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Quickstart tutorial Prerequisites Before reading this tutorial you should know a bit of Python. If you would like to refresh your memory, take a look at the Python tutorial. If you wish to work the examples in this tutorial, you must also have some software installed on your computer. Please see https://scipy.org/install.html for instructions. Learner profile This tutorial is intended as a quick overview of algebra and arrays in NumPy and want to understand how n-dimensional (n>=2) arrays are represented and can be manipulated. In particular, if you don’t know how to apply common functions to n-dimensional arrays (without using for-loops), or if you want to understand axis and shape properties for n-dimensional arrays, this tutorial might be of help. Learning Objectives After this tutorial, you should be able to: Understand the difference between one-, two- and n-dimensional arrays in NumPy; Understand how to apply some linear algebra operations to n-dimensional arrays without using for-loops; Understand axis and shape properties for n-dimensional arrays. The Basics NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes. For example, the coordinates of a point in 3D space [1, 2, 1] has one axis. That axis has 3 elements in it, so we say it has a length of 3. In the example pictured below, the array has 2 axes. The first axis has a length of 2, the second axis has a length of 3. [[ 1., 0., 0.], [ 0., 1., 2.]] NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are: ndarray.ndim the number of axes (dimensions) of the array. ndarray.shape the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim. ndarray.size the total number of elements of the array. This is equal to the product of the elements of shape. ndarray.dtype an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples. ndarray.itemsize the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize. ndarray.data the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities. An example >>> import numpy as np a = np.arange(15).reshape(3, 5) a array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) a.shape (3, 5) a.ndim 2 a.dtype.name 'int64' a.itemsize 8 a.size 15 type(a) <class 'numpy.ndarray'> b = np.array([6, 7, 8]) b array([6, 7, 8]) type(b) <class 'numpy.ndarray'> Array Creation There are several ways to create arrays. For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences. >>> >>> import numpy as np >>> a = np.array([2,3,4]) >>> a array([2, 3, 4]) >>> a.dtype dtype('int64') >>> b = np.array([1.2, 3.5, 5.1]) >>> b.dtype dtype('float64') A frequent error consists in calling array with multiple arguments, rather than providing a single sequence as an argument. >>> >>> a = np.array(1,2,3,4) # WRONG Traceback (most recent call last): ... TypeError: array() takes from 1 to 2 positional arguments but 4 were given >>> a = np.array([1,2,3,4]) # RIGHT array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on. >>> >>> b = np.array([(1.5,2,3), (4,5,6)]) >>> b array([[1.5, 2. , 3. ], [4. , 5. , 6. ]]) The type of the array can also be explicitly specified at creation time: >>> >>> c = np.array( [ [1,2], [3,4] ], dtype=complex ) >>> c array([[1.+0.j, 2.+0.j], [3.+0.j, 4.+0.j]]) Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64. >>> >>> np.zeros((3, 4)) array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.]]) >>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified array([[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]], dtype=int16) >>> np.empty( (2,3) ) # uninitialized array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260], # may vary [ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]]) To create sequences of numbers, NumPy provides the arange function which is analogous to the Python built-in range, but returns an array. >>> >>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step: >>> >>> from numpy import pi >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points >>> f = np.sin(x) See also array, zeros, zeros_like, ones, ones_like, empty, empty_like, arange, linspace, numpy.random.Generator.rand, numpy.random.Generator.randn, fromfunction, fromfile