def pinv(a, rcond=1e-15 ):
"""
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate the generalized inverse of a matrix using its
singular-value decomposition (SVD) and including all
`large` singular values.
Parameters
----------
a : array_like (M, N)
Matrix to be pseudo-inverted.
rcond : float
Cutoff for `small` singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
Returns
-------
B : ndarray (N, M)
The pseudo-inverse of `a`. If `a` is an np.matrix instance, then so
is `B`.
Raises
------
LinAlgError
In case SVD computation does not converge.
Examples
--------
>>> a = np.random.randn(9, 6)
>>> B = np.linalg.pinv(a)
>>> np.allclose(a, np.dot(a, np.dot(B, a)))
True
>>> np.allclose(B, np.dot(B, np.dot(a, B)))
True
"""
a, wrap = _makearray(a)
_assertNonEmpty(a)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond*maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1./s[i]
else:
s[i] = 0.;
res = dot(transpose(vt), multiply(s[:, newaxis],transpose(u)))
return wrap(res)
def pinv(a, rcond=1e-15):
"""
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate the generalized inverse of a matrix using its
singular-value decomposition (SVD) and including all
`large` singular values.
Parameters
----------
a : array_like (M, N)
Matrix to be pseudo-inverted.
rcond : float
Cutoff for `small` singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
Returns
-------
B : ndarray (N, M)
The pseudo-inverse of `a`. If `a` is an np.matrix instance, then so
is `B`.
Raises
------
LinAlgError
In case SVD computation does not converge.
Examples
--------
>>> a = np.random.randn(9, 6)
>>> B = np.linalg.pinv(a)
>>> np.allclose(a, np.dot(a, np.dot(B, a)))
True
>>> np.allclose(B, np.dot(B, np.dot(a, B)))
True
"""
a, wrap = _makearray(a)
_assertNonEmpty(a)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond * maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1. / s[i]
else:
s[i] = 0.
res = dot(transpose(vt), multiply(s[:, newaxis], transpose(u)))
return wrap(res)
def pinv(a, rcond=1e-15 ):
"""Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate a generalized inverse of a matrix using its
singular-value decomposition and including all 'large' singular
values.
Parameters
----------
a : array-like, shape (M, N)
Matrix to be pseudo-inverted
rcond : float
Cutoff for 'small' singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
Returns
-------
B : array, shape (N, M)
If a is a matrix, then so is B.
Raises LinAlgError if SVD computation does not converge
Examples
--------
>>> from numpy import *
>>> a = random.randn(9, 6)
>>> B = linalg.pinv(a)
>>> allclose(a, dot(a, dot(B, a)))
True
>>> allclose(B, dot(B, dot(a, B)))
True
"""
a, wrap = _makearray(a)
_assertNonEmpty(a)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond*maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1./s[i]
else:
s[i] = 0.;
res = dot(transpose(vt), multiply(s[:, newaxis],transpose(u)))
return wrap(res)
def pinv(a, rcond=1e-15):
"""Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate a generalized inverse of a matrix using its
singular-value decomposition and including all 'large' singular
values.
Parameters
----------
a : array-like, shape (M, N)
Matrix to be pseudo-inverted
rcond : float
Cutoff for 'small' singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
Returns
-------
B : array, shape (N, M)
If a is a matrix, then so is B.
Raises LinAlgError if SVD computation does not converge
Examples
--------
>>> from numpy import *
>>> a = random.randn(9, 6)
>>> B = linalg.pinv(a)
>>> allclose(a, dot(a, dot(B, a)))
True
>>> allclose(B, dot(B, dot(a, B)))
True
"""
a, wrap = _makearray(a)
_assertNonEmpty(a)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond * maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1. / s[i]
else:
s[i] = 0.
res = dot(transpose(vt), multiply(s[:, newaxis], transpose(u)))
return wrap(res)
def pinv(a, rcond=1e-15 ):
"""Return the (Moore-Penrose) pseudo-inverse of a 2-d array
This method computes the generalized inverse using the
singular-value decomposition and all singular values larger than
rcond of the largest.
"""
a, wrap = _makearray(a)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond*maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1./s[i]
else:
s[i] = 0.;
return wrap(dot(transpose(vt),
multiply(s[:, newaxis],transpose(u))))
def pinv(a, rcond=1e-15):
"""Return the (Moore-Penrose) pseudo-inverse of a 2-d array
This method computes the generalized inverse using the
singular-value decomposition and all singular values larger than
rcond of the largest.
