amoffat/python-cgla

Linear algebra library for computer graphics

Why

Doing simple matrix and vector operations with existing linear algebra libraries is very painful. This utility is a way of manipulating matrices and vectors intuitively to understand problems more quickly. It is designed for prototyping solutions quickly.

It is not designed to replace existing, far more robust libraries like NumPy. cgla is intuitive at the cost of efficiency and performance.

Examples

Creating a matrix

from cgla import Vec, Mat

# creating as a list of lists, with each sub list as a matrix row
mat = Mat([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])
print mat

# or if you're sloppy, each matrix row is an individual argument.  this has the
# exact same result as above
mat = Mat(
	[1, 2, 3]
	[4, 5, 6],
	[7, 8, 9]
)

# you can also create a matrix empty, just by specifying the number of columns
# and rows it should have
mat = Mat(3, 4)
print mat

Output:

| 1 2 3 |
| 4 5 6 |
| 7 8 9 |

| 0 0 0 |
| 0 0 0 |
| 0 0 0 |
| 0 0 0 |

Manipulating a matrix

from cgla import Vec, Mat

# create a 3x3 identity matrix
mat = Mat.new_identity(3)

# the coordinates are x, y, (or if you prefer: col, row)
print mat[1][2]
mat[1][2] = 997

print mat[1][2]

Output:

| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

|   1   0   0 |
|   0   1   0 |
|   0 997   1 |

Creating a vector

from cgla import Vec, Mat
from math import pi

# a three-dimensional vector
vec3 = Vec(1, 2, 3)
print vec3.z

# a two-dimensional vector
vec2 = Vec(4, 6)
print vec2.y  

# assignment by component name
vec2.x = 5
print vec2.x

Output:

3
6
5

Matrix columns are vectors

from cgla import Vec, Mat

mat = Mat(
	[1, 2, 3],
	[4, 5, 6],
	[7, 8, 9],
)

vec = mat[0]
print vec

# and changing that column vector changes the corresponding matrix column
# and vice versa
vec.x = 304
print mat

Output:

| 1 |
| 4 |
| 7 |

| 304   2   3 |
|   4   5   6 |
|   7   8   9 |

Rotating a vector

Rotating a vector involves multiplying a rotation matrix with a vector. The resulting vector is smart: when printed, any values that can be converted to a friendlier form will be substituted for the original numeric value.

from cgla import Vec, Mat
from math import pi

# create a new rotation matrix with 0 radian rotation around the x-axis,
# pi/4 radian (45 degrees) rotation around the y-axis, and 0 radian rotaiton
# about the z-axis
rot = Mat.new_rotation(0, pi/4, 0)

vec = Vec(1, 0, 0)

rotated_vec = rot * vec
print rotated_vec

Output:

|  cos(π/4) |
|         0 |
| sin(-π/4) |

Other vector operations

from cgla import Vec, Mat

vec = Vec(2, 3, 1.3)

# magnitude or length
print vec.magnitude()

# normalized
print vec.normalize()

# add vectors
print vec + Vec(1, 2, 1)

Output:

3.83275357935

| 0.52 |
| 0.78 |
| 0.34 |

|    3 |
|    5 |
| 2.30 |