ImageD11.rc_array | index /sware/exp/fable/standalone/redhate4-a64/lib/python2.5/site-packages/ImageD11/rc_array.py

`Row/column array type
Inherits from numpy.ndarray
To be used for lattice reduction to apply to g-vectors and patterson
peaks equally well and in a coherent way.`

Classes
`` |  | numpy.ndarray(__builtin__.object) rc_array
class rc_array(numpy.ndarray)
`` | `Row/Column array Represent a list of row or column vectors`
| Method resolution order: rc_array numpy.ndarray __builtin__.object Methods defined here: __array_finalize__(self, obj) `Fill in a default row arg to direction self/obj??` __iter__(self) `Iterate depending on rows columns Use to get [ v for v in rr_array ]` __str__(self) `Used for printing` check(self) `Ensure we have an rc_array which is well behaved Pattern assert(check(v)) should disappear in optimiser` flip(self, mat) `Flip row to col or col.row` inv(self) `Inverse matrix of self` nb_vector_axis(self) `The axis which has the n on it` norm2(self) `sum(v*v,axis=? for row or col` nvectors(self) other_direction(self) `The one which is not self.direction` vector_axis(self) `The axis which has the 3 on it` Static methods defined here: __new__(subtype, data, direction=None, dtype=None, copy=False) `Mostly as from example direction is one of row / column` Data descriptors defined here: __dict__ `dictionary for instance variables (if defined)` Methods inherited from numpy.ndarray: __abs__(...) `x.__abs__() <==> abs(x)` __add__(...) `x.__add__(y) <==> x+y` __and__(...) `x.__and__(y) <==> x&y` __array__(...) `a.__array__(|dtype) -> reference if type unchanged, copy otherwise. Returns either a new reference to self if dtype is not given or a new array of provided data type if dtype is different from the current dtype of the array.` __array_wrap__(...) `a.__array_wrap__(obj) -> Object of same type as a from ndarray obj.` __contains__(...) `x.__contains__(y) <==> y in x` __copy__(...) `a.__copy__(|order) -> copy, possibly with different order. Return a copy of the array. Argument: order -- Order of returned copy (default 'C') If order is 'C' (False) then the result is contiguous (default). If order is 'Fortran' (True) then the result has fortran order. If order is 'Any' (None) then the result has fortran order only if m is already in fortran order.;` __deepcopy__(...) `a.__deepcopy__() -> Deep copy of array. Used if copy.deepcopy is called on an array.` __delitem__(...) `x.__delitem__(y) <==> del x[y]` __delslice__(...) `x.__delslice__(i, j) <==> del x[i:j] Use of negative indices is not supported.` __div__(...) `x.__div__(y) <==> x/y` __divmod__(...) `x.__divmod__(y) <==> divmod(x, y)` __eq__(...) `x.__eq__(y) <==> x==y` __float__(...) `x.__float__() <==> float(x)` __floordiv__(...) `x.__floordiv__(y) <==> x//y` __ge__(...) `x.__ge__(y) <==> x>=y` __getitem__(...) `x.__getitem__(y) <==> x[y]` __getslice__(...) `x.__getslice__(i, j) <==> x[i:j] Use of negative indices is not supported.` __gt__(...) `x.__gt__(y) <==> x>y` __hex__(...) `x.__hex__() <==> hex(x)` __iadd__(...) `x.__iadd__(y) <==> x+y` __iand__(...) `x.__iand__(y) <==> x&y` __idiv__(...) `x.__idiv__(y) <==> x/y` __ifloordiv__(...) `x.__ifloordiv__(y) <==> x//y` __ilshift__(...) `x.__ilshift__(y) <==> x<<y` __imod__(...) `x.__imod__(y) <==> x%y` __imul__(...) `x.__imul__(y) <==> x*y` __index__(...) `x[y:z] <==> x[y.__index__():z.__index__()]` __int__(...) `x.__int__() <==> int(x)` __invert__(...) `x.__invert__() <==> ~x` __ior__(...) `x.__ior__(y) <==> x|y` __ipow__(...) `x.__ipow__(y) <==> x**y` __irshift__(...) `x.__irshift__(y) <==> x>>y` __isub__(...) `x.__isub__(y) <==> x-y` __itruediv__(...) `x.__itruediv__(y) <==> x/y` __ixor__(...) `x.__ixor__(y) <==> x^y` __le__(...) `x.__le__(y) <==> x<=y` __len__(...) `x.__len__() <==> len(x)` __long__(...) `x.__long__() <==> long(x)` __lshift__(...) `x.__lshift__(y) <==> x<<y` __lt__(...) `x.__lt__(y) <==> x<y` __mod__(...) `x.__mod__(y) <==> x%y` __mul__(...) `x.__mul__(y) <==> x*y` __ne__(...) `x.__ne__(y) <==> x!=y` __neg__(...) `x.__neg__() <==> -x` __nonzero__(...) `x.__nonzero__() <==> x != 0` __oct__(...) `x.__oct__() <==> oct(x)` __or__(...) `x.__or__(y) <==> x|y` __pos__(...) `x.__pos__() <==> +x` __pow__(...) `x.__pow__(y[, z]) <==> pow(x, y[, z])` __radd__(...) `x.