Printing Arrays When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout: the last axis is printed from left to right, the second-to-last is printed from top to bottom, the rest are also printed from top to bottom, with each slice separated from the next by an empty line. One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices. >>> >>> a = np.arange(6) # 1d array >>> print(a) [0 1 2 3 4 5] >>> >>> b = np.arange(12).reshape(4,3) # 2d array >>> print(b) [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] >>> >>> c = np.arange(24).reshape(2,3,4) # 3d array >>> print(c) [[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] [[12 13 14 15] [16 17 18 19] [20 21 22 23]]] See below to get more details on reshape. If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners: >>> >>> print(np.arange(10000)) [ 0 1 2 ... 9997 9998 9999] >>> >>> print(np.arange(10000).reshape(100,100)) [[ 0 1 2 ... 97 98 99] [ 100 101 102 ... 197 198 199] [ 200 201 202 ... 297 298 299] ... [9700 9701 9702 ... 9797 9798 9799] [9800 9801 9802 ... 9897 9898 9899] [9900 9901 9902 ... 9997 9998 9999]] To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions. >>> >>> np.set_printoptions(threshold=sys.maxsize) # sys module should be imported Basic Operations Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result. >>> >>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False]) Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot function or method: >>> >>> A = np.array( [[1,1], ... [0,1]] ) >>> B = np.array( [[2,0], ... [3,4]] ) >>> A * B # elementwise product array([[2, 0], [0, 4]]) >>> A @ B # matrix product array([[5, 4], [3, 4]]) >>> A.dot(B) # another matrix product array([[5, 4], [3, 4]]) Some operations, such as += and *=, act in place to modify an existing array rather than create a new one. >>> >>> rg = np.random.default_rng(1) # create instance of default random number generator >>> a = np.ones((2,3), dtype=int) >>> b = rg.random((2,3)) >>> a *= 3 >>> a array([[3, 3, 3], [3, 3, 3]]) >>> b += a >>> b array([[3.51182162, 3.9504637 , 3.14415961], [3.94864945, 3.31183145, 3.42332645]]) >>> a += b # b is not automatically converted to integer type Traceback (most recent call last): ... numpy.core._exceptions.UFuncTypeError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int64') with casting rule 'same_kind' When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting). >>> >>> a = np.ones(3, dtype=np.int32) >>> b = np.linspace(0,pi,3) >>> b.dtype.name 'float64' >>> c = a+b >>> c array([1. , 2.57079633, 4.14159265]) >>> c.dtype.name 'float64' >>> d = np.exp(c*1j) >>> d array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j, -0.54030231-0.84147098j]) >>> d.dtype.name 'complex128' Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class. >>> >>> a = rg.random((2,3)) >>> a array([[0.82770259, 0.40919914, 0.54959369], [0.02755911, 0.75351311, 0.53814331]]) >>> a.sum() 3.1057109529998157 >>> a.min() 0.027559113243068367 >>> a.max() 0.8277025938204418 By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array: >>> >>> b = np.arange(12).reshape(3,4) >>> b array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> b.sum(axis=0) # sum of each column array([12, 15, 18, 21]) >>> >>> b.min(axis=1) # min of each row array([0, 4, 8]) >>> >>> b.cumsum(axis=1) # cumulative sum along each row array([[ 0, 1, 3, 6], [ 4, 9, 15, 22], [ 8, 17, 27, 38]]) Universal Functions NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output. >>> >>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([2., 0., 6.]) See also all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor, inner, invert, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var, vdot, vectorize, where Indexing, Slicing and Iterating One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences. >>> >>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) # equivalent to a[0:6:2] = 1000; # from start to position 6, exclusive, set every 2nd element to 1000 >>> a[:6:2] = 1000 >>> a array([1000, 1, 1000, 27, 1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, 1000, 27, 1000, 1, 1000]) >>> for i in a: ... print(i**(1/3.)) ... 