"""
a, wrap = _makearray(a)
_assertNonEmpty(a)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
cutoff = rcond * maximum.reduce(s)
for i in range(min(n, m)):
if s[i] > cutoff:
s[i] = 1. / s[i]
else:
s[i] = 0.
return wrap(dot(transpose(vt), multiply(s[:, newaxis], transpose(u))))
def _inv(a, cf, rcond, epsilon):
"""
modified pseudo inverse
"""
def _assertNoEmpty2d(*arrays):
for a in arrays:
if a.size == 0 and product(a.shape[-2:]) == 0:
raise RuntimeError("Arrays cannot be empty")
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
a, wrap = _makearray(a)
_assertNoEmpty2d(a)
if epsilon is not None:
epsilon = numpy.repeat(epsilon, a.shape[0])
epsilon = numpy.diag(epsilon)
a = a + epsilon
a = a.conjugate()
#WARNING! the "s" eigenvalues might not equal the eigenvalues of eigh
u, s, vt = numpy.linalg.svd(a, 0)
m = u.shape[0]
n = vt.shape[1]
eigen = numpy.copy(s)
# cutoff = rcond*maximum.reduce(s)
cutoff = cf(s, rcond)
for i in range(min(n, m)):
# The first Singular Value will always be selected because we want at least one, and the first is the highest
if s[i] >= cutoff or i==0:
s[i] = 1. / s[i]
else:
s[i] = 0.
n_indep = numpy.count_nonzero(s)
res = dot(transpose(vt), multiply(s[:, newaxis], transpose(u)))
return wrap(res), n_indep, eigen
def _rawcb(self, msg):
#beam tilt is output by ps0 command, 600khz 30degs
ba_s = map(np.sin, self.beam_angles)
ba_c = map(np.cos, self.beam_angles)
A = np.zeros((len(msg.beam_velocity), 3))
A[0] = [-ba_s[0], 0, -ba_c[0]]
A[1] = [ba_s[1], 0, -ba_c[1]]
A[2] = [0, +ba_s[2], -ba_c[2]]
A[3] = [0, -ba_s[3], -ba_c[3]]
b = [x for x in msg.beam_velocity if x is not math.isnan(x)]
A = np.dot(inv(np.dot(transpose(A), A)), transpose(A))
x = np.dot(A, b)
if(abs(x[0]) > 5 or abs(x[1]) > 5 or abs(x[2]) > 5):
return
x = [x[1] * np.sin(self.ea) + x[0] * np.sin(self.ea),
-x[1] * np.cos(self.ea) + x[0] * np.cos(self.ea), x[2]]
self.vel_out.publish(dvl_vel(
header=msg.header,
velocity=Vector3(*x)
))
self.altitude_out.publish(Float32(msg.altitude))
object.__setattr__(self, attr, value)
# Only called after other approaches fail.
def __getattr__(self, attr):
if (attr == 'array'):
return object.__getattribute__(self, attr)
return self.array.__getattribute__(attr)
#############################################################
# Test of class container
#############################################################
if __name__ == '__main__':
temp = reshape(arange(10000), (100, 100))
ua = container(temp)
# new object created begin test
print(dir(ua))
print(shape(ua), ua.shape) # I have changed Numeric.py
ua_small = ua[:3, :5]
print(ua_small)
# this did not change ua[0,0], which is not normal behavior
ua_small[0, 0] = 10
print(ua_small[0, 0], ua[0, 0])
print(sin(ua_small) / 3. * 6. + sqrt(ua_small**2))
print(less(ua_small, 103), type(less(ua_small, 103)))
print(type(ua_small * reshape(arange(15), shape(ua_small))))
print(reshape(ua_small, (5, 3)))
print(transpose(ua_small))
def Heigenvectors(A):
w, v = linalg.eigh(A)
return w, transpose(v)
def lstsq(a, b, rcond=-1):
"""
Return the least-squares solution to an equation.
Solves the equation `a x = b` by computing a vector `x` that minimizes
the norm `|| b - a x ||`.
Parameters
----------
a : array_like, shape (M, N)
Input equation coefficients.
b : array_like, shape (M,) or (M, K)
Equation target values. If `b` is two-dimensional, the least
squares solution is calculated for each of the `K` target sets.
rcond : float, optional
Cutoff for ``small`` singular values of `a`.
Singular values smaller than `rcond` times the largest singular
value are considered zero.
