable across all points. The perceived sharpness is simply due to our limitation on available lines to draw them.
The approximate channel drawings also come equipped with style inputs, so you can control the type, color, and width of the regression, channel high, and channel low curves.
I also included an input to determine if the curves are updated continuously, or only upon the closing of a bar for reduced runtime demands. More about why this is important in the notes below.
For additional reference, I also included the option to display the current regression equation.
This allows you to easily track the polynomial function you're using, and to confirm that the polynomial is properly supported within Pine.
There are some cases that aren't supported properly due to Pine's limitations. More about this in the notes on the bottom.
In addition, I included a line of text beneath the equation to indicate how many bars left or right the calculated curve data is currently shifted.
The display label comes equipped with style editing inputs, so you can control the size, background color, and text color of the equation display.
The Polynomial LSMA, high band, and low band in this script are generated by tracking the current endpoints of the regression, channel high, and channel low curves respectively.
The output of these bands is similar in nature to Bollinger Bands, but with an obviously different derivation process.
By displaying the LSMA and bands in tandem with the polynomial channel, it's easy to visualize how LSMAs are derived, and how the process that goes into them is drastically different from a typical moving average.
The main difference between LSMA and other MAs is that LSMA is showing the value of the regression curve on the current bar, which is the result of a modelled relationship between x and the expected value of y.
With other MA / filter types, they are typically just averaging or frequency filtering the samples. This is an important distinction in interpretation. However, both can be applied similarly when trading.
An important distinction with the LSMA in this script is that since we can model higher degree polynomial relationships, the LSMA here is not limited to only linear as it is in TV's built in LSMA.
Bar colors are also included in this script. The color scheme is based on disparity between source and the LSMA.
This script is a great study for educating yourself on the process that goes into polynomial regression, as well as one of the many processes computers utilize to solve systems of equations.
Also, the Polynomial LSMA and bands are great components to try implementing into your own analysis setup.
I hope you all enjoy it!
--------------------------------------------------------
NOTES:
- Even though the algorithm used in this script can be implemented to find any order polynomial relationship, TV has a limit on the significant figures for its floating point outputs.
This means that as you increase your sampling period and / or polynomial order, some higher order coefficients will be output as 0 due to floating point round-off.
There is currently no viable workaround for this issue since there isn't a way to calculate more significant figures than the limit.
However, in my humble opinion, fitting a polynomial higher than cubic to most time series data is "overkill" due to bias-variance tradeoff.
Although, this tradeoff is also dependent on the sampling period. Keep that in mind. A good rule of thumb is to aim for a nice "middle ground" between bias and variance.
If TV ever chooses to expand its significant figure limits, then it will be possible to accurately calculate even higher order polynomials and periods if you feel the desire to do so.
To test if your polynomial is properly supported within Pine's constraints, check the equation label.
If you see a coefficient value of 0 in front of any of the x values, reduce your period and / or polynomial order.
- Although this algorithm has less computational complexity than most other linear system solving methods, this script itself can still be rather demanding on runtime resources - especially when drawing the curves.
In the event you find your current configuration is throwing back an error saying that the calculation takes too long, there are a few things you can try:
-> Refresh your chart or hide and unhide the indicator.
The runtime environment on TV is very dynamic and the allocation of available memory varies with collective server usage.
By refreshing, you can often get it to process since you're basically just waiting for your allotment to increase. This method works well in a lot of cases.
-> Change the curve update frequency to "Close Only".
If you've tried refreshing multiple times and still have the error, your configuration may simply be too demanding of resources.
v4 drawing objects, most notably lines, can be highly taxing on the servers. That's why Pine has a limit on how many can be displayed in the first place.
By limiting the curve updates to only bar closes, this will significantly reduce the runtime needs of the lines since they will only be calculated once per bar.
Note that doing this will only limit the visual output of the curve segments. It has no impact on regression calculation, equation display, or LSMA and band displays.
-> Uncheck the display boxes for the drawing objects.
If you still have troubles after trying the above options, then simply stop displaying the curve - unless it's important to you.
As I mentioned, v4 drawing objects can be rather resource intensive. So a simple fix that often works when other things fail is to just stop them from being displayed.
-> Reduce sampling period, polynomial order, or curve drawing step size.
If you're having runtime errors and don't want to sacrifice the curve drawings, then you'll need to reduce the calculation complexity.
If you're using a large sampling period, or high order polynomial, the operational complexity becomes significantly higher than lower periods and orders.
When you have larger step sizes, more historical referencing is used for x-axis locations, which does have an impact as well.
By reducing these parameters, the runtime issue will often be solved.
Another important detail to note with this is that you may have configurations that work just fine in real time, but struggle to load properly in replay mode.
