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diff --git a/venv/lib/python3.9/site-packages/numpy/doc/ufuncs.py b/venv/lib/python3.9/site-packages/numpy/doc/ufuncs.py new file mode 100644 index 00000000..c99e9abc --- /dev/null +++ b/venv/lib/python3.9/site-packages/numpy/doc/ufuncs.py @@ -0,0 +1,137 @@ +""" +=================== +Universal Functions +=================== + +Ufuncs are, generally speaking, mathematical functions or operations that are +applied element-by-element to the contents of an array. That is, the result +in each output array element only depends on the value in the corresponding +input array (or arrays) and on no other array elements. NumPy comes with a +large suite of ufuncs, and scipy extends that suite substantially. The simplest +example is the addition operator: :: + + >>> np.array([0,2,3,4]) + np.array([1,1,-1,2]) + array([1, 3, 2, 6]) + +The ufunc module lists all the available ufuncs in numpy. Documentation on +the specific ufuncs may be found in those modules. This documentation is +intended to address the more general aspects of ufuncs common to most of +them. All of the ufuncs that make use of Python operators (e.g., +, -, etc.) +have equivalent functions defined (e.g. add() for +) + +Type coercion +============= + +What happens when a binary operator (e.g., +,-,\\*,/, etc) deals with arrays of +two different types? What is the type of the result? Typically, the result is +the higher of the two types. For example: :: + + float32 + float64 -> float64 + int8 + int32 -> int32 + int16 + float32 -> float32 + float32 + complex64 -> complex64 + +There are some less obvious cases generally involving mixes of types +(e.g. uints, ints and floats) where equal bit sizes for each are not +capable of saving all the information in a different type of equivalent +bit size. Some examples are int32 vs float32 or uint32 vs int32. +Generally, the result is the higher type of larger size than both +(if available). So: :: + + int32 + float32 -> float64 + uint32 + int32 -> int64 + +Finally, the type coercion behavior when expressions involve Python +scalars is different than that seen for arrays. Since Python has a +limited number of types, combining a Python int with a dtype=np.int8 +array does not coerce to the higher type but instead, the type of the +array prevails. So the rules for Python scalars combined with arrays is +that the result will be that of the array equivalent the Python scalar +if the Python scalar is of a higher 'kind' than the array (e.g., float +vs. int), otherwise the resultant type will be that of the array. +For example: :: + + Python int + int8 -> int8 + Python float + int8 -> float64 + +ufunc methods +============= + +Binary ufuncs support 4 methods. + +**.reduce(arr)** applies the binary operator to elements of the array in + sequence. For example: :: + + >>> np.add.reduce(np.arange(10)) # adds all elements of array + 45 + +For multidimensional arrays, the first dimension is reduced by default: :: + + >>> np.add.reduce(np.arange(10).reshape(2,5)) + array([ 5, 7, 9, 11, 13]) + +The axis keyword can be used to specify different axes to reduce: :: + + >>> np.add.reduce(np.arange(10).reshape(2,5),axis=1) + array([10, 35]) + +**.accumulate(arr)** applies the binary operator and generates an +equivalently shaped array that includes the accumulated amount for each +element of the array. A couple examples: :: + + >>> np.add.accumulate(np.arange(10)) + array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45]) + >>> np.multiply.accumulate(np.arange(1,9)) + array([ 1, 2, 6, 24, 120, 720, 5040, 40320]) + +The behavior for multidimensional arrays is the same as for .reduce(), +as is the use of the axis keyword). + +**.reduceat(arr,indices)** allows one to apply reduce to selected parts + of an array. It is a difficult method to understand. See the documentation + at: + +**.outer(arr1,arr2)** generates an outer operation on the two arrays arr1 and + arr2. It will work on multidimensional arrays (the shape of the result is + the concatenation of the two input shapes.: :: + + >>> np.multiply.outer(np.arange(3),np.arange(4)) + array([[0, 0, 0, 0], + [0, 1, 2, 3], + [0, 2, 4, 6]]) + +Output arguments +================ + +All ufuncs accept an optional output array. The array must be of the expected +output shape. Beware that if the type of the output array is of a different +(and lower) type than the output result, the results may be silently truncated +or otherwise corrupted in the downcast to the lower type. This usage is useful +when one wants to avoid creating large temporary arrays and instead allows one +to reuse the same array memory repeatedly (at the expense of not being able to +use more convenient operator notation in expressions). Note that when the +output argument is used, the ufunc still returns a reference to the result. + + >>> x = np.arange(2) + >>> np.add(np.arange(2),np.arange(2.),x) + array([0, 2]) + >>> x + array([0, 2]) + +and & or as ufuncs +================== + +Invariably people try to use the python 'and' and 'or' as logical operators +(and quite understandably). But these operators do not behave as normal +operators since Python treats these quite differently. They cannot be +overloaded with array equivalents. Thus using 'and' or 'or' with an array +results in an error. There are two alternatives: + + 1) use the ufunc functions logical_and() and logical_or(). + 2) use the bitwise operators & and \\|. The drawback of these is that if + the arguments to these operators are not boolean arrays, the result is + likely incorrect. On the other hand, most usages of logical_and and + logical_or are with boolean arrays. As long as one is careful, this is + a convenient way to apply these operators. + +""" |