Returns
-------
x : ndarray, shape(N,) or (N, K)
Least squares solution. The shape of `x` depends on the shape of
`b`.
residues : ndarray, shape(), (1,), or (K,)
Sums of residues; squared Euclidian norm for each column in
`b - a x`.
If the rank of `a` is < N or > M, this is an empty array.
If `b` is 1-dimensional, this is a (1,) shape array.
Otherwise the shape is (K,).
rank : integer
Rank of matrix `a`.
s : ndarray, shape(min(M,N),)
Singular values of `a`.
Raises
------
LinAlgError
If computation does not converge.
Notes
-----
If `b` is a matrix, then all array results returned as
matrices.
Examples
--------
Fit a line, ``y = mx + c``, through some noisy data-points:
>>> x = np.array([0, 1, 2, 3])
>>> y = np.array([-1, 0.2, 0.9, 2.1])
By examining the coefficients, we see that the line should have a
gradient of roughly 1 and cuts the y-axis at more-or-less -1.
We can rewrite the line equation as ``y = Ap``, where ``A = [[x 1]]``
and ``p = [[m], [c]]``. Now use `lstsq` to solve for `p`:
>>> A = np.vstack([x, np.ones(len(x))]).T
>>> A
array([[ 0., 1.],
[ 1., 1.],
[ 2., 1.],
[ 3., 1.]])
>>> m, c = np.linalg.lstsq(A, y)[0]
>>> print m, c
1.0 -0.95
Plot the data along with the fitted line:
>>> import matplotlib.pyplot as plt
>>> plt.plot(x, y, 'o', label='Original data', markersize=10)
>>> plt.plot(x, m*x + c, 'r', label='Fitted line')
>>> plt.legend()
>>> plt.show()
"""
import math
a, _ = _makearray(a)
b, wrap = _makearray(b)
is_1d = len(b.shape) == 1
if is_1d:
b = b[:, newaxis]
_assertRank2(a, b)
m = a.shape[0]
n = a.shape[1]
n_rhs = b.shape[1]
ldb = max(n, m)
if m != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t, result_t = _commonType(a, b)
real_t = _linalgRealType(t)
bstar = zeros((ldb, n_rhs), t)
bstar[:b.shape[0], :n_rhs] = b.copy()
a, bstar = _fastCopyAndTranspose(t, a, bstar)
s = zeros((min(m, n), ), real_t)
nlvl = max(0, int(math.log(float(min(m, n)) / 2.)) + 1)
iwork = zeros((3 * min(m, n) * nlvl + 11 * min(m, n), ), fortran_int)
if isComplexType(t):
lapack_routine = lapack_lite.zgelsd
lwork = 1
rwork = zeros((lwork, ), real_t)
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
rwork = zeros((lwork, ), real_t)
a_real = zeros((m, n), real_t)
bstar_real = zeros((
ldb,
n_rhs,
), real_t)
results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m, bstar_real, ldb,
s, rcond, 0, rwork, -1, iwork, 0)
lrwork = int(rwork[0])
work = zeros((lwork, ), t)
rwork = zeros((lrwork, ), real_t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgelsd
lwork = 1
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, -1, iwork, 0)
lwork = int(work[0])
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = array([], t)
if is_1d:
x = array(ravel(bstar)[:n], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t)
else:
x = array(transpose(bstar)[:n, :], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = sum((transpose(bstar)[n:, :])**2, axis=0).astype(result_t)
st = s[:min(n, m)].copy().astype(_realType(result_t))
return wrap(x), wrap(resids), results['rank'], st
self.array.__setattr__(attr, value)
except AttributeError:
object.__setattr__(self, attr, value)
# Only called after other approaches fail.
def __getattr__(self,attr):
if (attr == 'array'):
return object.__getattribute__(self, attr)
return self.array.__getattribute__(attr)
#############################################################
# Test of class container
#############################################################
if __name__ == '__main__':
temp=reshape(arange(10000),(100,100))
ua=container(temp)
# new object created begin test
print dir(ua)
print shape(ua),ua.shape # I have changed Numeric.py
ua_small=ua[:3,:5]
print ua_small
ua_small[0,0]=10 # this did not change ua[0,0], which is not normal behavior
print ua_small[0,0],ua[0,0]
print sin(ua_small)/3.*6.+sqrt(ua_small**2)
print less(ua_small,103),type(less(ua_small,103))
print type(ua_small*reshape(arange(15),shape(ua_small)))
print reshape(ua_small,(5,3))
print transpose(ua_small)
def lstsq(a, b, rcond=-1):
"""returns x,resids,rank,s
where x minimizes 2-norm(|b - Ax|)
resids is the sum square residuals
rank is the rank of A
s is the rank of the singular values of A in descending order
If b is a matrix then x is also a matrix with corresponding columns.