This is because the replay framework also requires its own allotment of runtime, so that must be taken into consideration as well.
- Please note that the line and label objects are reprinted as new data emerges. That's simply the nature of drawing objects vs standard plots.
I do not recommend or endorse basing your trading decisions based on the drawn curve. That component is merely to serve as a visual reference of the current polynomial relationship.
No repainting occurs with the Polynomial LSMA and bands though. Once the bar is closed, that bar's calculated values are set.
So when using the LSMA and bands for trading purposes, you can rest easy knowing that history won't change on you when you come back to view them.
- For those who intend on utilizing or modifying the functions and calculations in this script for their own scripts, I included debug dialogues in the script for all of the arrays to make the process easier.
To use the debugs, see the "Debugs" section at the bottom. All dialogues are commented out by default.
The debugs are displayed using label objects. By default, I have them all located to the right of current price.
If you wish to display multiple debugs at once, it will be up to you to decide on display locations at your leisure.
When using the debugs, I recommend commenting out the other drawing objects (or even all plots) in the script to prevent runtime issues and overlapping displays.

Matrix functions - JD/////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// The arrays provided in Pinescript are linear 1D strucures that can be seen either as a large vertical stack or
// a horizontal row containing a list of values, colors, bools,..
//
// With the FUNCTIONS in this script the 1D ARRAY LIST can be CONVERTED INTO A 2D MATRIX form
//
//
///////////////////////////////////////////
/// BASIC INFO ON THE MATRIX STRUCTURE: ///
///////////////////////////////////////////
//
// The matrix is set up as an 2D structure and is devided in ROWS and COLUMNS.
// following the standard mathematical notation:
//
// a 3 x 4 matrix = 4 columns
// 0 1 2 3 column index
// 0
// 3 rows 1
// 2
// row
// index
//
// With the use of some purpose-built functions, values can be placed or retrieved in a specific column of a certain row
// this can be done by intuitively using row_nr and column_nr coördinates,
// without having to worry on what exact index of the Pine array this value is located (the functions do these conversions for you)
//
//
// the syntax I propose for the 2D Matrix array has the following structure:
//
// - the array starts with 2 VALUES describing the DIMENSION INFORMATION, (rows, columns)
// these are ignored in the actual calculations and serve as a metadata header (similar to the "location, time,... etc." data that is stored in photo files)
// so the array always carries it's own info about the nr. of rows and columns and doesn't need is seperate "info" file!
//
// To stay consistent with the standard Pinescript (array and ) indexing:
// - indexes for sheets and columns start from 0 (first) and run up to the (total nr of sheets or columns) - 1
// - indexes for rows also start from 0 (most recent, cfr. ) and run up to the (total nr of rows) - 1
//
// - this 2 value metadata header is followed by the actual df data
// the actual data array can consist of (100,000 - 2) usable items,
//
// In a theoretical example, you can have a matrix with almost 20,000 rows with each 5 columns of data (eg. open, high, low, close, volume) in it!!!
//
//
///////////////////////////////////
/// SCHEMATIC OF THE STRUCTURE: ///
///////////////////////////////////
//
////// (metadata header with dimensions info)
//
// (0) (1) (array index)
//

Correlation MatrixIn financial terms, 'correlation' is the numerical measure of the relationship between two variables (in this case, the variables are Forex pairs).
The range of the correlation coefficient is between -1 and +1. A correlation of +1 indicates that two currency pairs will flow in the same direction.
A correlation of -1 indicates that two currency pairs will move in the opposite direction.
Here, I multiplied correlation coefficient by 100 so that it is easier to read. Range between 100 and -100.
Color Coding:-
The darker the color, the higher the correlation positively or negatively.
Extra Light Blue (up to +29) : Weak correlation. Positions on these symbols will tend to move independently.
Light Blue (up to +49) : There may be similarity between positions on these symbols.
Medium Blue (up to +75) : Medium positive correlation.
Navy Blue (up to +100) : Strong positive correlation.
Extra Light Red (up to -30) : Weak correlation. Positions on these symbols will tend to move independently
Light Red (up to -49) : There may be similarity between positions on these symbols.
Dark Red: (up to -75) : Medium negative correlation.
Maroon: (up to -100) : Strong negative correlation.

Correlation MATRIX (Flexible version)Hey folks
A quick unrelated but interesting foreword
Hope you're all good and well and tanned
Me? I'm preparing the opening of my website where we're going to offer the Algorithm Builder Single Trend, Multiple Trends, Multi-Timeframe and plenty of others across many platforms (TradingView, FXCM, MT4, PRT). While others are at the beach and tanning (Yes I'm jealous, so what !?!), we're working our a** off to deliver an amazing looking website and great indicators and strategies for you guys.
