def __init__(self, K, Y, init=None, threshold=1e-9): N = np.shape(K)[0] f = np.zeros((N,1)) converged = False k = 0 innerC = 0 for i in xrange(N): pdfDiff = norm.logpdf(f) - norm.logcdf(Y*f) W = np.exp(2*pdfDiff) + Y*f*np.exp(pdfDiff) Wsqrt = np.sqrt(W) Wdiag= np.diag(Wsqrt.flatten()) B = np.identity(N) + np.dot(Wdiag, np.dot(K, Wdiag)) grad = Y*np.exp(pdfDiff) b = W*f + grad interim = np.dot(Wdiag, np.dot(K, b)) cgRes = Cg(B, interim, threshold=threshold) s1 = cgRes.result innerC = innerC + cgRes.iterations a = b - Wsqrt*s1 if(converged): break f_prev = f f = np.dot(K, a) diff = f - f_prev if (np.dot(diff.T,diff).flatten() < threshold*N or innerC>15000): converged = True k = k+1 self.result = f self.iterations = k + innerC
def applyBoundaryConditions(self, bFunc, cFunc):
bcs = {}
nt = len(self.boundaryPoints)
for i0 in range(nt):
x0, y0 = self.boundaryPoints[i0]
i1 = (i0 + 1) % nt
x1, y1 = self.boundaryPoints[i1]
x, y = 0.5 * (x0 + x1), 0.5 * (y0 + y1)
b, c = eval(bFunc), eval(cFunc)
bcs[i0, i1] = (b, c)
self.ellipt.applyBoundaryConditions(bcs)
self.slvr = Cg(self.ellipt.getStiffnessMatrix(), \
self.ellipt.getSourceVector())
def __init__(self,
K,
Y,
P,
init=None,
threshold=1e-9,
innerThreshold=1e-9):
mMax = 15
N = np.shape(K)[0]
if init is None:
init = np.zeros((N, 1))
self.K = K
self.P = P
self.Y = Y.flatten()
x = init
r_prev = np.zeros((N, 1))
r = Y - np.dot(self.K, x)
p = np.zeros(6000, dtype=object)
k = 0
innerC = 0
while True:
if (np.dot(r.T, r).flatten() < threshold * N or k > 50000):
break
interim = Cg(P, r, threshold=innerThreshold)
z = interim.result
count = interim.iterations
innerC = innerC + count
if (k == 0):
p[k] = z
else:
m = max(1, k % (mMax + 1))
sum = 0
if (k - m < 0):
start = 0
else:
start = k - m
for i in xrange((k - m), k):
frac = np.dot(z.T, np.dot(self.K, p[i])) / np.dot(
p[i].T, np.dot(self.K, p[i]))
sum = sum + frac * p[i]
p[k] = z - sum
alpha = np.dot(p[k].T, r) / np.dot(p[k].T, np.dot(self.K, p[k]))
x = x + alpha * p[k]
r_prev = r
r = r - alpha * np.dot(K, p[k])
k = k + 1
self.outer_iterations = k
self.result = x
self.iterations = innerC + k
def __init__(self, K, Y, P, init=None, threshold=1e-9, innerThreshold=1e-9):
N = np.shape(K)[0]
if init is None:
init = np.zeros(N)
self.K = K
self.P = P
self.Y = Y.flatten()
x = init
r_prev = np.zeros(N)
r = self.Y - np.dot(self.K, x)
p = np.zeros(6000,dtype=object)
k = 0
innerC = 0
while True:
diff = r - r_prev
if (np.dot(diff.T,diff).flatten() < threshold) or k>5000:
break
interim = Cg(P, r, threshold=innerThreshold)
z = interim.result
count = interim.iterations
innerC = innerC + count
if (k == 0):
p[k] = z
else:
sum = 0
for i in xrange(k):
frac = np.dot(z.T,np.dot(self.K,p[i]))/np.dot(p[i].T, np.dot(self.K, p[i]))
sum = sum + np.dot(frac, p[i])
p[k] = z - sum
alpha = np.dot(p[k].T, r) / np.dot(p[k].T, np.dot(self.K, p[k]))
x = x + np.dot(alpha,p[k])
r_prev = r
r = r - np.dot(alpha, np.dot(K, p[k]))
k = k + 1
self.result = x
self.iterations = innerC + k
class App(object):
def run(self):
self.window = self.create_window()
context = self.create_cg_context()
context.register_states()
context.manage_texture_parameters = True
effect = context.create_effect_from_file(join(ROOT, 'effect.cgfx'))
self.load_texture(join(ROOT, 'texture.png'),
effect.parameters.by_name['texture'])
self.time_parameter = effect.parameters.by_name['time']
self.model_view_proj = effect.parameters.by_name['modelViewProj']
valid_techniques = [t for t in effect.techniques if t.valid]