If the rank of A is less than the number of columns of A or greater than
the number of rows, then residuals will be returned as an empty array
otherwise resids = sum((b-dot(A,x)**2).
Singular values less than s[0]*rcond are treated as zero.
"""
import math
a = asarray(a)
b, wrap = _makearray(b)
one_eq = len(b.shape) == 1
if one_eq:
b = b[:, newaxis]
_assertRank2(a, b)
m = a.shape[0]
n = a.shape[1]
n_rhs = b.shape[1]
ldb = max(n, m)
if m != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t, result_t = _commonType(a, b)
real_t = _linalgRealType(t)
bstar = zeros((ldb, n_rhs), t)
bstar[:b.shape[0],:n_rhs] = b.copy()
a, bstar = _fastCopyAndTranspose(t, a, bstar)
s = zeros((min(m, n),), real_t)
nlvl = max( 0, int( math.log( float(min(m, n))/2. ) ) + 1 )
iwork = zeros((3*min(m, n)*nlvl+11*min(m, n),), fortran_int)
if isComplexType(t):
lapack_routine = lapack_lite.zgelsd
lwork = 1
rwork = zeros((lwork,), real_t)
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
rwork = zeros((lwork,), real_t)
a_real = zeros((m, n), real_t)
bstar_real = zeros((ldb, n_rhs,), real_t)
results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m,
bstar_real, ldb, s, rcond,
0, rwork, -1, iwork, 0)
lrwork = int(rwork[0])
work = zeros((lwork,), t)
rwork = zeros((lrwork,), real_t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgelsd
lwork = 1
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, -1, iwork, 0)
lwork = int(work[0])
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = array([], t)
if one_eq:
x = array(ravel(bstar)[:n], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t)
else:
x = array(transpose(bstar)[:n,:], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = sum((transpose(bstar)[n:,:])**2, axis=0).astype(result_t)
st = s[:min(n, m)].copy().astype(_realType(result_t))
return wrap(x), resids, results['rank'], st
def Heigenvectors(A):
w, v = linalg.eigh(A)
return w, transpose(v)
def coarseMolSurface(molFrag,XYZd,isovalue=5.0,resolution=-0.4,padding=0.0, name='CoarseMolSurface',geom=None):
"""
Function adapted from the Vision network which compute a coarse molecular
surface in PMV
@type molFrag: MolKit.AtomSet
@param molFrag: the atoms selection
@type XYZd: array
@param XYZd: shape of the volume
@type isovalue: float
@param isovalue: isovalue for the isosurface computation
@type resolution: float
@param resolution: resolution of the final mesh
@type padding: float
@param padding: the padding
@type name: string
@param name: the name of the resultante geometry
@type geom: DejaVu.Geom
@param geom: update geom instead of creating a new one
@rtype: DejaVu.Geom
@return: the created or updated DejaVu.Geom
"""
import pdb
from MolKit.molecule import Atom
atoms = molFrag.findType(Atom)
coords = atoms.coords
radii = atoms.vdwRadius
from UTpackages.UTblur import blur
import numpy.core as Numeric
volarr, origin, span = blur.generateBlurmap(coords, radii, XYZd,resolution, padding = 0.0)
volarr.shape = (XYZd[0],XYZd[1],XYZd[2])
volarr = Numeric.ascontiguousarray(Numeric.transpose(volarr), 'f')
weights = Numeric.ones(len(radii), 'f')
h = {}
from Volume.Grid3D import Grid3DF
maskGrid = Grid3DF( volarr, origin, span , h)
h['amin'], h['amax'],h['amean'],h['arms']= maskGrid.stats()
from UTpackages.UTisocontour import isocontour
isocontour.setVerboseLevel(0)
data = maskGrid.data
origin = Numeric.array(maskGrid.origin).astype('f')
stepsize = Numeric.array(maskGrid.stepSize).astype('f')
if data.dtype.char!=Numeric.float32:
data = data.astype('f')#Numeric.Float32)
newgrid3D = Numeric.ascontiguousarray(Numeric.reshape( Numeric.transpose(data),
(1, 1)+tuple(data.shape) ), data.dtype.char)
ndata = isocontour.newDatasetRegFloat3D(newgrid3D, origin, stepsize)
isoc = isocontour.getContour3d(ndata, 0, 0, isovalue,
isocontour.NO_COLOR_VARIABLE)
vert = Numeric.zeros((isoc.nvert,3)).astype('f')
norm = Numeric.zeros((isoc.nvert,3)).astype('f')
col = Numeric.zeros((isoc.nvert)).astype('f')
tri = Numeric.zeros((isoc.ntri,3)).astype('i')
isocontour.getContour3dData(isoc, vert, norm, col, tri, 0)
if maskGrid.crystal:
vert = maskGrid.crystal.toCartesian(vert)
return (vert, tri)
def lstsq(a, b, rcond=-1):
"""Compute least-squares solution to equation :math:`a x = b`
Compute a vector x such that the 2-norm :math:`|b - a x|` is minimised.