__radd__(y) <==> y+x` __rand__(...) `x.__rand__(y) <==> y&x` __rdiv__(...) `x.__rdiv__(y) <==> y/x` __rdivmod__(...) `x.__rdivmod__(y) <==> divmod(y, x)` __reduce__(...) `a.__reduce__() For pickling.` __repr__(...) `x.__repr__() <==> repr(x)` __rfloordiv__(...) `x.__rfloordiv__(y) <==> y//x` __rlshift__(...) `x.__rlshift__(y) <==> y<<x` __rmod__(...) `x.__rmod__(y) <==> y%x` __rmul__(...) `x.__rmul__(y) <==> y*x` __ror__(...) `x.__ror__(y) <==> y|x` __rpow__(...) `y.__rpow__(x[, z]) <==> pow(x, y[, z])` __rrshift__(...) `x.__rrshift__(y) <==> y>>x` __rshift__(...) `x.__rshift__(y) <==> x>>y` __rsub__(...) `x.__rsub__(y) <==> y-x` __rtruediv__(...) `x.__rtruediv__(y) <==> y/x` __rxor__(...) `x.__rxor__(y) <==> y^x` __setitem__(...) `x.__setitem__(i, y) <==> x[i]=y` __setslice__(...) `x.__setslice__(i, j, y) <==> x[i:j]=y Use of negative indices is not supported.` __setstate__(...) `a.__setstate__(version, shape, typecode, isfortran, rawdata) For unpickling. Arguments: version -- optional pickle version. If omitted defaults to 0. shape -- a tuple giving the shape typecode -- a typecode isFortran -- a bool stating if Fortran or no rawdata -- a binary string with the data (or a list if Object array)` __sub__(...) `x.__sub__(y) <==> x-y` __truediv__(...) `x.__truediv__(y) <==> x/y` __xor__(...) `x.__xor__(y) <==> x^y` all(...) `a.all(axis=None)` any(...) `a.any(axis=None, out=None)` argmax(...) `a.argmax(axis=None, out=None)` argmin(...) `a.argmin(axis=None, out=None)` argsort(...) `a.argsort(axis=-1, kind='quicksort', order=None) -> indices Perform an indirect sort along the given axis using the algorithm specified by the kind keyword. It returns an array of indices of the same shape as 'a' that index data along the given axis in sorted order. :Parameters: axis : integer Axis to be indirectly sorted. None indicates that the flattened array should be used. Default is -1. kind : string Sorting algorithm to use. Possible values are 'quicksort', 'mergesort', or 'heapsort'. Default is 'quicksort'. order : list type or None When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. :Returns: indices : integer array Array of indices that sort 'a' along the specified axis. :SeeAlso: - lexsort : indirect stable sort with multiple keys - sort : inplace sort :Notes: ------ The various sorts are characterized by average speed, worst case performance, need for work space, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The three available algorithms have the following properties: |------------------------------------------------------| | kind | speed | worst case | work space | stable| |------------------------------------------------------| |'quicksort'| 1 | O(n^2) | 0 | no | |'mergesort'| 2 | O(n*log(n)) | ~n/2 | yes | |'heapsort' | 3 | O(n*log(n)) | 0 | no | |------------------------------------------------------| All the sort algorithms make temporary copies of the data when the sort is not along the last axis. Consequently, sorts along the last axis are faster and use less space than sorts along other axis.` astype(...) `a.astype(t) -> Copy of array cast to type t. Cast array m to type t. t can be either a string representing a typecode, or a python type object of type int, float, or complex.` byteswap(...) `a.byteswap(False) -> View or copy. Swap the bytes in the array. Swap the bytes in the array. Return the byteswapped array. If the first argument is True, byteswap in-place and return a reference to self.` choose(...) `a.choose(b0, b1, ..., bn, out=None, mode='raise') Return an array that merges the b_i arrays together using 'a' as the index The b_i arrays and 'a' must all be broadcastable to the same shape. The output at a particular position is the input array b_i at that position depending on the value of 'a' at that position. Therefore, 'a' must be an integer array with entries from 0 to n+1.;` clip(...) `a.clip(min=, max=, out=None)` compress(...) `a.compress(condition=, axis=None, out=None)` conj(...) `a.conj()` conjugate(...) `a.conjugate()` copy(...) `a.copy(|order) -> copy, possibly with different order. Return a copy of the array. Argument: order -- Order of returned copy (default 'C') If order is 'C' (False) then the result is contiguous (default). If order is 'Fortran' (True) then the result has fortran