def cross_product(a, b, axis1=-1, axis2=-1):
"""Return the cross product of two vectors.
The cross product is performed over the last axes of a and b by default,
and can handle axes with dimensions 2 and 3. For a dimension of 2,
the z-component of the equivalent three-dimensional cross product is
returned.
"""
a = _move_axis_to_0(asarray(a), axis1)
b = _move_axis_to_0(asarray(b), axis2)
if a.shape[0] != b.shape[0]:
raise ValueError("incompatible dimensions for cross product")
elif a.shape[0] == 2:
return a[0] * b[1] - a[1] * b[0]
elif a.shape[0] == 3:
x = a[1] * b[2] - a[2] * b[1]
y = a[2] * b[0] - a[0] * b[2]
z = a[0] * b[1] - a[1] * b[0]
cp = array([x, y, z])
if len(cp.shape) == 1:
return cp
# we put the result (in the first axis) as the last axis
axes = range(1, len(cp.shape)) + [0]
return multiarray.transpose(cp, axes)
else:
raise ValueError(
"can only do cross product for axes with dimensions 2 or 3")
def solve_linear_equations(a, b):
one_eq = len(b.shape) == 1
if one_eq:
b = b[:, Numeric.NewAxis]
_assertRank2(a, b)
_assertSquareness(a)
n_eq = a.shape[0]
n_rhs = b.shape[1]
if n_eq != b.shape[0]:
raise LinAlgError, 'Incompatible dimensions'
t =_commonType(a, b)
# lapack_routine = _findLapackRoutine('gesv', t)
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite.zgesv
else:
lapack_routine = lapack_lite.dgesv
a, b = _fastCopyAndTranspose(t, a, b)
pivots = Numeric.zeros(n_eq, 'l')
results = lapack_routine(n_eq, n_rhs, a, n_eq, pivots, b, n_eq, 0)
if results['info'] > 0:
raise LinAlgError, 'Singular matrix'
if one_eq:
return Numeric.ravel(b) # I see no need to copy here
else:
return multiarray.transpose(b) # no need to copy
def cross_product(a, b, axis1=-1, axis2=-1):
"""Return the cross product of two vectors.
The cross product is performed over the last axes of a and b by default,
and can handle axes with dimensions 2 and 3. For a dimension of 2,
the z-component of the equivalent three-dimensional cross product is
returned.
"""
a = _move_axis_to_0(asarray(a), axis1)
b = _move_axis_to_0(asarray(b), axis2)
if a.shape[0] != b.shape[0]:
raise ValueError("incompatible dimensions for cross product")
elif a.shape[0] == 2:
return a[0]*b[1] - a[1]*b[0]
elif a.shape[0] == 3:
x = a[1]*b[2] - a[2]*b[1]
y = a[2]*b[0] - a[0]*b[2]
z = a[0]*b[1] - a[1]*b[0]
cp = array([x,y,z])
if len(cp.shape) == 1:
return cp
# we put the result (in the first axis) as the last axis
axes = range(1, len(cp.shape)) + [0]
return multiarray.transpose(cp, axes)
else:
raise ValueError("can only do cross product for axes with dimensions 2 or 3")
def transpose(a, axes=None):
"""transpose(a, axes=None) returns array with dimensions permuted
according to axes. If axes is None (default) returns array with
dimensions reversed.
"""
# if axes is None: # this test has been moved into multiarray.transpose
# axes = arange(len(array(a).shape))[::-1]
return multiarray.transpose(a, axes)
def transpose(a, axes=None):
"""transpose(a, axes=None) returns array with dimensions permuted
according to axes. If axes is None (default) returns array with
dimensions reversed.
