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# -*- coding: utf-8 -*-
# vispy: gallery 30
"""N-dimensional scatter plot with GPU-based projections.
The projection axes evolve smoothly over time, following a path on the
Lie group SO(n).
"""
from vispy import gloo
from vispy import app
from vispy.color import ColorArray
from vispy.io import load_iris
import numpy as np
from scipy.linalg import logm
VERT_SHADER = """
#version 120
attribute vec4 a_position;
attribute vec3 a_color;
attribute float a_size;
uniform vec2 u_pan;
uniform vec2 u_scale;
uniform vec4 u_vec1;
uniform vec4 u_vec2;
varying vec4 v_fg_color;
varying vec4 v_bg_color;
varying float v_radius;
varying float v_linewidth;
varying float v_antialias;
void main (void) {
v_radius = a_size;
v_linewidth = 1.0;
v_antialias = 1.0;
v_fg_color = vec4(0.0,0.0,0.0,0.5);
v_bg_color = vec4(a_color, 1.0);
vec2 position = vec2(dot(a_position, u_vec1),
dot(a_position, u_vec2));
vec2 position_tr = u_scale * (position + u_pan);
gl_Position = vec4(position_tr, 0.0, 1.0);
gl_PointSize = 2.0*(v_radius + v_linewidth + 1.5*v_antialias);
}
"""
FRAG_SHADER = """
#version 120
varying vec4 v_fg_color;
varying vec4 v_bg_color;
varying float v_radius;
varying float v_linewidth;
varying float v_antialias;
void main()
{
float size = 2.0*(v_radius + v_linewidth + 1.5*v_antialias);
float t = v_linewidth/2.0-v_antialias;
float r = length((gl_PointCoord.xy - vec2(0.5,0.5))*size);
float d = abs(r - v_radius) - t;
if( d < 0.0 )
gl_FragColor = v_fg_color;
else
{
float alpha = d/v_antialias;
alpha = exp(-alpha*alpha);
if (r > v_radius)
gl_FragColor = vec4(v_fg_color.rgb, alpha*v_fg_color.a);
else
gl_FragColor = mix(v_bg_color, v_fg_color, alpha);
}
}
"""
class Canvas(app.Canvas):
def __init__(self):
app.Canvas.__init__(self, position=(50, 50), keys='interactive')
ps = self.pixel_scale
# Load the Iris dataset and normalize.
iris = load_iris()
position = iris['data'].astype(np.float32)
n, ndim = position.shape
position -= position.mean()
position /= np.abs(position).max()
v_position = position*.75
v_color = ColorArray(['orange', 'magenta', 'darkblue'])
v_color = v_color.rgb[iris['group'], :].astype(np.float32)
v_color *= np.random.uniform(.5, 1.5, (n, 3))
v_color = np.clip(v_color, 0, 1)
v_size = np.random.uniform(2*ps, 12*ps, (n, 1)).astype(np.float32)
self.program = gloo.Program(VERT_SHADER, FRAG_SHADER)
self.program['a_position'] = gloo.VertexBuffer(v_position)
self.program['a_color'] = gloo.VertexBuffer(v_color)
self.program['a_size'] = gloo.VertexBuffer(v_size)
self.program['u_pan'] = (0., 0.)
self.program['u_scale'] = (1., 1.)
self.program['u_vec1'] = (1., 0., 0., 0.)
self.program['u_vec2'] = (0., 1., 0., 0.)
# Circulant matrix.
circ = np.diagflat(np.ones(ndim-1), 1)
circ[-1, 0] = -1 if ndim % 2 == 0 else 1
self.logcirc = logm(circ)
# We will solve the equation dX/dt = log(circ) * X in real time
# to compute the matrix exponential expm(t*log(circ)).
self.mat = np.eye(ndim)
self.dt = .001
gloo.set_state(clear_color=(1, 1, 1, 1), blend=True,
blend_func=('src_alpha', 'one_minus_src_alpha'))
gloo.set_viewport(0, 0, *self.physical_size)
self._timer = app.Timer('auto', connect=self.on_timer, start=True)
self.show()
def on_timer(self, event):
# We advance the numerical solver from as many dt there have been
# since the last update.
for t in np.arange(0., event.dt, self.dt):
self.mat += self.dt * np.dot(self.logcirc, self.mat).real
# We just keep the first two columns of the matrix.
self.program['u_vec1'] = self.mat[:, 0].squeeze()
self.program['u_vec2'] = self.mat[:, 1].squeeze()
self.update()
def on_resize(self, event):
gloo.set_viewport(0, 0, *event.physical_size)
def on_draw(self, event):
gloo.clear()
self.program.draw('points')
if __name__ == '__main__':
c = Canvas()
app.run()
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