order. If order is 'Any' (None) then the result has fortran order only if m is already in fortran order.;` cumprod(...) `a.cumprod(axis=None, dtype=None)` cumsum(...) `a.cumsum(axis=None, dtype=None, out=None)` diagonal(...) `a.diagonal(offset=0, axis1=0, axis2=1) -> diagonals If a is 2-d, return the diagonal of self with the given offset, i.e., the collection of elements of the form a[i,i+offset]. If a is n-d with n > 2, then the axes specified by axis1 and axis2 are used to determine the 2-d subarray whose diagonal is returned. The shape of the resulting array can be determined by removing axis1 and axis2 and appending an index to the right equal to the size of the resulting diagonals. :Parameters: offset : integer Offset of the diagonal from the main diagonal. Can be both positive and negative. Defaults to main diagonal. axis1 : integer Axis to be used as the first axis of the 2-d subarrays from which the diagonals should be taken. Defaults to first index. axis2 : integer Axis to be used as the second axis of the 2-d subarrays from which the diagonals should be taken. Defaults to second index. :Returns: array_of_diagonals : same type as original array If a is 2-d, then a 1-d array containing the diagonal is returned. If a is n-d, n > 2, then an array of diagonals is returned. :SeeAlso: - diag : matlab workalike for 1-d and 2-d arrays. - diagflat : creates diagonal arrays - trace : sum along diagonals Examples -------- >>> a = arange(4).reshape(2,2) >>> a array([[0, 1], [2, 3]]) >>> a.diagonal() array([0, 3]) >>> a.diagonal(1) array([1]) >>> a = arange(8).reshape(2,2,2) >>> a array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> a.diagonal(0,-2,-1) array([[0, 3], [4, 7]])` dump(...) `a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load Arguments: file -- string naming the dump file.` dumps(...) `a.dumps() returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array.` fill(...) `a.fill(value) -> None. Fill the array with the scalar value.` flatten(...) `a.flatten([fortran]) return a 1-d array (always copy)` getfield(...) `a.getfield(dtype, offset) -> field of array as given type. Returns a field of the given array as a certain type. A field is a view of the array data with each itemsize determined by the given type and the offset into the current array.` item(...) `a.item() -> copy of first array item as Python scalar. Copy the first element of array to a standard Python scalar and return it. The array must be of size one.` itemset(...) max(...) `a.max(axis=None)` mean(...) `a.mean(axis=None, dtype=None, out=None) -> mean Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. :Parameters: axis : integer Axis along which the means are computed. The default is to compute the standard deviation of the flattened array. dtype : type Type to use in computing the means. For arrays of integer type the default is float32, for arrays of float types it is the same as the array type. out : ndarray Alternative output array in which to place the result. It must have the same shape as the expected output but the type will be cast if necessary. :Returns: mean : The return type varies, see above. A new array holding the result is returned unless out is specified, in which case a reference to out is returned. :SeeAlso: - var : variance - std : standard deviation Notes ----- The mean is the sum of the elements along the axis divided by the number of elements.` min(...) `a.min(axis=None)` newbyteorder(...) `a.newbyteorder(<byteorder>) is equivalent to a.view(a.dtype.newbytorder(<byteorder>))` nonzero(...) `a.nonzero() returns a tuple of arrays Returns a tuple of arrays, one for each dimension of a, containing the indices of the non-zero elements in that dimension. The corresponding non-zero values can be obtained with a[a.nonzero()]. To group the indices by element, rather than dimension, use transpose(a.nonzero()) instead. The result of this is always a 2d array, with a row for each non-zero element.;` prod(...) `a.prod(axis=None, dtype=None)` ptp(...) `a.ptp(axis=None) a.max(axis)-a.min(axis)` put(...) `a.put(indices, values, mode) sets a.flat[n] = values[n] for each n in indices. If values is shorter than indices then it will repeat.