def byte_bounds(a):
"""
Returns pointers to the end-points of an array.
Parameters
----------
a : ndarray
Input array. It must conform to the Python-side of the array interface.
Returns
-------
(low, high) : tuple of 2 integers
The first integer is the first byte of the array, the second integer is
just past the last byte of the array. If `a` is not contiguous it
would not use every byte between the (`low`, `high`) values.
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
nd_a = len(ashape)
bytes_a = int(ai['typestr'][2:])
a_low = a_high = a_data
if astrides is None: # contiguous case
a_high += product(ashape, dtype=int)*bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape-1)*stride
else:
a_high += (shape-1)*stride
a_high += bytes_a
return a_low, a_high
def byte_bounds(a):
"""(low, high) are pointers to the end-points of an array
low is the first byte
high is just *past* the last byte
If the array is not single-segment, then it may not actually
use every byte between these bounds.
The array provided must conform to the Python-side of the array interface
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
nd_a = len(ashape)
bytes_a = int(ai['typestr'][2:])
a_low = a_high = a_data
if astrides is None: # contiguous case
a_high += product(ashape, dtype=int) * bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape - 1) * stride
else:
a_high += (shape - 1) * stride
a_high += bytes_a
return a_low, a_high
def byte_bounds(a):
"""
Returns pointers to the end-points of an array.
Parameters
----------
a : ndarray
Input array. It must conform to the Python-side of the array interface.
Returns
-------
(low, high) : tuple of 2 integers
The first integer is the first byte of the array, the second integer is
just past the last byte of the array. If `a` is not contiguous it
would not use every byte between the (`low`, `high`) values.
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
nd_a = len(ashape)
bytes_a = int(ai['typestr'][2:])
a_low = a_high = a_data
if astrides is None: # contiguous case
a_high += product(ashape, dtype=int) * bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape - 1) * stride
else:
a_high += (shape - 1) * stride
a_high += bytes_a
return a_low, a_high
def byte_bounds(a):
"""(low, high) are pointers to the end-points of an array
low is the first byte
high is just *past* the last byte
If the array is not single-segment, then it may not actually
use every byte between these bounds.
The array provided must conform to the Python-side of the array interface
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
nd_a = len(ashape)
bytes_a = int(ai['typestr'][2:])
a_low = a_high = a_data
if astrides is None: # contiguous case
a_high += product(ashape, dtype=int)*bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape-1)*stride
else:
a_high += (shape-1)*stride
a_high += bytes_a
return a_low, a_high
def who(vardict=None):
"""Print the Numpy arrays in the given dictionary (or globals() if None).
"""
if vardict is None:
frame = sys._getframe().f_back
vardict = frame.f_globals
sta = []
cache = {}
for name in vardict.keys():
if isinstance(vardict[name], ndarray):
var = vardict[name]
idv = id(var)
if idv in cache.keys():
namestr = name + " (%s)" % cache[idv]
original = 0
else:
cache[idv] = name
namestr = name
original = 1
shapestr = " x ".join(map(str, var.shape))
bytestr = str(var.itemsize * product(var.shape))
sta.append([namestr, shapestr, bytestr, var.dtype.name, original])
maxname = 0
maxshape = 0
maxbyte = 0
totalbytes = 0
for k in range(len(sta)):
val = sta[k]
if maxname < len(val[0]):
maxname = len(val[0])
if maxshape < len(val[1]):
maxshape = len(val[1])
if maxbyte < len(val[2]):
maxbyte = len(val[2])
if val[4]:
totalbytes += int(val[2])
if len(sta) > 0:
sp1 = max(10, maxname)
sp2 = max(10, maxshape)
sp3 = max(10, maxbyte)
prval = "Name %s Shape %s Bytes %s Type" % (sp1 * ' ', sp2 * ' ',
sp3 * ' ')
print prval + "\n" + "=" * (len(prval) + 5) + "\n"
for k in range(len(sta)):
val = sta[k]
print "%s %s %s %s %s %s %s" % (val[0], ' ' *
(sp1 - len(val[0]) + 4), val[1], ' ' *
(sp2 - len(val[1]) + 5), val[2], ' ' *
(sp3 - len(val[2]) + 5), val[3])
print "\nUpper bound on total bytes = %d" % totalbytes
return
def who(vardict=None):
"""Print the Numpy arrays in the given dictionary (or globals() if None).