"""
# if axes is None: # this test has been moved into multiarray.transpose
# axes = arange(len(array(a).shape))[::-1]
return multiarray.transpose(a, axes)
def _move_axis_to_0(a, axis):
if axis == 0:
return a
n = len(a.shape)
if axis < 0:
axis += n
axes = range(1, axis+1) + [0,] + range(axis+1, n)
return multiarray.transpose(a, axes)
def singular_value_decomposition(a, full_matrices=0):
_assertRank2(a)
n = a.shape[1]
m = a.shape[0]
t = _commonType(a)
real_t = _array_type[0][_array_precision[t]]
a = _fastCopyAndTranspose(t, a)
if full_matrices:
nu = m
nvt = n
option = 'A'
else:
nu = min(n, m)
nvt = min(n, m)
option = 'S'
s = Numeric.zeros((min(n, m), ), real_t)
u = Numeric.zeros((nu, m), t)
vt = Numeric.zeros((n, nvt), t)
iwork = Numeric.zeros((8 * min(m, n), ), 'i')
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite.zgesdd
rwork = Numeric.zeros((5 * min(m, n) * min(m, n) + 5 * min(m, n), ),
real_t)
lwork = 1
work = Numeric.zeros((lwork, ), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt, work,
-1, rwork, iwork, 0)
lwork = int(abs(work[0]))
work = Numeric.zeros((lwork, ), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt, work,
lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgesdd
lwork = 1
work = Numeric.zeros((lwork, ), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt, work,
-1, iwork, 0)
lwork = int(work[0])
work = Numeric.zeros((lwork, ), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt, work,
lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge'
return multiarray.transpose(u), s, multiarray.transpose(
vt) # why copy here?
def _move_axis_to_0(a, axis):
if axis == 0:
return a
n = len(a.shape)
if axis < 0:
axis += n
axes = range(1, axis + 1) + [
0,
] + range(axis + 1, n)
return multiarray.transpose(a, axes)
def singular_value_decomposition(a, full_matrices = 0):
_assertRank2(a)
n = a.shape[1]
m = a.shape[0]
t =_commonType(a)
real_t = _array_type[0][_array_precision[t]]
a = _fastCopyAndTranspose(t, a)
if full_matrices:
nu = m
nvt = n
option = 'A'
else:
nu = min(n,m)
nvt = min(n,m)
option = 'S'
s = Numeric.zeros((min(n,m),), real_t)
u = Numeric.zeros((nu, m), t)
vt = Numeric.zeros((n, nvt), t)
iwork = Numeric.zeros((8*min(m,n),), 'l')
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite.zgesdd
rwork = Numeric.zeros((5*min(m,n)*min(m,n) + 5*min(m,n),), real_t)
lwork = 1
work = Numeric.zeros((lwork,), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
work, -1, rwork, iwork, 0)
lwork = int(abs(work[0]))
work = Numeric.zeros((lwork,), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
work, lwork, rwork, iwork, 0)
else:
lapack_routine = lapack_lite.dgesdd
lwork = 1
work = Numeric.zeros((lwork,), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
work, -1, iwork, 0)
lwork = int(work[0])
work = Numeric.zeros((lwork,), t)
results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
work, lwork, iwork, 0)
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge'
return multiarray.transpose(u), s, multiarray.transpose(vt) # why copy here?
def swapaxes(a, axis1, axis2):
"""swapaxes(a, axis1, axis2) returns array a with axis1 and axis2
interchanged.
"""
a = array(a, copy=0)
n = len(a.shape)
if n <= 1: return a
if axis1 < 0: axis1 += n
if axis2 < 0: axis2 += n
if axis1 < 0 or axis1 >= n:
raise ValueError, "Bad axis1 argument to swapaxes."
if axis2 < 0 or axis2 >= n:
raise ValueError, "Bad axis2 argument to swapaxes."
new_axes = arange(n)
new_axes[axis1] = axis2
new_axes[axis2] = axis1
return multiarray.transpose(a, new_axes)
def swapaxes(a, axis1, axis2):
"""swapaxes(a, axis1, axis2) returns array a with axis1 and axis2
interchanged.
"""
a = array(a, copy=0)
n = len(a.shape)
if n <= 1: return a
if axis1 < 0: axis1 += n
if axis2 < 0: axis2 += n
if axis1 < 0 or axis1 >= n:
raise ValueError, "Bad axis1 argument to swapaxes."
if axis2 < 0 or axis2 >= n:
raise ValueError, "Bad axis2 argument to swapaxes."
new_axes = arange(n)
new_axes[axis1] = axis2
new_axes[axis2] = axis1
return multiarray.transpose(a, new_axes)
"""Numeric module defining a multi-dimensional array and useful procedures for
# This module is a lite version of LinAlg.py module which contains
"""Numeric module defining a multi-dimensional array and useful procedures for