` ravel(...) `a.ravel([fortran]) return a 1-d array (copy only if needed)` repeat(...) `a.repeat(repeats=, axis=none) copy elements of a, repeats times. the repeats argument must be a sequence of length a.shape[axis] or a scalar.` reshape(...) `a.reshape(d1, d2, ..., dn, order='c') Return a new array from this one. The new array must have the same number of elements as self. Also always returns a view or raises a ValueError if that is impossible.` resize(...) `a.resize(new_shape, refcheck=True, order=False) -> None. Change array shape. Change size and shape of self inplace. Array must own its own memory and not be referenced by other arrays. Returns None.` round(...) `a.round(decimals=0, out=None) -> out (a). Rounds to 'decimals' places. Keyword arguments: decimals -- number of decimals to round to (default 0). May be negative. out -- existing array to use for output (default a). Return: Reference to out, where None specifies the original array a. Round to the specified number of decimals. When 'decimals' is negative it specifies the number of positions to the left of the decimal point. The real and imaginary parts of complex numbers are rounded separately. Nothing is done if the array is not of float type and 'decimals' is >= 0. The keyword 'out' may be used to specify a different array to hold the result rather than the default 'a'. If the type of the array specified by 'out' differs from that of 'a', the result is cast to the new type, otherwise the original type is kept. Floats round to floats by default. Numpy rounds to even. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc. Results may also be surprising due to the inexact representation of decimal fractions in IEEE floating point and the errors introduced in scaling the numbers when 'decimals' is something other than 0.` searchsorted(...) `a.searchsorted(v, side='left') -> index array. Find the indices into a sorted array such that if the corresponding keys in v were inserted before the indices the order of a would be preserved. If side='left', then the first such index is returned. If side='right', then the last such index is returned. If there is no such index because the key is out of bounds, then the length of a is returned, i.e., the key would need to be appended. The returned index array has the same shape as v. :Parameters: v : array or list type Array of keys to be searched for in a. side : string Possible values are : 'left', 'right'. Default is 'left'. Return the first or last index where the key could be inserted. :Returns: indices : integer array The returned array has the same shape as v. :SeeAlso: - sort - histogram :Notes: ------- The array a must be 1-d and is assumed to be sorted in ascending order. Searchsorted uses binary search to find the required insertion points.` setfield(...) `m.setfield(value, dtype, offset) -> None. places val into field of the given array defined by the data type and offset.` setflags(...) `a.setflags(write=None, align=None, uic=None)` sort(...) `a.sort(axis=-1, kind='quicksort', order=None) -> None. Perform an inplace sort along the given axis using the algorithm specified by the kind keyword. :Parameters: axis : integer Axis to be sorted along. None indicates that the flattened array should be used. Default is -1. kind : string Sorting algorithm to use. Possible values are 'quicksort', 'mergesort', or 'heapsort'. Default is 'quicksort'. order : list type or None When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. :Returns: None :SeeAlso: - argsort : indirect sort - lexsort : indirect stable sort on multiple keys - searchsorted : find keys in sorted array :Notes: ------ The various sorts are characterized by average speed, worst case performance, need for work space, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The three available algorithms have the following properties: |------------------------------------------------------| | kind | speed | worst case | work space | stable| |------------------------------------------------------| |'quicksort'| 1 | O(n^2) | 0 | no | |'mergesort'| 2 | O(n*log(n)) | ~n/2 | yes | |'heapsort' | 3 | O(n*log(n)) | 0 | no | |------------------------------------------------------| All the sort algorithms make temporary copies of the data when the sort is not along the last axis. Consequently, sorts along the last axis are faster and use less space than sorts along other axis.