"""
if vardict is None:
frame = sys._getframe().f_back
vardict = frame.f_globals
sta = []
cache = {}
for name in vardict.keys():
if isinstance(vardict[name],ndarray):
var = vardict[name]
idv = id(var)
if idv in cache.keys():
namestr = name + " (%s)" % cache[idv]
original=0
else:
cache[idv] = name
namestr = name
original=1
shapestr = " x ".join(map(str, var.shape))
bytestr = str(var.itemsize*product(var.shape))
sta.append([namestr, shapestr, bytestr, var.dtype.name,
original])
maxname = 0
maxshape = 0
maxbyte = 0
totalbytes = 0
for k in range(len(sta)):
val = sta[k]
if maxname < len(val[0]):
maxname = len(val[0])
if maxshape < len(val[1]):
maxshape = len(val[1])
if maxbyte < len(val[2]):
maxbyte = len(val[2])
if val[4]:
totalbytes += int(val[2])
if len(sta) > 0:
sp1 = max(10,maxname)
sp2 = max(10,maxshape)
sp3 = max(10,maxbyte)
prval = "Name %s Shape %s Bytes %s Type" % (sp1*' ', sp2*' ', sp3*' ')
print prval + "\n" + "="*(len(prval)+5) + "\n"
for k in range(len(sta)):
val = sta[k]
print "%s %s %s %s %s %s %s" % (val[0], ' '*(sp1-len(val[0])+4),
val[1], ' '*(sp2-len(val[1])+5),
val[2], ' '*(sp3-len(val[2])+5),
val[3])
print "\nUpper bound on total bytes = %d" % totalbytes
return
def byte_bounds(a):
"""
Returns pointers to the end-points of an array.
Parameters
----------
a : ndarray
Input array. It must conform to the Python-side of the array interface.
Returns
-------
(low, high) : tuple of 2 integers
The first integer is the first byte of the array, the second integer is
just past the last byte of the array. If `a` is not contiguous it
will not use every byte between the (`low`, `high`) values.
Examples
--------
>>> I = np.eye(2, dtype='f'); I.dtype
dtype('float32')
>>> low, high = np.byte_bounds(I)
>>> high - low == I.size*I.itemsize
True
>>> I = np.eye(2, dtype='G'); I.dtype
dtype('complex192')
>>> low, high = np.byte_bounds(I)
>>> high - low == I.size*I.itemsize
True
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
nd_a = len(ashape)
bytes_a = int(ai['typestr'][2:])
a_low = a_high = a_data
if astrides is None: # contiguous case
a_high += product(ashape, dtype=int)*bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape-1)*stride
else:
a_high += (shape-1)*stride
a_high += bytes_a
return a_low, a_high
def byte_bounds(a):
"""
Returns pointers to the end-points of an array.
Parameters
----------
a : ndarray
Input array. It must conform to the Python-side of the array interface.
Returns
-------
(low, high) : tuple of 2 integers
The first integer is the first byte of the array, the second integer is
just past the last byte of the array. If `a` is not contiguous it
will not use every byte between the (`low`, `high`) values.
Examples
--------
>>> I = np.eye(2, dtype='f'); I.dtype
dtype('float32')
>>> low, high = np.byte_bounds(I)
>>> high - low == I.size*I.itemsize
True
>>> I = np.eye(2, dtype='G'); I.dtype
dtype('complex192')
>>> low, high = np.byte_bounds(I)
>>> high - low == I.size*I.itemsize
True
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
nd_a = len(ashape)
bytes_a = int(ai['typestr'][2:])
a_low = a_high = a_data
if astrides is None: # contiguous case
a_high += product(ashape, dtype=int) * bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape - 1) * stride
else:
a_high += (shape - 1) * stride
a_high += bytes_a
return a_low, a_high
def who(vardict=None):
"""
Print the Numpy arrays in the given dictionary.
If there is no dictionary passed in or `vardict` is None then returns
Numpy arrays in the globals() dictionary (all Numpy arrays in the
namespace).
Parameters
----------
vardict : dict, optional
A dictionary possibly containing ndarrays. Default is globals().
Returns
-------
out : None
Returns 'None'.
Notes
-----
Prints out the name, shape, bytes and type of all of the ndarrays present
in `vardict`.