Parameters
----------
a : array-like, shape (M, N)
b : array-like, shape (M,) or (M, K)
rcond : float
Cutoff for 'small' singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
Raises LinAlgError if computation does not converge
Returns
-------
x : array, shape (N,) or (N, K) depending on shape of b
Least-squares solution
residues : array, shape () or (1,) or (K,)
Sums of residues, squared 2-norm for each column in :math:`b - a x`
If rank of matrix a is < N or > M this is an empty array.
If b was 1-d, this is an (1,) shape array, otherwise the shape is (K,)
rank : integer
Rank of matrix a
s : array, shape (min(M,N),)
Singular values of a
If b is a matrix, then all results except the rank are also returned as
matrices.
"""
import math
a, _ = _makearray(a)
b, wrap = _makearray(b)
is_1d = len(b.shape) == 1
if is_1d:
b = b[:, newaxis]
_assertRank2(a, b)
m = a.shape[0]
n = a.shape[1]
n_rhs = b.shape[1]
ldb = max(n, m)
if m != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t, result_t = _commonType(a, b)
real_t = _linalgRealType(t)
bstar = zeros((ldb, n_rhs), t)
bstar[:b.shape[0], :n_rhs] = b.copy()
a, bstar = _fastCopyAndTranspose(t, a, bstar)
s = zeros((min(m, n), ), real_t)
nlvl = max(0, int(math.log(float(min(m, n)) / 2.)) + 1)
iwork = zeros((3 * min(m, n) * nlvl + 11 * min(m, n), ), fortran_int)
if isComplexType(t):
lapack_routine = lapack_lite.zgelsd
lwork = 1
rwork = zeros((lwork, ), real_t)
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
rwork = zeros((lwork, ), real_t)
a_real = zeros((m, n), real_t)
bstar_real = zeros((
ldb,
n_rhs,
), real_t)
results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m, bstar_real, ldb,
s, rcond, 0, rwork, -1, iwork, 0)
lrwork = int(rwork[0])
work = zeros((lwork, ), t)
rwork = zeros((lrwork, ), real_t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgelsd
lwork = 1
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, -1, iwork, 0)
lwork = int(work[0])
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = array([], t)
if is_1d:
x = array(ravel(bstar)[:n], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t)
else:
x = array(transpose(bstar)[:n, :], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = sum((transpose(bstar)[n:, :])**2, axis=0).astype(result_t)
st = s[:min(n, m)].copy().astype(_realType(result_t))
return wrap(x), wrap(resids), results['rank'], st
def _castCopyAndTranspose(type, *arrays):
if len(arrays) == 1:
return transpose(arrays[0]).astype(type)
else:
return [transpose(a).astype(type) for a in arrays]
def lstsq(a, b, rcond=-1):
"""returns x,resids,rank,s
where x minimizes 2-norm(|b - Ax|)
resids is the sum square residuals
rank is the rank of A
s is the rank of the singular values of A in descending order
If b is a matrix then x is also a matrix with corresponding columns.
If the rank of A is less than the number of columns of A or greater than
the number of rows, then residuals will be returned as an empty array
otherwise resids = sum((b-dot(A,x)**2).
Singular values less than s[0]*rcond are treated as zero.
