コード例 #1
0
ファイル: ThreeDeeMath.py プロジェクト: Complex501/visionegg
    def rotate(self, angle_degrees, axis_x, axis_y, axis_z ):
        """Follows the right hand rule.

        I visualize the right hand rule most easily as follows:
        Naturally, using your right hand, wrap it around the axis of
        rotation. Your fingers now point in the direction of rotation.

        """
        angleRadians = angle_degrees / 180.0 * math.pi
        u = self.__make_normalized_vert3(axis_x, axis_y, axis_z )
        u=-u #follow right hand rule
        S = Numeric.zeros( (3,3), Numeric.Float )
        S[0,1] = -u[2]
        S[0,2] = u[1]
        S[1,0] = u[2]
        S[1,2] = -u[0]
        S[2,0] = -u[1]
        S[2,1] = u[0]
        U = Numeric.outerproduct(u,u)
        R = U + math.cos(angleRadians)*(MLab.eye(3)-U) + math.sin(angleRadians)*S
        R = Numeric.concatenate( (R,Numeric.zeros( (3,1), Numeric.Float)), axis=1)
        R = Numeric.concatenate( (R,Numeric.zeros( (1,4), Numeric.Float)), axis=0)
        R[3,3] = 1.0
        self.matrix = numpy.dot(R,self.matrix)
コード例 #2
0
ファイル: ThreeDeeMath.py プロジェクト: Complex501/visionegg
 def scale(self, x, y, z):
     T = MLab.eye(4,typecode=Numeric.Float)
     T[0,0] = x
     T[1,1] = y
     T[2,2] = z
     self.matrix = numpy.dot(T,self.matrix)
コード例 #3
0
ファイル: ThreeDeeMath.py プロジェクト: Complex501/visionegg
 def translate(self, x, y, z):
     T = MLab.eye(4,typecode=Numeric.Float)
     T[3,0] = x
     T[3,1] = y
     T[3,2] = z
     self.matrix = numpy.dot(T,self.matrix)
コード例 #4
0
ファイル: ThreeDeeMath.py プロジェクト: Complex501/visionegg
 def __init__(self,matrix=None):
     if matrix is None:
         self.matrix = MLab.eye(4,typecode=Numeric.Float)
     else:
         self.matrix = matrix
コード例 #5
0
ファイル: optimize.py プロジェクト: neffmallon/pistol
def fminBFGS(f, x0, fprime=None, args=(), avegtol=1e-5, maxiter=None, fulloutput=0, printmessg=1):
    """xopt = fminBFGS(f, x0, fprime=None, args=(), avegtol=1e-5,
                       maxiter=None, fulloutput=0, printmessg=1)

    Optimize the function, f, whose gradient is given by fprime using the
    quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS)
    See Wright, and Nocedal 'Numerical Optimization', 1999, pg. 198.
    """

    app_fprime = 0
    if fprime is None:
        app_fprime = 1

    x0 = Num.asarray(x0)
    if maxiter is None:
        maxiter = len(x0)*200
    func_calls = 0
    grad_calls = 0
    k = 0
    N = len(x0)
    gtol = N*avegtol
    I = MLab.eye(N)
    Hk = I

    if app_fprime:
        gfk = apply(approx_fprime,(x0,f)+args)
        func_calls = func_calls + len(x0) + 1
    else:
        gfk = apply(fprime,(x0,)+args)
        grad_calls = grad_calls + 1
    xk = x0
    sk = [2*gtol]
    while (Num.add.reduce(abs(gfk)) > gtol) and (k < maxiter):
        pk = -Num.dot(Hk,gfk)
        alpha_k, fc, gc = line_search_BFGS(f,xk,pk,gfk,args)
        func_calls = func_calls + fc
        xkp1 = xk + alpha_k * pk
        sk = xkp1 - xk
        xk = xkp1
        if app_fprime:
            gfkp1 = apply(approx_fprime,(xkp1,f)+args)
            func_calls = func_calls + gc + len(x0) + 1
        else:
            gfkp1 = apply(fprime,(xkp1,)+args)
            grad_calls = grad_calls + gc + 1

        yk = gfkp1 - gfk
        k = k + 1

        rhok = 1 / Num.dot(yk,sk)
        A1 = I - sk[:,Num.NewAxis] * yk[Num.NewAxis,:] * rhok
        A2 = I - yk[:,Num.NewAxis] * sk[Num.NewAxis,:] * rhok
        Hk = Num.dot(A1,Num.dot(Hk,A2)) + rhok * sk[:,Num.NewAxis] * sk[Num.NewAxis,:]
        gfk = gfkp1


    if printmessg or fulloutput:
        fval = apply(f,(xk,)+args)
    if k >= maxiter:
        warnflag = 1
        if printmessg:
            print "Warning: Maximum number of iterations has been exceeded"
            print "         Current function value: %f" % fval
            print "         Iterations: %d" % k
            print "         Function evaluations: %d" % func_calls
            print "         Gradient evaluations: %d" % grad_calls
    else:
        warnflag = 0
        if printmessg:
            print "Optimization terminated successfully."
            print "         Current function value: %f" % fval
            print "         Iterations: %d" % k
            print "         Function evaluations: %d" % func_calls
            print "         Gradient evaluations: %d" % grad_calls

    if fulloutput:
        return xk, fval, func_calls, grad_calls, warnflag
    else:        
        return xk