All Samples(2491) | Call(2246) | Derive(0) | Import(245)
cos(x[, out])
Cosine elementwise.
Parameters
----------
x : array_like
Input array in radians.
out : ndarray, optional
Output array of same shape as `x`.
Returns
-------
y : ndarray
The corresponding cosine values.
Raises
------
ValueError: invalid return array shape
if `out` is provided and `out.shape` != `x.shape` (See Examples)
Notes
-----
If `out` is provided, the function writes the result into it,
and returns a reference to `out`. (See Examples)
References
----------
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.
New York, NY: Dover, 1972.
Examples
--------
>>> np.cos(np.array([0, np.pi/2, np.pi]))
array([ 1.00000000e+00, 6.12303177e-17, -1.00000000e+00])
>>>
>>> # Example of providing the optional output parameter
>>> out2 = np.cos([0.1], out1)
>>> out2 is out1
True
>>>
>>> # Example of ValueError due to provision of shape mis-matched `out`
>>> np.cos(np.zeros((3,3)),np.zeros((2,2)))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: invalid return array shapesrc/m/a/matplotlib-HEAD/py4science/examples/numpytemps.py matplotlib(Download)
import nose
# convenience global names
from numpy import (pi, sin, cos, add, subtract, multiply, power)
def test1():
"""Verify an expression using temporaries.
# 4.5*cos(3*x**2): 4
# The final temporaries for each term are added and the result stored as y,
# which is also created. So we have 1 array for the result and 7 temps.
y = sin(x) + sin(2*x) - 4.5*cos(3*x**2)
# Now we do it again, but here, we control the temporary creation
# ourselves. We use the output argument of all numpy functional forms of
# - 4.5*cos(3*x**2)
power(x,2,tmp)
multiply(3,tmp,tmp)
cos(tmp,tmp)
multiply(4.5,tmp,tmp)
subtract(z,tmp,z)
def test2():
"""Compute the same expression, using in-place operations
"""
x = np.linspace(0,2*pi,100)
y = sin(x) + sin(2*x) - 4.5*cos(3*x**2)
# - 4.5*cos(3*x**2)
power(x,2,tmp)
tmp *= 3
cos(tmp,tmp)
tmp *= 4.5
z -= tmp
src/a/u/aureservoir-HEAD/python/examples/filtering.py aureservoir(Download)
Afilt = N.zeros(3) # feedback path if( ftype=='LPF' ): Bfilt[0] = (1 - N.cos(w0)) / 2. Bfilt[1] = 1 - N.cos(w0) Bfilt[2] = (1 - N.cos(w0)) / 2. Afilt[0] = 1 + alpha Afilt[1] = -2*N.cos(w0) Afilt[2] = 1 - alpha elif( ftype=='HPF' ): Bfilt[0] = (1 + N.cos(w0))/2. Bfilt[1] = -(1 + N.cos(w0)) Bfilt[2] = (1 + N.cos(w0))/2.
Bfilt[1] = -(1 + N.cos(w0)) Bfilt[2] = (1 + N.cos(w0))/2. Afilt[0] = 1 + alpha Afilt[1] = -2*N.cos(w0) Afilt[2] = 1 - alpha elif( ftype=='BPF' ): # constant 0dB peak gain Bfilt[0] = alpha Bfilt[1] = 0 Bfilt[2] = -alpha Afilt[0] = 1 + alpha Afilt[1] = -2*N.cos(w0)
Afilt[2] = 1 - alpha elif( ftype=='notch' ): Bfilt[0] = 1. Bfilt[1] = -2*N.cos(w0) Bfilt[2] = 1. Afilt[0] = 1 + alpha Afilt[1] = -2*N.cos(w0) Afilt[2] = 1 - alpha elif( ftype=='APF' ): Bfilt[0] = 1 - alpha Bfilt[1] = -2*N.cos(w0) Bfilt[2] = 1 + alpha Afilt[0] = 1 + alpha Afilt[1] = -2*N.cos(w0)