9.999999999999998 1.0 9.999999999999998 3.0 9.999999999999998 4.999999999999999 5.999999999999999 6.999999999999999 7.999999999999999 8.999999999999998 Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas: >>> >>> def f(x,y): ... return 10*x+y ... >>> b = np.fromfunction(f,(5,4),dtype=int) >>> b array([[ 0, 1, 2, 3], [10, 11, 12, 13], [20, 21, 22, 23], [30, 31, 32, 33], [40, 41, 42, 43]]) >>> b[2,3] 23 >>> b[0:5, 1] # each row in the second column of b array([ 1, 11, 21, 31, 41]) >>> b[ : ,1] # equivalent to the previous example array([ 1, 11, 21, 31, 41]) >>> b[1:3, : ] # each column in the second and third row of b array([[10, 11, 12, 13], [20, 21, 22, 23]]) When fewer indices are provided than the number of axes, the missing indices are considered complete slices: >>> >>> b[-1] # the last row. Equivalent to b[-1,:] array([40, 41, 42, 43]) The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i,...]. The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is an array with 5 axes, then x[1,2,...] is equivalent to x[1,2,:,:,:], x[...,3] to x[:,:,:,:,3] and x[4,...,5,:] to x[4,:,:,5,:]. >>> >>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays) ... [ 10, 12, 13]], ... [[100,101,102], ... [110,112,113]]]) >>> c.shape (2, 2, 3) >>> c[1,...] # same as c[1,:,:] or c[1] array([[100, 101, 102], [110, 112, 113]]) >>> c[...,2] # same as c[:,:,2] array([[ 2, 13], [102, 113]]) Iterating over multidimensional arrays is done with respect to the first axis: >>> >>> for row in b: ... print(row) ... [0 1 2 3] [10 11 12 13] [20 21 22 23] [30 31 32 33] [40 41 42 43] However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array: >>> >>> for element in b.flat: ... print(element) ... 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 40 41 42 43 See also Indexing, Indexing (reference), newaxis, ndenumerate, indices Shape Manipulation Changing the shape of an array An array has a shape given by the number of elements along each axis: >>> >>> a = np.floor(10*rg.random((3,4))) >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.shape (3, 4) The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array: >>> >>> a.ravel() # returns the array, flattened array([3., 7., 3., 4., 1., 4., 2., 2., 7., 2., 4., 9.]) >>> a.reshape(6,2) # returns the array with a modified shape array([[3., 7.], [3., 4.], [1., 4.], [2., 2.], [7., 2.], [4., 9.]]) >>> a.T # returns the array, transposed array([[3., 1., 7.], [7., 4., 2.], [3., 2., 4.], [4., 2., 9.]]) >>> a.T.shape (4, 3) >>> a.shape (3, 4) The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest. The reshape function returns its argument with a modified shape, whereas the ndarray.resize method modifies the array itself: >>> >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.resize((2,6)) >>> a array([[3., 7., 3., 4., 1., 4.], [2., 2., 7., 2., 4., 9.]]) If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated: >>> >>> a.reshape(3,-1) array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) See also ndarray.shape, reshape, resize, ravel Stacking together different arrays Several arrays can be stacked together along different axes: >>> >>> a = np.floor(10*rg.random((2,2))) >>> a array([[9., 7.], [5., 2.]]) >>> b = np.floor(10*rg.random((2,2))) >>> b array([[1., 9.], [5., 1.]]) >>> np.vstack((a,b)) array([[9., 7.], [5., 2.], [1., 9.], [5., 1.]]) >>> np.hstack((a,b)) array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D arrays: >>> >>> from numpy import newaxis >>> np.column_stack((a,b)) # with 2D arrays array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) >>> a = np.array([4.,2.]) >>> b = np.array([3.,8.]) >>> np.column_stack((a,b)) # returns a 2D array array([[4., 3.], [2., 8.]]) >>> np.hstack((a,b)) # the result is different array([4., 2., 3., 8.]) >>> a[:,newaxis] # view `a` as a 2D column vector array([[4.], [2.]]) >>> np.column_stack((a[:,newaxis],b[:,newaxis])) array([[4., 3.], [2., 8.]]) >>> np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same