assert valid_techniques
self.technique = valid_techniques[0]
print('techniques:')
import pprint; pprint.pprint(effect.techniques.by_name)
print('parameters:')
import pprint; pprint.pprint(effect.parameters.by_name)
self.running = True
while self.running:
self.process_events()
self.window.clear(sfml.Color.BLACK)
self.render()
self.window.display()
context.dispose()
self.cg.dispose()
self.window.close()
def load_texture(self, filename, parameter):
image = Image.open(filename)
data = image.tostring('raw', 'RGB', 0, -1)
gl.glPixelStorei(gl.GL_UNPACK_ALIGNMENT, 1)
to = gl.glGenTextures(1)
gl.glBindTexture(gl.GL_TEXTURE_2D, to)
parameter.set_value(to)
gl.glTexImage2D(gl.GL_TEXTURE_2D, 0, gl.GL_RGB,
image.size[0], image.size[1], 0, gl.GL_RGB, gl.GL_UNSIGNED_BYTE, data)
def render(self):
t = clock()
self.time_parameter.set_value(t)
data = (
((-0.5, -0.5, 0), (0.0, 0.0)),
((0.5, -0.5, 0), (1.0, 0.0)),
((0, 0.5, 0), (0.5, 1.0)),
)
proj = matrix44.create_perspective_projection_matrix(
90, 4.0 / 3.0, 0.01, 100.0)
mv = matrix44.multiply(
matrix44.create_from_translation((sin(t * 10), 0.0, -3.0 * abs(sin(t * 30)))),
matrix44.create_from_z_rotation(t * 50),
)
mvp = matrix44.multiply(mv, proj)
self.model_view_proj.set_value(mvp)
for pass_ in self.technique.passes:
pass_.begin()
gl.glClear(gl.GL_COLOR_BUFFER_BIT | gl.GL_DEPTH_BUFFER_BIT)
gl.glBegin(gl.GL_TRIANGLES)
for position, texcoord in data:
gl.glMultiTexCoord2fv(gl.GL_TEXTURE0, texcoord)
gl.glVertex3fv(position)
gl.glEnd()
pass_.end()
def create_window(self):
window = sfml.RenderWindow(sfml.VideoMode(800, 600), 'python-cg example')
window.vertical_sync_enabled = True
return window
def create_cg_context(self):
self.cg = Cg()
return self.cg.create_context()
def process_events(self):
for event in self.window.iter_events():
if event.type == sfml.Event.CLOSED:
self.running = False
def create_cg_context(self): self.cg = Cg() return self.cg.create_context()
class Elliptic2dDriverBase:
def __init__(self, fFunc, gFunc, sFunc):
self.fFuncStr = fFunc
self.gFuncStr = gFunc
self.sFuncStr = sFunc
self.boundaryPoints = []
self.delny = None
self.ellipt = Elliptic2d(self.ffunc, self.gfunc, self.sfunc)
self.slvr = None
self.solution = None
def getTriangulation(self):
return self.delny
def getSolution(self):
return self.solution
def assemble(self):
self.ellipt.assemble(self.delny)
def ffunc(self, xy):
x, y = xy
return eval(self.fFuncStr)
def gfunc(self, xy):
x, y = xy
return eval(self.gFuncStr)
def sfunc(self, xy):
x, y = xy
return eval(self.sFuncStr)
def applyBoundaryConditions(self, bFunc, cFunc):
bcs = {}
nt = len(self.boundaryPoints)
for i0 in range(nt):
x0, y0 = self.boundaryPoints[i0]
i1 = (i0 + 1) % nt
x1, y1 = self.boundaryPoints[i1]
x, y = 0.5 * (x0 + x1), 0.5 * (y0 + y1)
b, c = eval(bFunc), eval(cFunc)
bcs[i0, i1] = (b, c)
self.ellipt.applyBoundaryConditions(bcs)
self.slvr = Cg(self.ellipt.getStiffnessMatrix(), \
self.ellipt.getSourceVector())
def solve(self):
# initial guess
self.n = len(self.delny.points)
mat = self.ellipt.getStiffnessMatrix()
# use diagonal matrix as preconditioner
precond = numpy.array([mat[i, i] for i in range(self.n)])
# initial guess
x0 = numpy.zeros((self.n, ), numpy.float64)
# max number of iterations
numIters = self.n
diag = {}
self.solution = self.slvr.solve(precond=precond,
x0=x0,
numIters=numIters,
tol=1.e-10,
verbose=True,
diag=diag)
return diag
def show(self):
from plot import Plot
pl = Plot(self.delny, width=500, height=500)
pl.show(self.solution)