"""
import math
a = asarray(a)
b, wrap = _makearray(b)
one_eq = len(b.shape) == 1
if one_eq:
b = b[:, newaxis]
_assertRank2(a, b)
m = a.shape[0]
n = a.shape[1]
n_rhs = b.shape[1]
ldb = max(n, m)
if m != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t, result_t = _commonType(a, b)
real_t = _linalgRealType(t)
bstar = zeros((ldb, n_rhs), t)
bstar[:b.shape[0], :n_rhs] = b.copy()
a, bstar = _fastCopyAndTranspose(t, a, bstar)
s = zeros((min(m, n), ), real_t)
nlvl = max(0, int(math.log(float(min(m, n)) / 2.)) + 1)
iwork = zeros((3 * min(m, n) * nlvl + 11 * min(m, n), ), fortran_int)
if isComplexType(t):
lapack_routine = lapack_lite.zgelsd
lwork = 1
rwork = zeros((lwork, ), real_t)
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
rwork = zeros((lwork, ), real_t)
a_real = zeros((m, n), real_t)
bstar_real = zeros((
ldb,
n_rhs,
), real_t)
results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m, bstar_real, ldb,
s, rcond, 0, rwork, -1, iwork, 0)
lrwork = int(rwork[0])
work = zeros((lwork, ), t)
rwork = zeros((lrwork, ), real_t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgelsd
lwork = 1
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, -1, iwork, 0)
lwork = int(work[0])
work = zeros((lwork, ), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0,
work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = array([], t)
if one_eq:
x = array(ravel(bstar)[:n], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t)
else:
x = array(transpose(bstar)[:n, :], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = sum((transpose(bstar)[n:, :])**2, axis=0).astype(result_t)
st = s[:min(n, m)].copy().astype(_realType(result_t))
return wrap(x), resids, results['rank'], st
except AttributeError:
object.__setattr__(self, attr, value)
# Only called after other approaches fail.
def __getattr__(self, attr):
if (attr == 'array'):
return object.__getattribute__(self, attr)
return self.array.__getattribute__(attr)
#############################################################
# Test of class container
#############################################################
if __name__ == '__main__':
temp = reshape(arange(10000), (100, 100))
ua = container(temp)
# new object created begin test
print(dir(ua))
print(shape(ua), ua.shape) # I have changed Numeric.py
ua_small = ua[:3, :5]
print(ua_small)
# this did not change ua[0,0], which is not normal behavior
ua_small[0, 0] = 10
print(ua_small[0, 0], ua[0, 0])
print(sin(ua_small) / 3. * 6. + sqrt(ua_small ** 2))
print(less(ua_small, 103), type(less(ua_small, 103)))
print(type(ua_small * reshape(arange(15), shape(ua_small))))
print(reshape(ua_small, (5, 3)))
print(transpose(ua_small))
def lstsq(a, b, rcond=-1):
"""Compute least-squares solution to equation :math:`a x = b`
Compute a vector x such that the 2-norm :math:`|b - a x|` is minimised.
Parameters
----------
a : array-like, shape (M, N)
b : array-like, shape (M,) or (M, K)
rcond : float
Cutoff for 'small' singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
Raises LinAlgError if computation does not converge
Returns
-------
x : array, shape (N,) or (N, K) depending on shape of b
Least-squares solution
residues : array, shape () or (1,) or (K,)
Sums of residues, squared 2-norm for each column in :math:`b - a x`
If rank of matrix a is < N or > M this is an empty array.
If b was 1-d, this is an (1,) shape array, otherwise the shape is (K,)
rank : integer
Rank of matrix a
s : array, shape (min(M,N),)
Singular values of a
If b is a matrix, then all results except the rank are also returned as
matrices.
"""
import math
a, _ = _makearray(a)
b, wrap = _makearray(b)
is_1d = len(b.shape) == 1
if is_1d:
b = b[:, newaxis]
_assertRank2(a, b)
m = a.shape[0]
n = a.shape[1]
n_rhs = b.shape[1]
ldb = max(n, m)
if m != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t, result_t = _commonType(a, b)
real_t = _linalgRealType(t)
bstar = zeros((ldb, n_rhs), t)
bstar[:b.shape[0],:n_rhs] = b.copy()
a, bstar = _fastCopyAndTranspose(t, a, bstar)
s = zeros((min(m, n),), real_t)
nlvl = max( 0, int( math.log( float(min(m, n))/2. ) ) + 1 )
iwork = zeros((3*min(m, n)*nlvl+11*min(m, n),), fortran_int)
if isComplexType(t):
lapack_routine = lapack_lite.zgelsd
lwork = 1
rwork = zeros((lwork,), real_t)
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
rwork = zeros((lwork,), real_t)
a_real = zeros((m, n), real_t)
bstar_real = zeros((ldb, n_rhs,), real_t)
results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m,
bstar_real, ldb, s, rcond,
0, rwork, -1, iwork, 0)
lrwork = int(rwork[0])
work = zeros((lwork,), t)
rwork = zeros((lrwork,), real_t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgelsd
lwork = 1
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, -1, iwork, 0)
lwork = int(work[0])
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = array([], t)
if is_1d:
x = array(ravel(bstar)[:n], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t)
else:
x = array(transpose(bstar)[:n,:], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = sum((transpose(bstar)[n:,:])**2, axis=0).astype(result_t)
st = s[:min(n, m)].copy().astype(_realType(result_t))
return wrap(x), wrap(resids), results['rank'], st
def lstsq(a, b, rcond=-1):
"""
Return the least-squares solution to an equation.