array([[4., 3.], [2., 8.]]) On the other hand, the function row_stack is equivalent to vstack for any input arrays. In fact, row_stack is an alias for vstack: >>> >>> np.column_stack is np.hstack False >>> np.row_stack is np.vstack True In general, for arrays with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen. Note In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals (“:”) >>> >>> np.r_[1:4,0,4] array([1, 2, 3, 0, 4]) When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but allow for an optional argument giving the number of the axis along which to concatenate. See also hstack, vstack, column_stack, concatenate, c_, r_ Splitting one array into several smaller ones Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur: >>> >>> a = np.floor(10*rg.random((2,12))) >>> a array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.], [8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]]) # Split a into 3 >>> np.hsplit(a,3) [array([[6., 7., 6., 9.], [8., 5., 5., 7.]]), array([[0., 5., 4., 0.], [1., 8., 6., 7.]]), array([[6., 8., 5., 2.], [1., 8., 1., 0.]])] # Split a after the third and the fourth column >>> np.hsplit(a,(3,4)) [array([[6., 7., 6.], [8., 5., 5.]]), array([[9.], [7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.], [1., 8., 6., 7., 1., 8., 1., 0.]])] vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split. Copies and Views When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases: No Copy at All Simple assignments make no copy of objects or their data. >>> >>> a = np.array([[ 0, 1, 2, 3], ... [ 4, 5, 6, 7], ... [ 8, 9, 10, 11]]) >>> b = a # no new object is created >>> b is a # a and b are two names for the same ndarray object True Python passes mutable objects as references, so function calls make no copy. >>> >>> def f(x): ... print(id(x)) ... >>> id(a) # id is a unique identifier of an object 148293216 # may vary >>> f(a) 148293216 # may vary View or Shallow Copy Different array objects can share the same data. The view method creates a new array object that looks at the same data. >>> >>> c = a.view() >>> c is a False >>> c.base is a # c is a view of the data owned by a True >>> c.flags.owndata False >>> >>> c = c.reshape((2, 6)) # a's shape doesn't change >>> a.shape (3, 4) >>> c[0, 4] = 1234 # a's data changes >>> a array([[ 0, 1, 2, 3], [1234, 5, 6, 7], [ 8, 9, 10, 11]]) Slicing an array returns a view of it: >>> >>> s = a[ : , 1:3] # spaces added for clarity; could also be written "s = a[:, 1:3]" >>> s[:] = 10 # s[:] is a view of s. Note the difference between s = 10 and s[:] = 10 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Deep Copy The copy method makes a complete copy of the array and its data. >>> >>> d = a.copy() # a new array object with new data is created >>> d is a False >>> d.base is a # d doesn't share anything with a False >>> d[0,0] = 9999 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Sometimes copy should be called after slicing if the original array is not required anymore. For example, suppose a is a huge intermediate result and the final result b only contains a small fraction of a, a deep copy should be made when constructing b with slicing: >>> >>> a = np.arange(int(1e8)) >>> b = a[:100].copy() >>> del a # the memory of ``a`` can be released. If b = a[:100] is used instead, a is referenced by b and will persist in memory even if del a is executed. Functions and Methods Overview Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list. Array Creation arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r_, zeros, zeros_like Conversions ndarray.astype, atleast_1d, atleast_2d, atleast_3d, mat Manipulations array_split, column_stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, ndarray.item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack Questions all, any, nonzero, where Ordering argmax, argmin, argsort, max, min, ptp, searchsorted, sort Operations choose, compress, cumprod, cumsum, inner, ndarray.fill, imag, prod, put, putmask, real, sum Basic Statistics cov, mean, std, var Basic Linear Algebra cross, dot, outer, linalg.svd, vdot Less