Examples
--------
>>> d = {'x': arange(2.0), 'y': arange(3.0), 'txt': 'Some str', 'idx': 5}
>>> np.whos(d)
Name Shape Bytes Type
===========================================================
y 3 24 float64
x 2 16 float64
Upper bound on total bytes = 40
"""
if vardict is None:
frame = sys._getframe().f_back
vardict = frame.f_globals
sta = []
cache = {}
for name in vardict.keys():
if isinstance(vardict[name],ndarray):
var = vardict[name]
idv = id(var)
if idv in cache.keys():
namestr = name + " (%s)" % cache[idv]
original=0
else:
cache[idv] = name
namestr = name
original=1
shapestr = " x ".join(map(str, var.shape))
bytestr = str(var.itemsize*product(var.shape))
sta.append([namestr, shapestr, bytestr, var.dtype.name,
original])
maxname = 0
maxshape = 0
maxbyte = 0
totalbytes = 0
for k in range(len(sta)):
val = sta[k]
if maxname < len(val[0]):
maxname = len(val[0])
if maxshape < len(val[1]):
maxshape = len(val[1])
if maxbyte < len(val[2]):
maxbyte = len(val[2])
if val[4]:
totalbytes += int(val[2])
if len(sta) > 0:
sp1 = max(10,maxname)
sp2 = max(10,maxshape)
sp3 = max(10,maxbyte)
prval = "Name %s Shape %s Bytes %s Type" % (sp1*' ', sp2*' ', sp3*' ')
print prval + "\n" + "="*(len(prval)+5) + "\n"
for k in range(len(sta)):
val = sta[k]
print "%s %s %s %s %s %s %s" % (val[0], ' '*(sp1-len(val[0])+4),
val[1], ' '*(sp2-len(val[1])+5),
val[2], ' '*(sp3-len(val[2])+5),
val[3])
print "\nUpper bound on total bytes = %d" % totalbytes
return
def who(vardict=None):
"""
Print the Numpy arrays in the given dictionary.
If there is no dictionary passed in or `vardict` is None then returns
Numpy arrays in the globals() dictionary (all Numpy arrays in the
namespace).
Parameters
----------
vardict : dict, optional
A dictionary possibly containing ndarrays. Default is globals().
Returns
-------
out : None
Returns 'None'.
Notes
-----
Prints out the name, shape, bytes and type of all of the ndarrays present
in `vardict`.
Examples
--------
>>> d = {'x': arange(2.0), 'y': arange(3.0), 'txt': 'Some str', 'idx': 5}
>>> np.whos(d)
Name Shape Bytes Type
===========================================================
<BLANKLINE>
y 3 24 float64
x 2 16 float64
<BLANKLINE>
Upper bound on total bytes = 40
"""
if vardict is None:
frame = sys._getframe().f_back
vardict = frame.f_globals
sta = []
cache = {}
for name in vardict.keys():
if isinstance(vardict[name], ndarray):
var = vardict[name]
idv = id(var)
if idv in cache.keys():
namestr = name + " (%s)" % cache[idv]
original = 0
else:
cache[idv] = name
namestr = name
original = 1
shapestr = " x ".join(map(str, var.shape))
bytestr = str(var.itemsize * product(var.shape))
sta.append([namestr, shapestr, bytestr, var.dtype.name, original])
maxname = 0
maxshape = 0
maxbyte = 0
totalbytes = 0
for k in range(len(sta)):
val = sta[k]
if maxname < len(val[0]):
maxname = len(val[0])
if maxshape < len(val[1]):
maxshape = len(val[1])
if maxbyte < len(val[2]):
maxbyte = len(val[2])
if val[4]:
totalbytes += int(val[2])
if len(sta) > 0:
sp1 = max(10, maxname)
sp2 = max(10, maxshape)
sp3 = max(10, maxbyte)
prval = "Name %s Shape %s Bytes %s Type" % (sp1 * ' ', sp2 * ' ',
sp3 * ' ')
print prval + "\n" + "=" * (len(prval) + 5) + "\n"
for k in range(len(sta)):
val = sta[k]
print "%s %s %s %s %s %s %s" % (val[0], ' ' *
(sp1 - len(val[0]) + 4), val[1], ' ' *
(sp2 - len(val[1]) + 5), val[2], ' ' *
(sp3 - len(val[2]) + 5), val[3])
print "\nUpper bound on total bytes = %d" % totalbytes
return
def _assertNoEmpty2d(*arrays):
for a in arrays:
if a.size == 0 and product(a.shape[-2:]) == 0:
raise RuntimeError("Arrays cannot be empty")
def _is_empty_2d(arr):
return arr.size == 0 and product(arr.shape[-2:]) == 0
