GRFMatrixMath
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This script functions as a specialized mathematical toolkit designed to perform complex linear algebra operations within the MetaTrader platform. Essentially, it provides a foundation for advanced calculations that involve "matrices"—which are simply organized grids of numbers used to solve multi-variable equations, model physical systems, or handle sophisticated data transformations.
The logic is divided into several core capabilities:
Core Arithmetic Operations The script allows for the basic manipulation of these numerical grids. It can add two matrices together (with an optional weight applied to one), multiply a matrix by a single constant value (scaling), and perform standard matrix multiplication. Matrix multiplication is a specific mathematical process where rows and columns are combined; this script automates that heavy lifting to ensure accuracy.
Structural Transformations It includes utilities to reorganize data layouts, such as:
- Transposition: Flipping a grid over its diagonal (turning rows into columns).
- Zeroing: Clearing all values in a grid to zero.
- Identity Creation: Generating an "Identity Matrix," which acts like the number "1" in matrix math (a grid with 1s on the main diagonal and 0s everywhere else).
Advanced Analytical Calculations The script handles more sophisticated mathematical concepts necessary for high-level modeling:
- Determinants: It calculates a specific single value (the determinant) from a grid. This is often used to determine if a system of equations has a unique solution or to calculate the "scaling factor" of a linear transformation.
- Inversion: One of the most complex tasks provided is finding the "Inverse" of a matrix. In math, multiplying a matrix by its inverse brings you back to the identity state; this is crucial for solving systems of linear equations where you need to isolate a specific variable.
Validation and Safety To ensure the calculations remain accurate, the script includes built-in checks. It verifies that matrices are "square" (having an equal number of rows and columns) before attempting certain operations. It also identifies "unstable" matrices—situations where a calculation might result in an error or an undefined value—and handles these cases to prevent the software from crashing or producing nonsensical data.
Summary for the User While this script doesn't perform a specific trade by itself, it provides the "engine" required for advanced trading algorithms. It allows a developer to perform the heavy mathematical lifting needed for complex indicators, risk models, or automated systems that rely on multi-dimensional data analysis.
//+------------------------------------------------------------------+
//| MatrixMath.mq4 |
//| Copyleft© 2007, GammaRatForex |
//| http://gwmmarat.com/Forex/ |
//+------------------------------------------------------------------+
#property copyright "Copyleft© 2007, GammaRatForex"
#property link "http://gwmmarat.com/Forex/"
#property library
//+------------------------------------------------------------------+
//| MatrixAdd |
//+------------------------------------------------------------------+
double determinant_fixed(double a[][], int k){
double z;
switch(k){
case 1: return(a[0][0]);
break;
case 2: return( a[0][0]*a[1][1]-a[1][0]*a[0][1]);
break;
case 3:
z = a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] +
a[0][2]*a[1][0]*a[2][1] -
(a[2][0]*a[1][1]*a[0][2] + a[1][0]*a[0][1]*a[2][2] +
a[0][0]*a[2][1]*a[1][2]);
return(z);
break;
default:
Print("array_range too large for determinant calculation");
return(0);
}
}
double determinant(double a[][]){
double z;
if(ArrayRange(a,0) != ArrayRange(a,1)){
Print("Non-square array entered into determinant");
return(0);
}
switch(ArrayRange(a,0)){
case 1: return(a[0][0]);
break;
case 2: return( a[0][0]*a[1][1]-a[1][0]*a[0][1]);
break;
case 3:
z = a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] +
a[0][2]*a[1][0]*a[2][1] -
(a[2][0]*a[1][1]*a[0][2] + a[1][0]*a[0][1]*a[2][2] +
a[0][0]*a[2][1]*a[1][2]);
return(z);
break;
default:
Print("array_range too large for determinant calculation");
return(0);
}
}
int MatrixAdd(double a[][], double b[][],double & c[][],double w=1){
int i,j;
for(i=0;i<ArrayRange(c,0);i++){
for(j=0;j<ArrayRange(c,1);j++){
c[i][j] = a[i][j]+w*b[i][j];
}
}
return(0);
}
int MatrixMul(double a[][], double b[][],double & c[][]){
int i,j, k;
if(ArrayRange(a,1) != ArrayRange(b,0)){
Print("array Range Mismatch in Matrix Mul");
return(-1);
}
for(i=0;i<ArrayRange(a,0);i++){
for(j=0;j<ArrayRange(b,1);j++){
c[i][j] = 0;
for(k=0;k<ArrayRange(a,1);k++){
c[i][j] += (a[i][k]*b[k][j]);
}
}
}
return(0);
}
int MatrixScalarMul(double b,double & a[][]){
int i,j;
for(i =0;i<ArrayRange(a,0);i++){
for(j=0;j<ArrayRange(a,1);j++){
a[i][j] *= b;
}
}
}
int MatrixInvert(double a[][],double & b[][]){
double d;
double temp1[4][4],temp2[4][4];
int i,j,i1,j1,k;
if(ArrayRange(a,0) != ArrayRange(a,1)){
Print("Matrix Inverse attempted on non square matrix. Not implemented yet");
return(-1);
}
if(ArrayRange(a,1) > 3){
Print("Bugger off, not implemented yet");
return(-1);
}
d = determinant(a);
if(MathAbs(d)<0.000001){
Print("unstable matrix");
d = 1;
}
k = ArrayRange(a,0);
if(k==0){
b[0][0]=1./a[0][0];
return(0);
}
d = determinant(a);
for(i1=0;i1<k;i1++){
for(j1=0;j1<k;j1++){
temp1[i1][j1] = a[i1][j1];
}
}
for(i=0;i<k;i++){
for(j=0;j<k;j++){
//copy the arry. There must be a better way!!
ArrayCopy(temp2,temp1);
for(j1=0;j1<k;j1++){
if(j1==j){
temp2[i][j1] = 1;
}else{
temp2[i][j1] = 0;
}
}
b[i][j]=determinant_fixed(temp2,k)/d;
}
}
}
int MatrixTranspose(double a[][],double & b[][]){
int i,j;
for(i=0;i<ArrayRange(a,0);i++){
for(j=0;j<ArrayRange(a,1);j++){
b[j][i] = a[i][j];
}
}
return(0);
}
int MatrixZero(double & a[][]){
int i,j;
for(i= 0;i<ArrayRange(a,0);i++){
for(j=0;j<ArrayRange(a,1);j++){
a[i][j]=0;
}
}
return(0);
}
int MatrixEye(double & a[][]){
int i,j;
for(i= 0;i<ArrayRange(a,0);i++){
for(j=0;j<ArrayRange(a,1);j++){
a[i][j]=0;
if(i==j)a[i][j]=1;
}
}
return(0);
}
int MatrixPrint(double a[][]){
int i,j;
for(i= 0;i<ArrayRange(a,0);i++){
for(j=0;j<ArrayRange(a,1);j++){
Print(i," ,",j," ,",a[i][j]);
}
}
return(0);
}
//+------------------------------------------------------------------+
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