Basic Broadcasting rules Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape. The first rule of broadcasting is that if all input arrays do not have the same number of dimensions, a “1” will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions. The second rule of broadcasting ensures that arrays with a size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the “broadcast” array. After application of the broadcasting rules, the sizes of all arrays must match. More details can be found in Broadcasting. Advanced indexing and index tricks NumPy offers more indexing facilities than regular Python sequences. In addition to indexing by integers and slices, as we saw before, arrays can be indexed by arrays of integers and arrays of booleans. Indexing with Arrays of Indices >>> >>> a = np.arange(12)**2 # the first 12 square numbers >>> i = np.array([1, 1, 3, 8, 5]) # an array of indices >>> a[i] # the elements of a at the positions i array([ 1, 1, 9, 64, 25]) >>> >>> j = np.array([[3, 4], [9, 7]]) # a bidimensional array of indices >>> a[j] # the same shape as j array([[ 9, 16], [81, 49]]) When the indexed array a is multidimensional, a single array of indices refers to the first dimension of a. The following example shows this behavior by converting an image of labels into a color image using a palette. >>> >>> palette = np.array([[0, 0, 0], # black ... [255, 0, 0], # red ... [0, 255, 0], # green ... [0, 0, 255], # blue ... [255, 255, 255]]) # white >>> image = np.array([[0, 1, 2, 0], # each value corresponds to a color in the palette ... [0, 3, 4, 0]]) >>> palette[image] # the (2, 4, 3) color image array([[[ 0, 0, 0], [255, 0, 0], [ 0, 255, 0], [ 0, 0, 0]], [[ 0, 0, 0], [ 0, 0, 255], [255, 255, 255], [ 0, 0, 0]]]) We can also give indexes for more than one dimension. The arrays of indices for each dimension must have the same shape. >>> >>> a = np.arange(12).reshape(3,4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> i = np.array([[0, 1], # indices for the first dim of a ... [1, 2]]) >>> j = np.array([[2, 1], # indices for the second dim ... [3, 3]]) >>> >>> a[i, j] # i and j must have equal shape array([[ 2, 5], [ 7, 11]]) >>> >>> a[i, 2] array([[ 2, 6], [ 6, 10]]) >>> >>> a[:, j] # i.e., a[ : , j] array([[[ 2, 1], [ 3, 3]], [[ 6, 5], [ 7, 7]], [[10, 9], [11, 11]]]) In Python, arr[i, j] is exactly the same as arr[(i, j)]—so we can put i and j in a tuple and then do the indexing with that. >>> >>> l = (i, j) # equivalent to a[i, j] >>> a[l] array([[ 2, 5], [ 7, 11]]) However, we can not do this by putting i and j into an array, because this array will be interpreted as indexing the first dimension of a. >>> >>> s = np.array([i, j]) # not what we want >>> a[s] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: index 3 is out of bounds for axis 0 with size 3 # same as a[i, j] >>> a[tuple(s)] array([[ 2, 5], [ 7, 11]]) Another common use of indexing with arrays is the search of the maximum value of time-dependent series: >>> >>> time = np.linspace(20, 145, 5) # time scale >>> data = np.sin(np.arange(20)).reshape(5,4) # 4 time-dependent series >>> time array([ 20. , 51.25, 82.5 , 113.75, 145. ]) >>> data array([[ 0. , 0.84147098, 0.90929743, 0.14112001], [-0.7568025 , -0.95892427, -0.2794155 , 0.6569866 ], [ 0.98935825, 0.41211849, -0.54402111, -0.99999021], [-0.53657292, 0.42016704, 0.99060736, 0.65028784], [-0.28790332, -0.96139749, -0.75098725, 0.14987721]]) # index of the maxima for each series >>> ind = data.argmax(axis=0) >>> ind array([2, 0, 3, 1]) # times corresponding to the maxima >>> time_max = time[ind] >>> >>> data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]... >>> time_max array([ 82.5 , 20. , 113.75, 51.25]) >>> data_max array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ]) >>> np.all(data_max == data.max(axis=0)) True You can also use indexing with arrays as a target to assign to: >>> >>> a = np.arange(5) >>> a array([0, 1, 2, 3, 4]) >>> a[[1,3,4]] = 0 >>> a array([0, 0, 2, 0, 0]) However, when the list of indices contains repetitions, the assignment is done several times, leaving behind the