overrides.array_function_dispatch, module='numpy.linalg'); _N = b'N'; _V = b'V'; _A = b'A'; _S = b'S'; _L = b'L' fortran_int = intc @set_module('numpy.linalg') class LinAlgError(Exception): def _determine_error_states(): errobj = geterrobj() bufsize = errobj[0] with errstate(invalid='call', over='ignore', divide='ignore', under='ignore'): invalid_call_errmask = geterrobj()[1] return [bufsize, invalid_call_errmask, None]; _linalg_error_extobj = _determine_error_states(); del _determine_error_states; def _raise_linalgerror_singular(err, flag): raise LinAlgError("Singular matrix"); def _raise_linalgerror_nonposdef(err, flag): raise LinAlgError("Matrix is not positive definite"); def _raise_linalgerror_eigenvalues_nonconvergence(err, flag): raise LinAlgError("Eigenvalues did not converge"); def _raise_linalgerror_svd_nonconvergence(err, flag): raise LinAlgError("SVD did not converge"); def _raise_linalgerror_lstsq(err, flag): raise LinAlgError("SVD did not converge in Linear Least Squares"); def get_linalg_error_extobj(callback): extobj = list(_linalg_error_extobj); extobj[2] = callback; return extobj; def _makearray(a): new = asarray(a); wrap = getattr(a, "__array_prepare__", new.__array_wrap__); return new, wrap; def isComplexType(t): return issubclass(t, complexfloating); _real_types_map = {single: single,; double: double,; csingle: single,; cdouble: double}; _complex_types_map = {single: csingle,; double: cdouble,; csingle: csingle,; cdouble: cdouble}; def _realType(t, default=double): return _real_types_map.get(t, default); def _complexType(t, default=cdouble): return _complex_types_map.get(t, default); def _linalgRealType(t): """Cast the type t to either double or cdouble."""; return double; def _commonType(*arrays): result_type = single; is_complex = False; for a in arrays: if issubclass(a.dtype.type, inexact): if isComplexType(a.dtype.type): is_complex = True; rt = _realType(a.dtype.type, default=None); if rt is None: raise TypeError("array type %s is unsupported in linalg" %; (a.dtype.name,)); else: rt = double; if rt is double: result_type = double; if is_complex: t = cdouble; result_type = _complex_types_map[result_type]; else: t = double; return t, result_type; _fastCT = fastCopyAndTranspose; def _to_native_byte_order(*arrays): ret = []; for arr in arrays: if arr.dtype.byteorder not in ('=', '|'): ret.append(asarray(arr, dtype=arr.dtype.newbyteorder('='))); else: ret.append(arr); if len(ret) == 1: return ret[0]; else: return ret; def _fastCopyAndTranspose(type, *arrays): cast_arrays = (); for a in arrays: if a.dtype.type is type: cast_arrays = cast_arrays + (_fastCT(a),); else: cast_arrays = cast_arrays + (_fastCT(a.astype(type)),); if len(cast_arrays) == 1: return cast_arrays[0]; else: return cast_arrays; def _assert_2d(*arrays): for a in arrays: if a.ndim != 2: raise LinAlgError('%d-dimensional array given. Array must be '; 'two-dimensional' % a.ndim); def _assert_stacked_2d(*arrays): for a in arrays: if a.ndim < 2: raise LinAlgError('%d-dimensional array given. Array must be '; 'at least two-dimensional' % a.ndim); def _assert_stacked_square(*arrays): for a in arrays: m, n = a.shape[-2:]; if m != n: raise LinAlgError('Last 2 dimensions of the array must be square'); def _assert_finite(*arrays): for a in arrays: if not isfinite(a).all(): raise LinAlgError("Array must not contain infs or NaNs"); def _is_empty_2d(arr): return arr.size == 0 and product(arr.shape[-2:]) == 0; def transpose(a): a, wrap = _makearray(a); b = asarray(b); an = a.ndim; if axes is not None: allaxes = list(range(0, an)); for k in axes: allaxes.remove(k); allaxes.insert(an, k); a = a.transpose(allaxes); oldshape = a.shape[-(an-b.ndim):]; prod = 1; for k in oldshape: prod *= k; a = a.reshape(-1, prod); b = b.ravel(); res = wrap(solve(a, b)); res.shape = oldshape; return res; def _solve_dispatcher(a, b): return (a, b); @array_function_dispatch(_solve_dispatcher); def solve(a, b): a, _ = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); b, wrap = _makearray(b); t, result_t = _commonType(a, b); if b.ndim == a.ndim - 1: gufunc = _umath_linalg.solve1; else: gufunc = _umath_linalg.solve; signature = 'DD->D' if isComplexType(t) else 'dd->d'; extobj = get_linalg_error_extobj(_raise_linalgerror_singular); r = gufunc(a, b, signature=signature, extobj=extobj); return wrap(r.astype(result_t, copy=False)); def _tensorinv_dispatcher(a, ind=None): return (a,); @array_function_dispatch(_tensorinv_dispatcher); def tensorinv(a, ind=2): a = asarray(a); oldshape = a.shape; prod = 1; if ind > 0: invshape = oldshape[ind:] + oldshape[:ind]; for k in oldshape[ind:]: prod *= k; else: raise ValueError("Invalid ind argument."); a = a.reshape(prod, -1); ia = inv(a); return ia.reshape(*invshape); def _unary_dispatcher(a): return (a,); @array_function_dispatch(_unary_dispatcher); def inv(a): a, wrap = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); t, result_t = _commonType(a); signature = 'D->D' if isComplexType(t) else 'd->d'; extobj = get_linalg_error_extobj(_raise_linalgerror_singular); ainv = _umath_linalg.inv(a, signature=signature, extobj=extobj); return wrap(ainv.astype(result_t, copy=False)); def _matrix_power_dispatcher(a, n): return (a,); @array_function_dispatch(_matrix_power_dispatcher); def matrix_power(a, n): a = asanyarray(a); _assert_stacked_2d(a); _assert_stacked_square(a); try: n = operator.index(n); except TypeError: raise TypeError("exponent must be an integer"); if a.dtype != object: fmatmul = matmul; elif a.ndim == 2: fmatmul = dot; else: raise NotImplementedError(; "matrix_power not supported for stacks of object arrays"); if n == 0: a = empty_like(a); a[...] = eye(a.shape[-2], dtype=a.dtype); return a; elif n < 0: a = inv(a); n = abs(n); if n == 1: return a; elif n == 2: return fmatmul(a, a); elif n == 3: return fmatmul(fmatmul(a, a), a); z = result = None; while n > 0: z = a if z is None else fmatmul(z, z); n, bit = divmod(n, 2); if bit: result = z if result is None else fmatmul(result, z); return result; @array_function_dispatch(_unary_dispatcher); def cholesky(a): extobj = get_linalg_error_extobj(_raise_linalgerror_nonposdef); gufunc = _umath_linalg.cholesky_lo; a, wrap = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); t, result_t = _commonType(a); signature = 'D->D' if isComplexType(t) else 'd->d'; r = gufunc(a, signature=signature, extobj=extobj); return wrap(r.astype(result_t, copy=False)); def _qr_dispatcher(a, mode=None): return (a,); @array_function_dispatch(_qr_dispatcher); def qr(a, mode='reduced'): if mode not in ('reduced', 'complete',x 'r', 'raw'): if mode in ('f', 'full'): msg = "".join((; "The 'full' option is deprecated in favor of 'reduced'.\n",; "For backward compatibility let mode default.")); warnings.warn(msg, DeprecationWarning, stacklevel=3); mode = 'reduced'; elif mode in ('e', 'economic'): msg = "The 'economic' option is deprecated."; warnings.warn(msg, DeprecationWarning, stacklevel=3); mode = 'economic'; else: raise ValueError("Unrecognized mode '%s'" % mode); a, wrap = _makearray(a); _assert_2d(a); m, n = a.shape; t, result_t = _commonType(a); a = _fastCopyAndTranspose(t, a); a = _to_native_byte_order(a); mn = min(m, n); tau = zeros((mn,), t); if isComplexType(t): lapack_routine = lapack_lite.zgeqrf; routine_name = 'zgeqrf'; else: lapack_routine = lapack_lite.dgeqrf; routine_name = 'dgeqrf'; lwork = 1; work = zeros((lwork,), t); results = lapack_routine(m, n, a, max(1, m), tau, work, -1, 0); if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])); lwork = max(1, n, int(abs(work[0]))); work = zeros((lwork,), t); results = lapack_routine(m, n, a, max(1, m), tau, work, lwork, 0); if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])); if mode == 'r': r = _fastCopyAndTranspose(result_t, a[:, :mn]); return wrap(triu(r)); if mode == 'raw': return a, tau; if mode == 'economic': if t != result_t : a = a.astype(result_t, copy=False); return wrap(a.T); if mode == 'complete' and m > n: mc = m; q = empty((m, m), t); else: mc = mn; q = empty((n, m), t); q[:n] = a; if