Solves the equation `a x = b` by computing a vector `x` that minimizes
the norm `|| b - a x ||`.
Parameters
----------
a : array_like, shape (M, N)
Input equation coefficients.
b : array_like, shape (M,) or (M, K)
Equation target values. If `b` is two-dimensional, the least
squares solution is calculated for each of the `K` target sets.
rcond : float, optional
Cutoff for ``small`` singular values of `a`.
Singular values smaller than `rcond` times the largest singular
value are considered zero.
Returns
-------
x : ndarray, shape(N,) or (N, K)
Least squares solution. The shape of `x` depends on the shape of
`b`.
residues : ndarray, shape(), (1,), or (K,)
Sums of residues; squared Euclidian norm for each column in
`b - a x`.
If the rank of `a` is < N or > M, this is an empty array.
If `b` is 1-dimensional, this is a (1,) shape array.
Otherwise the shape is (K,).
rank : integer
Rank of matrix `a`.
s : ndarray, shape(min(M,N),)
Singular values of `a`.
Raises
------
LinAlgError
If computation does not converge.
Notes
-----
If `b` is a matrix, then all array results returned as
matrices.
Examples
--------
Fit a line, ``y = mx + c``, through some noisy data-points:
>>> x = np.array([0, 1, 2, 3])
>>> y = np.array([-1, 0.2, 0.9, 2.1])
By examining the coefficients, we see that the line should have a
gradient of roughly 1 and cuts the y-axis at more-or-less -1.
We can rewrite the line equation as ``y = Ap``, where ``A = [[x 1]]``
and ``p = [[m], [c]]``. Now use `lstsq` to solve for `p`:
>>> A = np.vstack([x, np.ones(len(x))]).T
>>> A
array([[ 0., 1.],
[ 1., 1.],
[ 2., 1.],
[ 3., 1.]])
>>> m, c = np.linalg.lstsq(A, y)[0]
>>> print m, c
1.0 -0.95
Plot the data along with the fitted line:
>>> import matplotlib.pyplot as plt
>>> plt.plot(x, y, 'o', label='Original data', markersize=10)
>>> plt.plot(x, m*x + c, 'r', label='Fitted line')
>>> plt.legend()
>>> plt.show()
"""
import math
a, _ = _makearray(a)
b, wrap = _makearray(b)
is_1d = len(b.shape) == 1
if is_1d:
b = b[:, newaxis]
_assertRank2(a, b)
m = a.shape[0]
n = a.shape[1]
n_rhs = b.shape[1]
ldb = max(n, m)
if m != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t, result_t = _commonType(a, b)
real_t = _linalgRealType(t)
bstar = zeros((ldb, n_rhs), t)
bstar[:b.shape[0],:n_rhs] = b.copy()
a, bstar = _fastCopyAndTranspose(t, a, bstar)
s = zeros((min(m, n),), real_t)
nlvl = max( 0, int( math.log( float(min(m, n))/2. ) ) + 1 )
iwork = zeros((3*min(m, n)*nlvl+11*min(m, n),), fortran_int)
if isComplexType(t):
lapack_routine = lapack_lite.zgelsd
lwork = 1
rwork = zeros((lwork,), real_t)
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
rwork = zeros((lwork,), real_t)
a_real = zeros((m, n), real_t)
bstar_real = zeros((ldb, n_rhs,), real_t)
results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m,
bstar_real, ldb, s, rcond,
0, rwork, -1, iwork, 0)
lrwork = int(rwork[0])
work = zeros((lwork,), t)
rwork = zeros((lrwork,), real_t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgelsd
lwork = 1
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, -1, iwork, 0)
lwork = int(work[0])
work = zeros((lwork,), t)
results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond,
0, work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = array([], t)
if is_1d:
x = array(ravel(bstar)[:n], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t)
else:
x = array(transpose(bstar)[:n,:], dtype=result_t, copy=True)
if results['rank'] == n and m > n:
resids = sum((transpose(bstar)[n:,:])**2, axis=0).astype(result_t)
st = s[:min(n, m)].copy().astype(_realType(result_t))
return wrap(x), wrap(resids), results['rank'], st
def _castCopyAndTranspose(type, *arrays):
if len(arrays) == 1:
return transpose(arrays[0]).astype(type)
else:
return [transpose(a).astype(type) for a in arrays]
object.__setattr__(self, attr, value)