Afilt[2] = 1 - alpha elif( ftype=='peakingEQ' ): Bfilt[0] = 1 + alpha*A Bfilt[1] = -2*N.cos(w0) Bfilt[2] = 1 - alpha*A Afilt[0] = 1 + alpha/A Afilt[1] = -2*N.cos(w0) Afilt[2] = 1 - alpha/A elif( ftype=='lowShelf' ): Bfilt[0] = A*((A+1)-(A-1)*N.cos(w0) + 2*N.sqrt(A)*alpha) Bfilt[1] = 2*A*( (A-1) - (A+1)*N.cos(w0) ) Bfilt[2] = A*((A+1)-(A-1)*N.cos(w0)-2*N.sqrt(A)*alpha) Afilt[0] = (A+1)+(A-1)*N.cos(w0)+2*N.sqrt(A)*alpha Afilt[1] = -2*( (A-1) + (A+1)*N.cos(w0))
Bfilt[2] = A*((A+1)-(A-1)*N.cos(w0)-2*N.sqrt(A)*alpha) Afilt[0] = (A+1)+(A-1)*N.cos(w0)+2*N.sqrt(A)*alpha Afilt[1] = -2*( (A-1) + (A+1)*N.cos(w0)) Afilt[2] = (A+1) + (A-1)*N.cos(w0)-2*N.sqrt(A)*alpha elif( ftype=='highShelf' ): Bfilt[0] = A*((A+1)+(A-1)*N.cos(w0)+2*N.sqrt(A)*alpha) Bfilt[1] = -2*A*( (A-1) + (A+1)*N.cos(w0) ) Bfilt[2] = A*( (A+1) + (A-1)*N.cos(w0)-2*N.sqrt(A)*alpha ) Afilt[0] = (A+1) - (A-1)*N.cos(w0) + 2*N.sqrt(A)*alpha Afilt[1] = 2*( (A-1) - (A+1)*N.cos(w0) ) Afilt[2] = (A+1) - (A-1)*N.cos(w0) - 2*N.sqrt(A)*alpha
# calculate gain factor gain = abs( (-2*N.exp(4*1j*cf*N.pi*T)*T + \ 2*N.exp(-(B*T) + 2*1j*cf*N.pi*T) * T * \ (N.cos(2*cf*N.pi*T) - N.sqrt(3. - 2**(3./2.)) * \ N.sin(2*cf*N.pi*T))) * (-2*N.exp(4*1j*cf*N.pi*T)*T + \ 2*N.exp(-(B*T) + 2*1j*cf*N.pi*T) * T * \ (N.cos(2*cf*N.pi*T) + N.sqrt(3. - 2**(3./2.)) * \ N.sin(2*cf*N.pi*T))) * (-2*N.exp(4*1j*cf*N.pi*T)*T + \ 2*N.exp(-(B*T) + 2*1j*cf*N.pi*T) * T * (N.cos(2*cf*N.pi*T) - \ N.sqrt(3. + 2**(3./2.)) * N.sin(2*cf*N.pi*T))) * \ (-2*N.exp(4*1j*cf*N.pi*T)*T + 2*N.exp(-(B*T) + \ 2*1j*cf*N.pi*T) * T * (N.cos(2*cf*N.pi*T) + \
Afilt = N.zeros((len(cf),9)) # feedback path Bfilt = N.zeros((len(cf),5)) # forward path Bfilt[:,0] = T**4 / gain Bfilt[:,1] = -4*T**4*N.cos(2*cf*N.pi*T) / N.exp(B*T) / gain Bfilt[:,2] = 6*T**4*N.cos(4*cf*N.pi*T) / N.exp(2*B*T) / gain Bfilt[:,3] = -4*T**4*N.cos(6*cf*N.pi*T) / N.exp(3*B*T) / gain Bfilt[:,4] = T**4*N.cos(8*cf*N.pi*T) / N.exp(4*B*T) / gain Afilt[:,0] = 1. Afilt[:,1] = -8*N.cos(2*cf*N.pi*T) / N.exp(B*T) Afilt[:,2] = 4*(4 + 3*N.cos(4*cf*N.pi*T)) / N.exp(2*B*T) Afilt[:,3] = -8*(6*N.cos(2*cf*N.pi*T) + N.cos(6*cf*N.pi*T)) / N.exp(3*B*T) Afilt[:,4] = 2*(18 + 16*N.cos(4*cf*N.pi*T)+N.cos(8*cf*N.pi*T)) / N.exp(4*B*T) Afilt[:,5] = -8*(6*N.cos(2*cf*N.pi*T) + N.cos(6*cf*N.pi*T)) / N.exp(5*B*T) Afilt[:,6] = 4*(4 + 3*N.cos(4*cf*N.pi*T)) / N.exp(6*B*T)
Afilt[:,4] = 2*(18 + 16*N.cos(4*cf*N.pi*T)+N.cos(8*cf*N.pi*T)) / N.exp(4*B*T) Afilt[:,5] = -8*(6*N.cos(2*cf*N.pi*T) + N.cos(6*cf*N.pi*T)) / N.exp(5*B*T) Afilt[:,6] = 4*(4 + 3*N.cos(4*cf*N.pi*T)) / N.exp(6*B*T) Afilt[:,7] = -8*N.cos(2*cf*N.pi*T) / N.exp(7*B*T) Afilt[:,8] = N.exp(-8*B*T) return Bfilt,Afilt