isComplexType(t): lapack_routine = lapack_lite.zungqr; routine_name = 'zungqr'; else: lapack_routine = lapack_lite.dorgqr; routine_name = 'dorgqr'; lwork = 1; work = zeros((lwork,), t); results = lapack_routine(m, mc, mn, q, max(1, m), tau, work, -1, 0); if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])); lwork = max(1, n, int(abs(work[0]))); work = zeros((lwork,), t); results = lapack_routine(m, mc, mn, q, max(1, m), tau, work, lwork, 0); if results['info'] != 0: raise LinAlgError('%s returns %d' % (routine_name, results['info'])); q = _fastCopyAndTranspose(result_t, q[:mc]); r = _fastCopyAndTranspose(result_t, a[:, :mc]); return wrap(q), wrap(triu(r)); @array_function_dispatch(_unary_dispatcher); def eigvals(a): a, wrap = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); _assert_finite(a); t, result_t = _commonType(a); extobj = get_linalg_error_extobj(; _raise_linalgerror_eigenvalues_nonconvergence); signature = 'D->D' if isComplexType(t) else 'd->D'; w = _umath_linalg.eigvals(a, signature=signature, extobj=extobj); if not isComplexType(t): if all(w.imag == 0): w = w.real; result_t = _realType(result_t); else: result_t = _complexType(result_t); return w.astype(result_t, copy=False); def _eigvalsh_dispatcher(a, UPLO=None): return (a,); @array_function_dispatch(_eigvalsh_dispatcher); def eigvalsh(a, UPLO='L'): UPLO = UPLO.upper(); if UPLO not in ('L', 'U'): raise ValueError("UPLO argument must be 'L' or 'U'"); extobj = get_linalg_error_extobj(; _raise_linalgerror_eigenvalues_nonconvergence); if UPLO == 'L': gufunc = _umath_linalg.eigvalsh_lo; else: gufunc = _umath_linalg.eigvalsh_up; a, wrap = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); t, result_t = _commonType(a); signature = 'D->d' if isComplexType(t) else 'd->d'; w = gufunc(a, signature=signature, extobj=extobj); return w.astype(_realType(result_t), copy=False); def _convertarray(a): t, result_t = _commonType(a); a = _fastCT(a.astype(t)); return a, t, result_t; def eig(a): a, wrap = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); _assert_finite(a); t, result_t = _commonType(a); extobj = get_linalg_error_extobj(; _raise_linalgerror_eigenvalues_nonconvergence); signature = 'D->DD' if isComplexType(t) else 'd->DD'; w, vt = _umath_linalg.eig(a, signature=signature, extobj=extobj); if not isComplexType(t) and all(w.imag == 0.0): w = w.real; vt = vt.real; result_t = _realType(result_t); else: result_t = _complexType(result_t); vt = vt.astype(result_t, copy=False); return w.astype(result_t, copy=False), wrap(vt); @array_function_dispatch(_eigvalsh_dispatcher); def eigh(a, UPLO='L'): UPLO = UPLO.upper(); if UPLO not in ('L', 'U'): raise ValueError("UPLO argument must be 'L' or 'U'"); a, wrap = _makearray(a); _assert_stacked_2d(a); _assert_stacked_square(a); t, result_t = _commonType(a); extobj = get_linalg_error_extobj(; _raise_linalgerror_eigenvalues_nonconvergence); if UPLO == 'L': gufunc = _umath_linalg.eigh_lo; else: gufunc = _umath_linalg.eigh_up; signature = 'D->dD' if isComplexType(t) else 'd->dd'; w, vt = gufunc(a, signature=signature, extobj=extobj); w = w.astype(_realType(result_t), copy=False); vt = vt.astype(result_t, copy=False); return w, wrap(vt); def _svd_dispatcher(a, full_matrices=None, compute_uv=None, hermitian=None): return (a,); @array_function_dispatch(_svd_dispatcher); def svd(a, full_matrices=True, compute_uv=True, hermitian=False): a, wrap = _makearray(a); if hermitian: if compute_uv: s, u = eigh(a); s = s[..., ::-1]; u = u[..., ::-1]; vt = transpose(u * sign(s)[..., None, :]).conjugate(); s = abs(s); return wrap(u), s, wrap(vt); else: s = eigvalsh(a); s = s[..., ::-1]; s = abs(s); return s; _assert_stacked_2d(a); t, result_t = _commonType(a); extobj = get_linalg_error_extobj(_raise_linalgerror_svd_nonconvergence); m, n = a.shape[-2:]; if compute_uv: if full_matrices: if m < n: gufunc = _umath_linalg.svd_m_f; else: gufunc = _umath_linalg.svd_n_f; else: if m < n: gufunc = _umath_linalg.svd_m_s; else: gufunc = _umath_linalg.svd_n_s; signature = 'D->DdD' if isComplexType(t) else 'd->ddd'; u, s, vh = gufunc(a, signature=signature, extobj=extobj); u = u.astype(result_t, copy=False); s = s.astype(_realType(result_t), copy=False); vh = vh.astype(result_t, copy=False); return wrap(u), s, wrap(vh); else: if m < n: gufunc = _umath_linalg.svd_m; else: gufunc = _umath_linalg.svd_n; signature = 'D->d' if isComplexType(t) else 'd->d'; s = gufunc(a, signature=signature, extobj=extobj); s = s.astype(_realType(result_t), copy=False); return s; def _cond_dispatcher(x, p=None): return (x,); @array_function_dispatch(_cond_dispatcher); def cond(x, p=None): x = asarray(x); if _is_empty_2d(x): raise LinAlgError("cond is not defined on empty arrays"); if p is None or p == 2 or p == -2: s = svd(x, compute_uv=False); with errstate(all='ignore'): if p == -2: r = s[..., -1] / s[..., 0]; else: r = s[..., 0] / s[..., -1]; else: _assert_stacked_2d(x); _assert_stacked_square(x); t, result_t = _commonType(x); signature = 'D->D' if isComplexType(t) else 'd->d'; with errstate(all='ignore'): invx = _umath_linalg.inv(x, signature=signature); r = norm(x, p, axis=(-2, -1)) * norm(invx, p, axis=(-2, -1)); r = r.astype(result_t, copy=False); r = asarray(r); nan_mask = isnan(r); if nan_mask.any(): nan_mask &= ~isnan(x).any(axis=(-2, -1)); if r.ndim > 0: r[nan_mask] = Inf; elif nan_mask: r[()] = Inf; if r.ndim == 0: r = r[()]; return r; def _matrix_rank_dispatcher(M, tol=None, hermitian=None): return (M,); @array_function_dispatch(_matrix_rank_dispatcher); def matrix_rank(M, tol=None, hermitian=False): M = asarray(M); if M.ndim < 2: return int(not all(M==0)); S = svd(M, compute_uv=False, hermitian=hermitian); if tol is None: tol = S.max(axis=-1, keepdims=True) * max(M.shape[-2:]) * finfo(S.dtype).eps; else: tol = asarray(tol)[..., newaxis]; return count_nonzero(S > tol, axis=-1); def pinv(a, rcond=1e-15, hermitian=False): a, wrap = _makearray(a); rcond = asarray(rcond); if _is_empty_2d(a): m, n = a.shape[-2:]; res = empty(a.shape[:-2] + (n, m), dtype=a.dtype); return wrap(res); a = a.conjugate(); u, s, vt = svd(a, full_matrices=False, hermitian=hermitian); cutoff = rcond[..., newaxis] * amax(s, axis=-1, keepdims=True); large = s > cutoff; s = divide(1, s, where=large, out=s); s[~large] = 0; res = matmul(transpose(vt), multiply(s[..., newaxis], transpose(u))); return wrap(res); def slogdet(a): a = asarray(a); _assert_stacked_2d(a); _assert_stacked_square(a); t, result_t = _commonType(a); real_t = _realType(result_t); signature = 'D->Dd' if isComplexType(t) else 'd->dd'; sign, logdet = _umath_linalg.slogdet(a, signature=signature); sign = sign.astype(result_t, copy=False); logdet = logdet.astype(real_t, copy=False); return sign, logdet; @array_function_dispatch(_unary_dispatcher); def det(a): a = asarray(a); _assert_stacked_2d(a); _assert_stacked_square(a); t, result_t = _commonType(a); signature = 'D->D' if isComplexType(t) else 'd->d'; r = _umath_linalg.det(a, signature=signature); r = r.astype(result_t, copy=False); return r; def lstsq(a, b, rcond="warn"): a, _ = _makearray(a); b, wrap = _makearray(b); is_1d = b.ndim == 1; if is_1d: b = b[:, newaxis]; _assert_2d(a, b); m, n = a.shape[-2:]; m2, n_rhs = b.shape[-2:]; if m != m2: raise LinAlgError('Incompatible dimensions'); t, result_t = _commonType(a, b); real_t = _linalgRealType(t); result_real_t = _realType(result_t); if rcond == "warn": warnings.warn("`rcond` parameter will change to the default of "; "machine precision times ``max(M, N)`` where M and N "; "are the input matrix dimensions.