Vectors and Matrices

In this tutorial, we will discuss how to work with vectors (a.k.a. N-tuples) and their multi-dimensional extensions matrices.

Constructing, Concatenating, and Transposing...

We'll focus on constructing the following 3x3 matrix:

1	2	3
4	5	6
7	8	9

Here are some different examples of syntax to do just that. You may run this code snippet within your own JAVA main() program, Groovy script, etc. For a review of how to get started see Basic Usage;

import  com.mockturtlesolutions.snifflib.datatypes.DblMatrix;
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. 
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//Construction from a String. Here are the guidelines...
//   * Square brackets indicated concatenation.
//   * Commas and/or spaces indicate column increment.
//   * Semicolons indicate row increment.
DblMatrix X = new DblMatrix("[1 2 3; 4 5 6; 7 8 9]");
X.show("X");

//Concatenation of rows...
DblMatrix Y = new DblMatrix("[1 2 3]");
Y = Y.concat(new DblMatrix("[4 5 6]",1);
Y = Y.concat(new DblMatrix("[7 8 9]",1);
Y.show("Y is just like X");

//Concatenation of columns...
DblMatrix Z = new DblMatrix("[1; 4; 7]");
Z = Z.concat(new DblMatrix("[2;5;8]"),2);
Z = Z.concat(new DblMatrix("[3;6;9]"),2);
Z.show("Another matrix...");

//Fill-in following the assumed "row-first" ordering...
int[] siz = new int[]{3,3};
//Note, in Groovy you'd create an int[] using the syntax
//def siz = [3,3] as int[];
W = new DblMatrix(siz);
for (int k=0;k<9;k++)
{
    W.setDoubleAt(new Double(k+1),k);
}
W = W.transpose();
W.show("W looks nice!","0");

//Notice that the last show() uses a formatted display for single-digit integers.

Matrix Algebra

Here are some commonly used matrix algebra operations using the DblMatrix class.

import  com.mockturtlesolutions.snifflib.datatypes.DblMatrix;
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. 
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DblMatrix X = new DblMatrix("[1 2 3; 4 5 6; 7 8 9]");
X.show("X");

//Create an 3x3 identity matrix.
DblMatrix F = DblMatrix.I(3);
F.show("Identity matrix");

//Inner product between two matrices.
P = W.dot(F);
P.show("P")

//Element-by-element multiplication between two matrices. 
Q = W.times(F);
Q.show("Q")

//Addition of two matrices.
M = P.plus(Q);
M.show("Addition");

//Subtraction of two matrices.
M = P.minus(Q);
M.show("Subtraction");

//Element-by-element powering of one matrix by another.         
M = P.pow(Q);
M.show("Power");

To see the many more class methods possible, see the DblMatrix API .