# calculate gain factor gain = abs( (-2*N.exp(4*1j*cf*N.pi*T)*T + \ 2*N.exp(-(B*T) + 2*1j*cf*N.pi*T) * T * \ (N.cos(2*cf*N.pi*T) - N.sqrt(3. - 2**(3./2.)) * \ N.sin(2*cf*N.pi*T))) * (-2*N.exp(4*1j*cf*N.pi*T)*T + \ 2*N.exp(-(B*T) + 2*1j*cf*N.pi*T) * T * \ (N.cos(2*cf*N.pi*T) + N.sqrt(3. - 2**(3./2.)) * \ N.sin(2*cf*N.pi*T))) * (-2*N.exp(4*1j*cf*N.pi*T)*T + \ 2*N.exp(-(B*T) + 2*1j*cf*N.pi*T) * T * (N.cos(2*cf*N.pi*T) - \ N.sqrt(3. + 2**(3./2.)) * N.sin(2*cf*N.pi*T))) * \ (-2*N.exp(4*1j*cf*N.pi*T)*T + 2*N.exp(-(B*T) + \ 2*1j*cf*N.pi*T) * T * (N.cos(2*cf*N.pi*T) + \
# init all 4 biquads for n in range(4): Afilt[:,n,0] = 1. Afilt[:,n,1] = -2 * N.cos(2*cf*N.pi*T) / N.exp(B*T) Afilt[:,n,2] = N.exp(-2*B*T) Bfilt[:,n,0] = T Bfilt[:,n,2] = 0. # init the rest tmp = 2*T*N.cos(2*cf*N.pi*T) / N.exp(B*T)
src/p/y/pyfusion-HEAD/examples/Boyds/wid_specgram.py pyfusion(Download)
""" from matplotlib.widgets import RadioButtons, Button import pylab as pl from numpy import sin, pi, ones, hanning, hamming, bartlett, kaiser, arange, blackman, cos, sqrt, log10, fft import pyfusion
def local_wider(vec):
""" Flat top in middle, cos at edges - meant to be narrower in f
but not as good in the wings
"""
N=len(vec)
k=arange(N)
w = sqrt(sqrt(1 - cos(2*pi*k/(N-1))))
def local_flat_top_freq(vec):
N=len(vec)
k=arange(N)
w = (1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1))
-0.388*cos(6*pi*k/(N-1)) +0.032*cos(8*pi*k/(N-1)))
return(w)
src/m/a/matplotlib-HEAD/matplotlib/examples/pylab_examples/quadmesh_demo.py matplotlib(Download)
x = np.linspace(-1.5,1.5,n) y = np.linspace(-1.5,1.5,n*2) X,Y = np.meshgrid(x,y); Qx = np.cos(Y) - np.cos(X) Qz = np.sin(Y) + np.sin(X) Qx = (Qx + 1.1) Z = np.sqrt(X**2 + Y**2)/5;
src/m/a/matplotlib-HEAD/examples/pylab_examples/quadmesh_demo.py matplotlib(Download)
x = np.linspace(-1.5,1.5,n) y = np.linspace(-1.5,1.5,n*2) X,Y = np.meshgrid(x,y); Qx = np.cos(Y) - np.cos(X) Qz = np.sin(Y) + np.sin(X) Qx = (Qx + 1.1) Z = np.sqrt(X**2 + Y**2)/5;
src/a/l/algopy-HEAD/documentation/AD_tutorial_TU_Berlin/example7_simple_computation_of_the_hessian.py algopy(Download)
at x = (3,7)
"""
import numpy; from numpy import sin,cos, array, zeros
from taylorpoly import UTPS
def f_fcn(x):
return sin(x[0] + cos(x[1])*x[0])
def H_fcn(x):
H11 = -(1+cos(x[1]))**2*sin(x[0]+cos(x[1])*x[0])
H21 = -sin(x[1]) * cos(x[0] + cos(x[1])*x[0]) \
+sin(x[1]) *x[0]*(1+ cos(x[1]))*sin(x[0]+cos(x[1])*x[0])
H22 = -cos(x[1])*x[0]*cos(x[0]+cos(x[1])*x[0])\
-(sin(x[1])*x[0])**2*sin(x[0]+cos(x[1])*x[0])
return array([[H11, H21],[H21,H22]])
src/o/p/openrave-HEAD/trunk/python/examples/hanoi.py openrave(Download)