` squeeze(...) `m.squeeze() eliminate all length-1 dimensions` std(...) `a.std(axis=None, dtype=None, out=None) -> standard deviation. Returns the standard deviation of the array elements, a measure of the spread of a distribution. The standard deviation is computed for the flattened array by default, otherwise over the specified axis. :Parameters: axis : integer Axis along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array. dtype : type Type to use in computing the standard deviation. For arrays of integer type the default is float32, for arrays of float types it is the same as the array type. out : ndarray Alternative output array in which to place the result. It must have the same shape as the expected output but the type will be cast if necessary. :Returns: standard deviation : The return type varies, see above. A new array holding the result is returned unless out is specified, in which case a reference to out is returned. :SeeAlso: - var : variance - mean : average Notes ----- The standard deviation is the square root of the average of the squared deviations from the mean, i.e. var = sqrt(mean((x - x.mean())**2)). The computed standard deviation is biased, i.e., the mean is computed by dividing by the number of elements, N, rather than by N-1.` sum(...) `a.sum(axis=None, dtype=None) -> Sum of array over given axis. Sum the array over the given axis. If the axis is None, sum over all dimensions of the array. The optional dtype argument is the data type for the returned value and intermediate calculations. The default is to upcast (promote) smaller integer types to the platform-dependent int. For example, on 32-bit platforms: a.dtype default sum dtype --------------------------------------------------- bool, int8, int16, int32 int32 Warning: The arithmetic is modular and no error is raised on overflow. Examples: >>> array([0.5, 1.5]).sum() 2.0 >>> array([0.5, 1.5]).sum(dtype=int32) 1 >>> array([[0, 1], [0, 5]]).sum(axis=0) array([0, 6]) >>> array([[0, 1], [0, 5]]).sum(axis=1) array([1, 5]) >>> ones(128, dtype=int8).sum(dtype=int8) # overflow! -128` swapaxes(...) `a.swapaxes(axis1, axis2) -> new view with axes swapped.` take(...) `a.take(indices, axis=None, out=None, mode='raise') -> new array. The new array is formed from the elements of a indexed by indices along the given axis.` tofile(...) `a.tofile(fid, sep="", format="%s") -> None. Write the data to a file. Required arguments: file -- an open file object or a string containing a filename Keyword arguments: sep -- separator for text output. Write binary if empty (default "") format -- format string for text file output (default "%s") A convenience function for quick storage of array data. Information on endianess and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianess. Some of these problems can be overcome by outputting the data as text files at the expense of speed and file size. If 'sep' is empty this method is equivalent to file.write(a.tostring()). If 'sep' is not empty each data item is converted to the nearest Python type and formatted using "format"%item. The resulting strings are written to the file separated by the contents of 'sep'. The data is always written in "C" (row major) order independent of the order of 'a'. The data produced by this method can be recovered by using the function fromfile().` tolist(...) `a.tolist() -> Array as hierarchical list. Copy the data portion of the array to a hierarchical python list and return that list. Data items are converted to the nearest compatible Python type.` tostring(...) `a.tostring(order='C') -> raw copy of array data as a Python string. Keyword arguments: order -- order of the data item in the copy {"C","F","A"} (default "C") Construct a Python string containing the raw bytes in the array. The order of the data in arrays with ndim > 1 is specified by the 'order' keyword and this keyword overrides the order of the array. The choices are: "C" -- C order (row major) "Fortran" -- Fortran order (column major) "Any" -- Current order of array. None -- Same as "Any"` trace(...) `a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) return the sum along the offset diagonal of the array's indicated axis1 and axis2.