last value: >>> >>> a = np.arange(5) >>> a[[0,0,2]]=[1,2,3] >>> a array([2, 1, 3, 3, 4]) This is reasonable enough, but watch out if you want to use Python’s += construct, as it may not do what you expect: >>> >>> a = np.arange(5) >>> a[[0,0,2]]+=1 >>> a array([1, 1, 3, 3, 4]) Even though 0 occurs twice in the list of indices, the 0th element is only incremented once. This is because Python requires “a+=1” to be equivalent to “a = a + 1”. Indexing with Boolean Arrays When we index arrays with arrays of (integer) indices we are providing the list of indices to pick. With boolean indices the approach is different; we explicitly choose which items in the array we want and which ones we don’t. The most natural way one can think of for boolean indexing is to use boolean arrays that have the same shape as the original array: >>> >>> a = np.arange(12).reshape(3,4) >>> b = a > 4 >>> b # b is a boolean with a's shape array([[False, False, False, False], [False, True, True, True], [ True, True, True, True]]) >>> a[b] # 1d array with the selected elements array([ 5, 6, 7, 8, 9, 10, 11]) This property can be very useful in assignments: >>> >>> a[b] = 0 # All elements of 'a' higher than 4 become 0 >>> a array([[0, 1, 2, 3], [4, 0, 0, 0], [0, 0, 0, 0]]) You can look at the following example to see how to use boolean indexing to generate an image of the Mandelbrot set: >>> import numpy as np import matplotlib.pyplot as plt def mandelbrot( h,w, maxit=20 ): """Returns an image of the Mandelbrot fractal of size (h,w).""" y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ] c = x+y*1j z = c divtime = maxit + np.zeros(z.shape, dtype=int) for i in range(maxit): z = z**2 + c diverge = z*np.conj(z) > 2**2 # who is diverging div_now = diverge & (divtime==maxit) # who is diverging now divtime[div_now] = i # note when z[diverge] = 2 # avoid diverging too much return divtime plt.imshow(mandelbrot(400,400)) ../_images/quickstart-1.png The second way of indexing with booleans is more similar to integer indexing; for each dimension of the array we give a 1D boolean array selecting the slices we want: >>> >>> a = np.arange(12).reshape(3,4) >>> b1 = np.array([False,True,True]) # first dim selection >>> b2 = np.array([True,False,True,False]) # second dim selection >>> >>> a[b1,:] # selecting rows array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[b1] # same thing array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[:,b2] # selecting columns array([[ 0, 2], [ 4, 6], [ 8, 10]]) >>> >>> a[b1,b2] # a weird thing to do array([ 4, 10]) Note that the length of the 1D boolean array must coincide with the length of the dimension (or axis) you want to slice. In the previous example, b1 has length 3 (the number of rows in a), and b2 (of length 4) is suitable to index the 2nd axis (columns) of a. The ix_() function The ix_ function can be used to combine different vectors so as to obtain the result for each n-uplet. For example, if you want to compute all the a+b*c for all the triplets taken from each of the vectors a, b and c: >>> >>> a = np.array([2,3,4,5]) >>> b = np.array([8,5,4]) >>> c = np.array([5,4,6,8,3]) >>> ax,bx,cx = np.ix_(a,b,c) >>> ax array([[[2]], [[3]], [[4]], [[5]]]) >>> bx array([[[8], [5], [4]]]) >>> cx array([[[5, 4, 6, 8, 3]]]) >>> ax.shape, bx.shape, cx.shape ((4, 1, 1), (1, 3, 1), (1, 1, 5)) >>> result = ax+bx*cx >>> result array([[[42, 34, 50, 66, 26], [27, 22, 32, 42, 17], [22, 18, 26, 34, 14]], [[43, 35, 51, 67, 27], [28, 23, 33, 43, 18], [23, 19, 27, 35, 15]], [[44, 36, 52, 68, 28], [29, 24, 34, 44, 19], [24, 20, 28, 36, 16]], [[45, 37, 53, 69, 29], [30, 25, 35, 45, 20], [25, 21, 29, 37, 17]]]) >>> result[3,2,4] 17 >>> a[3]+b[2]*c[4] 17 You could also implement the reduce as follows: >>> >>> def ufunc_reduce(ufct, *vectors): ... vs = np.ix_(*vectors) ... r = ufct.identity ... for v in vs: ... r = ufct(r,v) ... return r and then use it as: >>> >>> ufunc_reduce(np.add,a,b,c) array([[[15, 14, 16, 18, 13], [12, 11, 13, 15, 10], [11, 10, 12, 14, 9]], [[16, 15, 17, 19, 14], [13, 12, 14, 16, 11], [12, 11, 13, 15, 10]], [[17, 16, 18, 20, 15], [14, 13, 15, 17, 12], [13, 12, 14, 16, 11]], [[18, 17, 19, 21, 16], [15, 14, 16, 18, 13], [14, 13, 15, 17, 12]]]) The advantage of this version of reduce compared to the normal ufunc.reduce is that it makes use of the Broadcasting Rules in order to avoid creating an argument array the size of the output times the number of vectors. Indexing with strings See Structured arrays. Linear Algebra Work in progress. Basic linear algebra to be included here. Simple Array Operations See linalg.py in numpy folder for more. >>> >>> import numpy as np >>> a = np.array([[1.0, 2.0], [3.0, 4.0]]) >>> print(a) [[1. 