# Only called after other approaches fail.
def __getattr__(self, attr):
if (attr == 'array'):
return object.__getattribute__(self, attr)
return self.array.__getattribute__(attr)
#############################################################
# Test of class container
#############################################################
if __name__ == '__main__':
temp = reshape(arange(10000), (100, 100))
ua = container(temp)
# new object created begin test
print dir(ua)
print shape(ua), ua.shape # I have changed Numeric.py
ua_small = ua[:3, :5]
print ua_small
ua_small[
0, 0] = 10 # this did not change ua[0,0], which is not normal behavior
print ua_small[0, 0], ua[0, 0]
print sin(ua_small) / 3. * 6. + sqrt(ua_small**2)
print less(ua_small, 103), type(less(ua_small, 103))
print type(ua_small * reshape(arange(15), shape(ua_small)))
print reshape(ua_small, (5, 3))
print transpose(ua_small)
def coarseMolSurface(molFrag,
XYZd,
isovalue=5.0,
resolution=-0.4,
padding=0.0,
name='CoarseMolSurface',
geom=None):
"""
Function adapted from the Vision network which compute a coarse molecular
surface in PMV
@type molFrag: MolKit.AtomSet
@param molFrag: the atoms selection
@type XYZd: array
@param XYZd: shape of the volume
@type isovalue: float
@param isovalue: isovalue for the isosurface computation
@type resolution: float
@param resolution: resolution of the final mesh
@type padding: float
@param padding: the padding
@type name: string
@param name: the name of the resultante geometry
@type geom: DejaVu.Geom
@param geom: update geom instead of creating a new one
@rtype: DejaVu.Geom
@return: the created or updated DejaVu.Geom
"""
import pdb
from MolKit.molecule import Atom
atoms = molFrag.findType(Atom)
coords = atoms.coords
radii = atoms.vdwRadius
from UTpackages.UTblur import blur
import numpy.core as Numeric
volarr, origin, span = blur.generateBlurmap(coords,
radii,
XYZd,
resolution,
padding=0.0)
volarr.shape = (XYZd[0], XYZd[1], XYZd[2])
volarr = Numeric.ascontiguousarray(Numeric.transpose(volarr), 'f')
weights = Numeric.ones(len(radii), 'f')
h = {}
from Volume.Grid3D import Grid3DF
maskGrid = Grid3DF(volarr, origin, span, h)
h['amin'], h['amax'], h['amean'], h['arms'] = maskGrid.stats()
from UTpackages.UTisocontour import isocontour
isocontour.setVerboseLevel(0)
data = maskGrid.data
origin = Numeric.array(maskGrid.origin).astype('f')
stepsize = Numeric.array(maskGrid.stepSize).astype('f')
if data.dtype.char != Numeric.float32:
data = data.astype('f') #Numeric.Float32)
newgrid3D = Numeric.ascontiguousarray(
Numeric.reshape(Numeric.transpose(data), (1, 1) + tuple(data.shape)),
data.dtype.char)
ndata = isocontour.newDatasetRegFloat3D(newgrid3D, origin, stepsize)
isoc = isocontour.getContour3d(ndata, 0, 0, isovalue,
isocontour.NO_COLOR_VARIABLE)
vert = Numeric.zeros((isoc.nvert, 3)).astype('f')
norm = Numeric.zeros((isoc.nvert, 3)).astype('f')
col = Numeric.zeros((isoc.nvert)).astype('f')
tri = Numeric.zeros((isoc.ntri, 3)).astype('i')
isocontour.getContour3dData(isoc, vert, norm, col, tri, 0)
if maskGrid.crystal:
vert = maskGrid.crystal.toCartesian(vert)
return (vert, tri)