` transpose(...) `a.transpose(*axes) Returns a view of 'a' with axes transposed. If no axes are given, or None is passed, switches the order of the axes. For a 2-d array, this is the usual matrix transpose. If axes are given, they describe how the axes are permuted. Example: >>> a = array([[1,2],[3,4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1,0)) array([[1, 3], [2, 4]]) >>> a.transpose(1,0) array([[1, 3], [2, 4]])` var(...) `a.var(axis=None, dtype=None, out=None) -> variance Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis. :Parameters: axis : integer Axis along which the variance is computed. The default is to compute the variance of the flattened array. dtype : type Type to use in computing the variance. For arrays of integer type the default is float32, for arrays of float types it is the same as the array type. out : ndarray Alternative output array in which to place the result. It must have the same shape as the expected output but the type will be cast if necessary. :Returns: variance : The return type varies, see above. A new array holding the result is returned unless out is specified, in which case a reference to out is returned. :SeeAlso: - std : standard deviation - mean: average Notes ----- The variance is the average of the squared deviations from the mean, i.e. var = mean((x - x.mean())**2). The computed variance is biased, i.e., the mean is computed by dividing by the number of elements, N, rather than by N-1.` view(...) `a.view(<type>) -> new view of array with same data. Type can be either a new sub-type object or a data-descriptor object` Data descriptors inherited from numpy.ndarray: T `Same as transpose() except self is returned for self.ndim < 2.` __array_interface__ `Array protocol: Python side.` __array_priority__ `Array priority.` __array_struct__ `Array protocol: C-struct side.` base `Base object if memory is from some other object.` ctypes `A ctypes interface object.` data `Buffer object pointing to the start of the data.` dtype `Data-type for the array.` flags `Special object providing array flags.` flat `A 1-d flat iterator.` imag `Imaginary part of the array.` itemsize `Length of one element in bytes.` nbytes `Number of bytes in the array.` ndim `Number of array dimensions.` real `Real part of the array.` shape `Tuple of array dimensions.` size `Number of elements in the array.` strides `Tuple of bytes to step in each dimension.`

Functions
`` |  | array(...) `array(object, dtype=None, copy=1,order=None, subok=0,ndmin=0) Return an array from object with the specified date-type. Inputs: object - an array, any object exposing the array interface, any object whose __array__ method returns an array, or any (nested) sequence. dtype - The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. This argument can only be used to 'upcast' the array. For downcasting, use the .astype(t) method. copy - If true, then force a copy. Otherwise a copy will only occur if __array__ returns a copy, obj is a nested sequence, or a copy is needed to satisfy any of the other requirements order - Specify the order of the array. If order is 'C', then the array will be in C-contiguous order (last-index varies the fastest). If order is 'FORTRAN', then the returned array will be in Fortran-contiguous order (first-index varies the fastest). If order is None, then the returned array may be in either C-, or Fortran-contiguous order or even discontiguous. subok - If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array ndmin - Specifies the minimum number of dimensions that the resulting array should have. 1's will be pre-pended to the shape as needed to meet this requirement.` dot(...) where(...) `where(condition, | x, y) The result is shaped like condition and has elements of x and y where condition is respectively true or false. If x or y are not given, then it is equivalent to condition.nonzero(). To group the indices by element, rather than dimension, use transpose(where(condition, | x, y)) instead. This always results in a 2d array, with a row of indices for each element that satisfies the condition.` zeros(...) `zeros((d1,...,dn),dtype=float,order='C') Return a new array of shape (d1,...,dn) and type typecode with all it's entries initialized to zero.`

Data
`` |  | fabs = <ufunc 'fabs'> sqrt = <ufunc 'sqrt'>