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dot(a, b)
Dot product of two arrays.
For 2-D arrays it is equivalent to matrix multiplication, and for 1-D
arrays to inner product of vectors (without complex conjugation). For
N dimensions it is a sum product over the last axis of `a` and
the second-to-last of `b`::
dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
Parameters
----------
a : array_like
First argument.
b : array_like
Second argument.
Returns
-------
output : ndarray
Returns the dot product of `a` and `b`. If `a` and `b` are both
scalars or both 1-D arrays then a scalar is returned; otherwise
an array is returned.
Raises
------
ValueError
If the last dimension of `a` is not the same size as
the second-to-last dimension of `b`.
See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
Examples
--------
>>> np.dot(3, 4)
12
Neither argument is complex-conjugated:
>>> np.dot([2j, 3j], [2j, 3j])
(-13+0j)
For 2-D arrays it's the matrix product:
>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([[4, 1],
[2, 2]])
>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128src/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:
Tpeg = destpeg.GetTransform()
src_upvec = Tsrcpeg[0:3,2:3]
dest_upvec = Tpeg[0:3,2:3]
Tdiff = dot(linalg.inv(Tdisk), Thand)
# iterate across all possible orientations the destination peg can be in
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)
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)
Tgrasp = r_[c_[xdir,ydir,zdir,pos],[[0,0,0,1]]]
return [Tgrasp,dot(Tgrasp, array([[-1,0,0,0],[0,1,0,0],[0,0,-1,0],[0,0,0,1]]))]
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:
Tpeg = destpeg.GetTransform()
src_upvec = Tsrcpeg[0:3,2:3]
dest_upvec = Tpeg[0:3,2:3]
Tdiff = dot(linalg.inv(Tdisk), Thand)
# iterate across all possible orientations the destination peg can be in
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)
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)
Tgrasp = r_[c_[xdir,ydir,zdir,pos],[[0,0,0,1]]]
return [Tgrasp,dot(Tgrasp, array([[-1,0,0,0],[0,1,0,0],[0,0,-1,0],[0,0,0,1]]))]
src/p/y/pylon-HEAD/examples/pips/nlp.py pylon(Download)
""" This example demonstrates how to use the Python Interior Point Solver using the problem from http://en.wikipedia.org/wiki/Nonlinear_programming. """ from numpy import array, r_, float64, dot from scipy.sparse import csr_matrix from pips import pips
def gh2(x):
h = dot(array([ [1, -1, 1], [1, 1, 1] ]), x**2) + array([-2.0, -10.0])
dh = 2 * csr_matrix( array([ [x[0], x[0]], [-x[1], x[1]], [x[2], x[2]] ]) )
g = array([])
dg = None
return h, g, dh, dg
def hess2(x, lam):
mu = lam["ineqnonlin"]
Lxx = csr_matrix( array([ r_[dot(2 * array([1, 1]), mu), -1, 0],
r_[-1, dot(2 * array([-1, 1]), mu), -1],
r_[0, -1, dot(2 * array([1, 1]), mu)] ]) )
src/b/i/biflib-HEAD/bal/python/examples/lyap.py biflib(Download)
def gsr(x):
from numpy import zeros, dot, sqrt
from numpy.linalg import norm
N = len(x)
n = int(sqrt(N))
znorm = zeros(n)
znorm[0] = norm(x[0:n])
xnorm = zeros(N)
xnorm[0:n] = x[0:n] / znorm[0]
for i in range(1,n):
tmp = x[n*i:n*(i+1)].copy()
for j in range(i):
d = dot(x[n*i:n*(i+1)],xnorm[n*j:n*(j+1)])
tmp = x[n*i:n*(i+1)].copy()
for j in range(i):
d = dot(x[n*i:n*(i+1)],xnorm[n*j:n*(j+1)])
tmp = tmp - dot(x[n*i:n*(i+1)],xnorm[n*j:n*(j+1)])*xnorm[n*j:n*(j+1)]
znorm[i] = norm(tmp)
xnorm[n*i:n*(i+1)] = tmp / znorm[i]
return xnorm,znorm
src/a/r/arboris-python-HEAD/examples/test_weight.py arboris-python(Download)
from arboris.core import World, simulate from pylab import plot, show, legend, xlabel, ylabel, title from arboris.core import Observer from numpy import arange, dot, eye, array import arboris.homogeneousmatrix as homogeneousmatrix from arboris.core import Body, SubFrame from arboris.joints import FreeJoint
def update(self, dt):
self.timeline.append(self.world.current_time)
self.height.append(dot(self.world.up, self.frame.pose[0:3,3]))
print self.frame.pose[0:3,3]
def finish(self):
pass
twist_c = array([0.,0.,0.,0.,0.,0.])
