def _gaussian(sigma, mew, npoints, sigmas):
ox = num.arange(mew-sigmas*sigma,
mew+sigmas*sigma,
2*sigmas*sigma/npoints, type=num.Float64)
x = ox-mew
x /= sigma
x = x * x
x *= -1/2
x = num.exp(x)
return ox, 1/(sigma * num.sqrt(2*num.pi)) * x
def _gaussian(sigma, mew, npoints, sigmas):
ox = num.arange(mew - sigmas * sigma,
mew + sigmas * sigma,
2 * sigmas * sigma / npoints,
type=num.Float64)
x = ox - mew
x /= sigma
x = x * x
x *= -1 / 2
x = num.exp(x)
return ox, 1 / (sigma * num.sqrt(2 * num.pi)) * x
def multivariate_normal(mean, cov, shape=[]):
"""multivariate_normal(mean, cov) or multivariate_normal(mean, cov, [m, n, ...])
Returns an array containing multivariate normally distributed
random numbers with specified mean and covariance.
|mean| must be a one-dimensional array. |cov| must be a square
two-dimensional array with the same number of rows and columns as
|mean| has elements.
The first form returns a single 1-D array containing a
multivariate normal.
The second form returns an array of shape (m, n, ...,
cov.getshape()[0]). In this case, output[i,j,...,:] is a 1-D array
containing a multivariate normal.
"""
# Check preconditions on arguments
mean = num.array(mean)
cov = num.array(cov)
if len(mean.getshape()) != 1:
raise ArgumentError, "mean must be 1 dimensional."
if (len(cov.getshape()) != 2) or (cov.getshape()[0] != cov.getshape()[1]):
raise ArgumentError, "cov must be 2 dimensional and square."
if mean.getshape()[0] != cov.getshape()[0]:
raise ArgumentError, "mean and cov must have same length."
# Compute shape of output
if isinstance(shape, _types.IntType): shape = [shape]
final_shape = list(shape[:])
final_shape.append(mean.getshape()[0])
# Create a matrix of independent standard normally distributed random
# numbers. The matrix has rows with the same length as mean and as
# many rows are necessary to form a matrix of shape final_shape.
x = ranlib.standard_normal(num.multiply.reduce(final_shape))
x.setshape(num.multiply.reduce(final_shape[0:len(final_shape) - 1]),
mean.getshape()[0])
# Transform matrix of standard normals into matrix where each row
# contains multivariate normals with the desired covariance.
# Compute A such that matrixmultiply(transpose(A),A) == cov.
# Then the matrix products of the rows of x and A has the desired
# covariance. Note that sqrt(s)*v where (u,s,v) is the singular value
# decomposition of cov is such an A.
(u, s, v) = linalg.singular_value_decomposition(cov)
x = num.matrixmultiply(x * num.sqrt(s), v)
# The rows of x now have the correct covariance but mean 0. Add
# mean to each row. Then each row will have mean mean.
num.add(mean, x, x)
x.setshape(final_shape)
return x
def multivariate_normal(mean, cov, shape=[]):
"""multivariate_normal(mean, cov) or multivariate_normal(mean, cov, [m, n, ...])
Returns an array containing multivariate normally distributed
random numbers with specified mean and covariance.
|mean| must be a one-dimensional array. |cov| must be a square
two-dimensional array with the same number of rows and columns as
|mean| has elements.
The first form returns a single 1-D array containing a
multivariate normal.
The second form returns an array of shape (m, n, ...,
cov.getshape()[0]). In this case, output[i,j,...,:] is a 1-D array
containing a multivariate normal.
"""
# Check preconditions on arguments
mean = num.array(mean)
cov = num.array(cov)
if len(mean.getshape()) != 1:
raise ArgumentError, "mean must be 1 dimensional."
if (len(cov.getshape()) != 2) or (cov.getshape()[0] != cov.getshape()[1]):
raise ArgumentError, "cov must be 2 dimensional and square."
if mean.getshape()[0] != cov.getshape()[0]:
raise ArgumentError, "mean and cov must have same length."
# Compute shape of output
if isinstance(shape, _types.IntType): shape = [shape]
final_shape = list(shape[:])
final_shape.append(mean.getshape()[0])
# Create a matrix of independent standard normally distributed random
# numbers. The matrix has rows with the same length as mean and as
# many rows are necessary to form a matrix of shape final_shape.
x = ranlib.standard_normal(num.multiply.reduce(final_shape))
x.setshape(num.multiply.reduce(final_shape[0:len(final_shape)-1]),
mean.getshape()[0])
# Transform matrix of standard normals into matrix where each row
# contains multivariate normals with the desired covariance.
# Compute A such that matrixmultiply(transpose(A),A) == cov.
# Then the matrix products of the rows of x and A has the desired
# covariance. Note that sqrt(s)*v where (u,s,v) is the singular value
# decomposition of cov is such an A.
(u,s,v) = linalg.singular_value_decomposition(cov)
x = num.matrixmultiply(x*num.sqrt(s),v)
# The rows of x now have the correct covariance but mean 0. Add
# mean to each row. Then each row will have mean mean.
num.add(mean,x,x)
x.setshape(final_shape)
return x