\n"; "To use the future default and silence this warning "; "we advise to pass `rcond=None`, to keep using the old, "; "explicitly pass `rcond=-1`.",; FutureWarning, stacklevel=3); rcond = -1; if rcond is None: rcond = finfo(t).eps * max(n, m); if m <= n: gufunc = _umath_linalg.lstsq_m; else: gufunc = _umath_linalg.lstsq_n; signature = 'DDd->Ddid' if isComplexType(t) else 'ddd->ddid'; extobj = get_linalg_error_extobj(_raise_linalgerror_lstsq); if n_rhs == 0: b = zeros(b.shape[:-2] + (m, n_rhs + 1), dtype=b.dtype); x, resids, rank, s = gufunc(a, b, rcond, signature=signature, extobj=extobj); if m == 0: x[...] = 0; if n_rhs == 0: x = x[..., :n_rhs]; resids = resids[..., :n_rhs]; if is_1d: x = x.squeeze(axis=-1); if rank != n or m <= n: resids = array([], result_real_t); s = s.astype(result_real_t, copy=False); resids = resids.astype(result_real_t, copy=False); x = x.astype(result_t, copy=True); return wrap(x), wrap(resids), rank, s; def _multi_svd_norm(x, row_axis, col_axis, op): y = moveaxis(x, (row_axis, col_axis), (-2, -1)); result = op(svd(y, compute_uv=False), axis=-1); return result; def _norm_dispatcher(x, ord=None, axis=None, keepdims=None): return (x,); @array_function_dispatch(_norm_dispatcher); def norm(x, ord=None, axis=None, keepdims=False): x = asarray(x); if not issubclass(x.dtype.type, (inexact, object_)): x = x.astype(float); if axis is None: ndim = x.ndim; if ((ord is None) or; (ord in ('f', 'fro') and ndim == 2) or; (ord == 2 and ndim == 1)): x = x.ravel(order='K'); if isComplexType(x.dtype.type): sqnorm = dot(x.real, x.real) + dot(x.imag, x.imag); else: sqnorm = dot(x, x); ret = sqrt(sqnorm); if keepdims: ret = ret.reshape(ndim*[1]); return ret; nd = x.ndim; if axis is None: axis = tuple(range(nd)); elif not isinstance(axis, tuple): try: axis = int(axis); except Exception: raise TypeError("'axis' must be None, an integer or a tuple of integers"); axis = (axis,); if len(axis) == 1: if ord == Inf: return abs(x).max(axis=axis, keepdims=keepdims); elif ord == -Inf: return abs(x).min(axis=axis, keepdims=keepdims); elif ord == 0: return (x != 0).astype(x.real.dtype).sum(axis=axis, keepdims=keepdims); elif ord == 1: return add.reduce(abs(x), axis=axis, keepdims=keepdims); elif ord is None or ord == 2: s = (x.conj() * x).real; return sqrt(add.reduce(s, axis=axis, keepdims=keepdims)); else: try: ord + 1; except TypeError: raise ValueError("Invalid norm order for vectors."); absx = abs(x); absx **= ord; ret = add.reduce(absx, axis=axis, keepdims=keepdims); ret **= (1 / ord); return ret; elif len(axis) == 2: row_axis, col_axis = axis; row_axis = normalize_axis_index(row_axis, nd); col_axis = normalize_axis_index(col_axis, nd); if row_axis == col_axis: raise ValueError('Duplicate axes given.'); if ord == 2: ret =_multi_svd_norm(x, row_axis, col_axis, amax); elif ord == -2: ret = _multi_svd_norm(x, row_axis, col_axis, amin); elif ord == 1: if col_axis > row_axis: col_axis -= 1; ret = add.reduce(abs(x), axis=row_axis).max(axis=col_axis); elif ord == Inf: if row_axis > col_axis: row_axis -= 1; ret = add.reduce(abs(x), axis=col_axis).max(axis=row_axis); elif ord == -1: if col_axis > row_axis: col_axis -= 1; ret = add.reduce(abs(x), axis=row_axis).min(axis=col_axis); elif ord == -Inf: if row_axis > col_axis: row_axis -= 1; ret = add.reduce(abs(x), axis=col_axis).min(axis=row_axis); elif ord in [None, 'fro', 'f']: ret = sqrt(add.reduce((x.conj() * x).real, axis=axis)); elif ord == 'nuc': ret = _multi_svd_norm(x, row_axis, col_axis, sum); else: raise ValueError("Invalid norm order for matrices."); if keepdims: ret_shape = list(x.shape); ret_shape[axis[0]] = 1; ret_shape[axis[1]] = 1; ret = ret.reshape(ret_shape); return ret; else: raise ValueError("Improper number of dimensions to norm."); def multi_dot(arrays): n = len(arrays); if n < 2: raise ValueError("Expecting at least two arrays."); elif n == 2: return dot(arrays[0], arrays[1]); arrays = [asanyarray(a) for a in arrays]; ndim_first, ndim_last = arrays[0].ndim, arrays[-1].ndim; if arrays[0].ndim == 1: arrays[0] = atleast_2d(arrays[0]); if arrays[-1].ndim == 1: arrays[-1] = atleast_2d(arrays[-1]).T; _assert_2d(*arrays)