Module vectors
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Vector and coordinate identities and transformations
General conventions:
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theta is the colatitude, i.e. the angle from the Z-axis
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phi is the longitude
Transform cartesian coordinates to spherical coordinates and back
>>> x,y,z = np.random.uniform(low=-1,high=1,size=(3,10))
>>> r,phi,theta = cart2spher_coord(x,y,z)
>>> x_,y_,z_ = spher2cart_coord(r,phi,theta)
>>> np.allclose(x,x_),np.allclose(y,y_),np.allclose(z,z_)
(True, True, True)
Transform cartesian vectors to spherical vectors and back
>>> x0,y0,z0 = np.random.uniform(low=-1,high=1,size=(3,10))
>>> x1,y1,z1 = np.random.uniform(low=-1,high=1,size=(3,10))
>>> r0,phi0,theta0 = cart2spher_coord(x0,y0,z0)
>>> r1,phi1,theta1 = cart2spher((x0,y0,z0),(x1,y1,z1))
>>> x1_,y1_,z1_ = spher2cart((r0,phi0,theta0),(r1,phi1,theta1))
>>> np.allclose(x1,x1_),np.allclose(y1,y1_),np.allclose(z1,z1_)
(True, True, True)
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spher2cart_coord(r,
phi,
theta)
Spherical to Cartesian coordinates |
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cart2spher_coord(x,
y,
z)
theta colatitude phi longitude |
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rotate(x,
y,
theta,
x0=0.,
y0=0.)
Rotate counter clockwise. |
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spher2cart((r, phi, theta),
(a_r, a_phi, a_theta))
theta is angle from z-axis (colatitude) phi is longitude |
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cart2spher((x0, y0, z0),
(x1, y1, z1))
theta is angle from z-axis (colatitude) phi is longitude |
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angle(vec1,
vec2)
Compute angle between two vectors (or between two grids of vectors). |
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cos_angle(vec1,
vec2)
Compute cosine of angle between two vectors (or between two grids of
vectors). |
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spher2cart((r, phi, theta),
(a_r, a_phi, a_theta))
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theta is angle from z-axis (colatitude) phi is longitude
E.g.
http://www.engin.brown.edu/courses/en3/Notes/Vector_Web2/Vectors6a/Vectors6a.htm
>>> np.random.seed(111)
>>> r,phi,theta = np.random.uniform(low=-1,high=1,size=(3,2))
>>> a_r,a_phi,a_theta = np.random.uniform(low=-1,high=1,size=(3,2))
>>> a_x,a_y,a_z = spher2cart((r,phi,theta),(a_r,a_phi,a_theta))
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theta is angle from z-axis (colatitude) phi is longitude
return r,phi,theta
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Euclidic norm of a vector (or of a grid of vectors)
Input vectors should be numpy arrays.
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Compute angle between two vectors (or between two grids of
vectors).
Input vectors should be numpy arrays.
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Compute cosine of angle between two vectors (or between two grids of
vectors).
Input vectors should be numpy arrays.
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