from openravepy import Environment, IkParameterization, planning_error, raveLogInfo, raveLogWarn, OpenRAVEGlobalArguments, RaveDestroy from openravepy.interfaces import BaseManipulation, TaskManipulation from openravepy.databases import inversekinematics from numpy import array, arange, linalg, pi, dot, vstack, cos, sin, cross, r_, c_ from optparse import OptionParser class HanoiPuzzle:
for ang in arange(-pi,pi,0.3):
# find the dest position
p = Tpeg[0:3,3:4] + height * dest_upvec
R = dot(Tpeg[0:3,0:3], array(((cos(ang),-sin(ang),0),(sin(ang),cos(ang),0),(0,0,1))))
T = dot(r_[c_[R,p], [[0,0,0,1]]], Tdiff)
with self.env:
# check the IK of the destination
def GetGrasp(self, Tdisk, radius, angles):
""" returns the transform of the grasp given its orientation and the location/size of the disk"""
zdir = -dot(Tdisk[0:3,0:3],vstack([cos(angles[0])*cos(angles[1]),-cos(angles[0])*sin(angles[1]),-sin(angles[0])]))
pos = Tdisk[0:3,3:4] + radius*dot(Tdisk[0:3,0:3],vstack([cos(angles[1]),-sin(angles[1]),0]))
xdir = cross(Tdisk[0:3,1:2],zdir,axis=0)
xdir = xdir / linalg.norm(xdir)
ydir = cross(zdir,xdir,axis=0)
src/m/a/Matplotlib--JJ-s-dev-HEAD/examples/pylab_examples/quadmesh_demo.py Matplotlib--JJ-s-dev(Download)
x = np.linspace(-1.5,1.5,n) y = np.linspace(-1.5,1.5,n*2) X,Y = np.meshgrid(x,y); Qx = np.cos(Y) - np.cos(X) Qz = np.sin(Y) + np.sin(X) Qx = (Qx + 1.1) Z = np.sqrt(X**2 + Y**2)/5;
src/o/p/openrave-HEAD/python/examples/hanoi.py openrave(Download)
from openravepy import Environment, IkParameterization, planning_error, raveLogInfo, raveLogWarn, OpenRAVEGlobalArguments from openravepy.interfaces import BaseManipulation, TaskManipulation from openravepy.databases import inversekinematics from numpy import array, arange, linalg, pi, dot, vstack, cos, sin, cross, r_, c_ from optparse import OptionParser class HanoiPuzzle:
for ang in arange(-pi,pi,0.3):
# find the dest position
p = Tpeg[0:3,3:4] + height * dest_upvec
R = dot(Tpeg[0:3,0:3], array(((cos(ang),-sin(ang),0),(sin(ang),cos(ang),0),(0,0,1))))
T = dot(r_[c_[R,p], [[0,0,0,1]]], Tdiff)
with self.env:
# check the IK of the destination
def GetGrasp(self, Tdisk, radius, angles):
""" returns the transform of the grasp given its orientation and the location/size of the disk"""
zdir = -dot(Tdisk[0:3,0:3],vstack([cos(angles[0])*cos(angles[1]),-cos(angles[0])*sin(angles[1]),-sin(angles[0])]))
pos = Tdisk[0:3,3:4] + radius*dot(Tdisk[0:3,0:3],vstack([cos(angles[1]),-sin(angles[1]),0]))
xdir = cross(Tdisk[0:3,1:2],zdir,axis=0)
xdir = xdir / linalg.norm(xdir)
ydir = cross(zdir,xdir,axis=0)
src/m/a/matplotlib-HEAD/matplotlib/examples/mplot3d/surface3d_demo2.py matplotlib(Download)
u = np.linspace(0, 2 * np.pi, 100) v = np.linspace(0, np.pi, 100) x = 10 * np.outer(np.cos(u), np.sin(v)) y = 10 * np.outer(np.sin(u), np.sin(v)) z = 10 * np.outer(np.ones(np.size(u)), np.cos(v)) ax.plot_surface(x, y, z, rstride=4, cstride=4, color='b')
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