else:
twist_c = array([1,1,1,0,0,0.])
twist_b = dot(homogeneousmatrix.adjoint(H_bc), twist_c)
freejoint = FreeJoint(gpos=homogeneousmatrix.inv(H_bc), gvel=twist_b)
w.add_link(w.ground, freejoint, body)
w.register(Box(subframe, half_extents))
src/o/p/openrave-HEAD/trunk/python/examples/tutorial_003.py openrave(Download)
__copyright__ = '2010 Makoto Furukawa'
__license__ = 'Apache License, Version 2.0'
from openravepy import Environment, rotationMatrixFromAxisAngle, axisAngleFromRotationMatrix, matrixFromAxisAngle
from numpy import eye, dot, pi
def run(args=None):
try:
deg = -45
rot_mat = rotationMatrixFromAxisAngle([1,0,0],float(deg)*pi/180.0)
print 'AxisAngle = ',axisAngleFromRotationMatrix(rot_mat)
tran[0:3,0:3] = dot(rot_mat, tran[0:3,0:3])
body.SetTransform(tran)
P1 = dot(rot_mat, [0,0,1])
deg = 45
rot_mat = rotationMatrixFromAxisAngle([0,1,0],float(deg)*pi/180.0)
print 'AxisAngle = ',axisAngleFromRotationMatrix(rot_mat)
tran[0:3,0:3] = dot(rot_mat, tran[0:3,0:3])
body.SetTransform(tran)
P2 = dot(rot_mat, P1)
handles.append(env.drawarrow([0.0,0.0,0.0],P2,linewidth=0.01,color=[1.0,1.0,0.0]))
while True:
raw_input('キーを押すと回転しながら移動します．')
Tdelta = matrixFromAxisAngle ([0,0,0.5])
Tdelta[2,3] = 0.01
tran = dot(tran, Tdelta)
src/s/l/Slycot-HEAD/slycot/examples.py Slycot(Download)
def sb02od_example(): from numpy import zeros, shape, dot, ones A = array([ [0, 1], [0, 0]]) B = array([ [0], [1]]) C = array([ [1, 0], [0, 1], [0, 0]]) Q = dot(C.T,C)
src/o/p/openrave-HEAD/python/examples/tutorial_003.py openrave(Download)
__copyright__ = '2010 Makoto Furukawa'
__license__ = 'Apache License, Version 2.0'
from openravepy import Environment, rotationMatrixFromAxisAngle, axisAngleFromRotationMatrix, matrixFromAxisAngle
from numpy import eye, dot, pi
def run(args=None):
try:
deg = -45
rot_mat = rotationMatrixFromAxisAngle([1,0,0],float(deg)*pi/180.0)
print 'AxisAngle = ',axisAngleFromRotationMatrix(rot_mat)
tran[0:3,0:3] = dot(rot_mat, tran[0:3,0:3])
body.SetTransform(tran)
P1 = dot(rot_mat, [0,0,1])
deg = 45
rot_mat = rotationMatrixFromAxisAngle([0,1,0],float(deg)*pi/180.0)
print 'AxisAngle = ',axisAngleFromRotationMatrix(rot_mat)
tran[0:3,0:3] = dot(rot_mat, tran[0:3,0:3])
body.SetTransform(tran)
P2 = dot(rot_mat, P1)
handles.append(env.drawarrow([0.0,0.0,0.0],P2,linewidth=0.01,color=[1.0,1.0,0.0]))
while True:
raw_input('キーを押すと回転しながら移動します．')
Tdelta = matrixFromAxisAngle ([0,0,0.5])
Tdelta[2,3] = 0.01
tran = dot(tran, Tdelta)
src/c/s/csc-pysparse-HEAD/examples/jdsym_test.py csc-pysparse(Download)
from pysparse import spmatrix, jdsym, itsolvers
from numpy import zeros, dot, allclose, multiply
from math import sqrt
import RandomArray
class diagPrecShifted:
def __init__(self, A, M, sigma):
else:
t = u
r = r - lmbd[k]*t
residuals[k] = sqrt(dot(r,r))
return residuals
n = 1000; ncv = 5; tol = 1e-6
src/p/y/pysparse-HEAD/trunk/examples/jdsym_test.py pysparse(Download)
from pysparse.sparse import spmatrix from pysparse.eigen import jdsym from pysparse.itsolvers.krylov import qmrs from numpy import zeros, dot, allclose, multiply, random from math import sqrt class diagPrecShifted:
else:
t = u
r = r - lmbd[k]*t
residuals[k] = sqrt(dot(r,r))
return residuals
n = 1000; ncv = 5; tol = 1e-6
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