Today I worked in including the Trade Manager Pro version and the Risk/Reward Pro version into all our Algorithm Builders. Here's a teaser
We're going to have a few indicators/strategies packages and subscriptions will open very soon.
The website should open in a few weeks and we still have loads to do ... (#no #summer #holidays #for #dave)
I see every message asking me to allow access to my Algorithm Builders but with the website opening shortly, it will be better for me to manage the trials from there - otherwise, it's duplicated and I can't follow all those requests
As you can probably all understand, it becomes very challenging to publish once a day with all that workload so I'll probably slow down (just a bit) and maybe posting once every 2/3 days until the website will be over (please forgive me for failing you). But once it will open, the daily publishing will resume again :) (here's when you're supposed to be clapping guys....)
While I'm so honored by all the likes, private messages and comments encouraging me, you have to realize that a script always takes me about 2/3 hours of work (with research, coding, debugging) but I'm doing it because I like it. Only pushing the brake a bit because of other constraints
INDICATOR OF THE DAY
I made a more flexible version of my Correlation Matrix .
You can now select the symbols you want and the matrix will update automatically !!! Let me repeat it once more because this is very cool... You can now select the symbols you want and the matrix will update automatically :)
Actually, I have nothing more to say about it... that's all :) Ah yes, I added a condition to detect negative correlation and they're being flagged with a black dot
Definition : Negative correlation or inverse correlation is a relationship between two variables whereby they move in opposite directions.
A negative correlation is a key concept in portfolio construction, as it enables the creation of diversified portfolios that can better withstand portfolio volatility and smooth out returns.
Correlation between two variables can vary widely over time. Stocks and bonds generally have a negative correlation, but in the decade to 2018, their correlation has ranged from -0.8 to 0.2. (Source : www.investopedia.com
See you maybe tomorrow or in a few days for another script/idea.
Be sure to hit the thumbs up to cheer me up as your likes will be the only sunlight I'll get for the next weeks.... because working on building a great offer for you guys.
Dave
____________________________________________________________
- I'm an officially approved PineEditor/LUA/MT4 approved mentor on codementor. You can request a coaching with me if you want and I'll teach you how to build kick-ass indicators and strategies
Jump on a 1 to 1 coaching with me
- You can also hire for a custom dev of your indicator/strategy/bot/chrome extension/python

Correlation Matrix by DaveattHi everyone
A co-pinescripter friend told me this was impossible to do and we bet a free dinner tomorrow. Guess who's going to be invited to a very fancy restaurant tomorrow :) :) :) (hint: not him)
What's the today script is about?
This script is based on this MT4 correlation matrix
Asset correlation is a measure of how investments move in relation to one another and when. ... Under what is known as modern portfolio theory, you can reduce the overall risk in an investment portfolio and even boost your overall returns by investing in asset combinations that are not correlated.
I did it because it wasn't existing before with this format. What I discovered was only correlations shown as plot lines... #this #is #not #pretty
How does it work?
The correlation matrix will not be based on the current asset of the chart BUT will be based on the current timeframe (confusing? if yes, read it again until you'll get it)
- Numbers of bars back: numbers of bars used for the correlation calculation
- High correlation level: Correlation upper threshold. If above, then the correlation will be green
- Low correlation level: Correlation lower threshold. If below, then the correlation will be red
If the correlation is between the high and low levels, then it will be displayed in orange
- FOREX/INDEX: You can choose between displaying the correlation matrix between 3 FOREX or 3 INDEX assets
Also...
So far the scale doesn't respond too well to the matrix so you'll have to adapt the scale manually. I'll publish a V2 if I'll find a way to solve this issue from the code directly #new #challenge
A quick final note on why I'm sharing so much?
It challenges me to think out of the norm, get out of my bubble and explore areas of Pinescript that I still don't know. This "a script a day" challenge allows me to speed up my learning curve on Pinescript by a billion factor (and I get a few interesting gigs as well)
Let's bring this indicator to 100 LIKES guys !!!!! I think it deserves it, don't you think? :)
PS
Before all copy/pasters will add a version with crypto tomorrow, don't bother, I already did it and will post it in a few minutes for FREE :p
____________________________________________________________
Be sure to hit the thumbs up as it shows me that I'm not doing this for nothing and will motivate to deliver more quality content in the future.
- I'm an officially approved PineEditor/LUA/MT4 approved mentor on codementor. You can request a coaching with me if you want and I'll teach you how to build kick-ass indicators and strategies
Jump on a 1 to 1 coaching with me
- You can also hire for a custom dev of your indicator/strategy/bot/chrome extension/python