2.] [3. 4.]] >>> a.transpose() array([[1., 3.], [2., 4.]]) >>> np.linalg.inv(a) array([[-2. , 1. ], [ 1.5, -0.5]]) >>> u = np.eye(2) # unit 2x2 matrix; "eye" represents "I" >>> u array([[1., 0.], [0., 1.]]) >>> j = np.array([[0.0, -1.0], [1.0, 0.0]]) >>> j @ j # matrix product array([[-1., 0.], [ 0., -1.]]) >>> np.trace(u) # trace 2.0 >>> y = np.array([[5.], [7.]]) >>> np.linalg.solve(a, y) array([[-3.], [ 4.]]) >>> np.linalg.eig(j) (array([0.+1.j, 0.-1.j]), array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]])) Parameters: square matrix Returns The eigenvalues, each repeated according to its multiplicity. The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]`` . Tricks and Tips Here we give a list of short and useful tips. “Automatic” Reshaping To change the dimensions of an array, you can omit one of the sizes which will then be deduced automatically: >>> >>> a = np.arange(30) >>> b = a.reshape((2, -1, 3)) # -1 means "whatever is needed" >>> b.shape (2, 5, 3) >>> b array([[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11], [12, 13, 14]], [[15, 16, 17], [18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]]) Vector Stacking How do we construct a 2D array from a list of equally-sized row vectors? In MATLAB this is quite easy: if x and y are two vectors of the same length you only need do m=[x;y]. In NumPy this works via the functions column_stack, dstack, hstack and vstack, depending on the dimension in which the stacking is to be done. For example: >>> >>> x = np.arange(0,10,2) >>> y = np.arange(5) >>> m = np.vstack([x,y]) >>> m array([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]]) >>> xy = np.hstack([x,y]) >>> xy array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4]) The logic behind those functions in more than two dimensions can be strange. See also NumPy for Matlab users Histograms The NumPy histogram function applied to an array returns a pair of vectors: the histogram of the array and a vector of the bin edges. Beware: matplotlib also has a function to build histograms (called hist, as in Matlab) that differs from the one in NumPy. The main difference is that pylab.hist plots the histogram automatically, while numpy.histogram only generates the data. >>> import numpy as np rg = np.random.default_rng(1) import matplotlib.pyplot as plt # Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2 mu, sigma = 2, 0.5 v = rg.normal(mu,sigma,10000) # Plot a normalized histogram with 50 bins plt.hist(v, bins=50, density=1) # matplotlib version (plot) # Compute the histogram with numpy and then plot it (n, bins) = np.histogram(v, bins=50, density=True) # NumPy version (no plot) plt.plot(.5*(bins[1:]+bins[:-1]), n) ../_images/quickstart-2.png Further reading The Python tutorial NumPy Reference SciPy Tutorial SciPy Lecture Notes A matlab, R, IDL, NumPy/SciPy dictionary © Copyright 2008-2020, The SciPy community. Last updated on Jun 29, 2020. Created using Sphinx 2.4.4.
GitHub Repo
https://github.com/JuanchoGithub/png-url-to-svg
JuanchoGithub/png-url-to-svg
Vectorize images from a URL, or upload your own. Handles color and other edge cases.
GitHub Repo
https://github.com/rkapl123/ScriptAddin
rkapl123/ScriptAddin
Simple Excel-DNA based Add-in for handling Scripts (R, Python, Perl, whatever you define) from Excel, storing input objects (scalars/vectors/matrices) and retrieving result objects (scalars/vectors/matrices) as text files (currently restricted to tab separated). Graphics are retrieved from produced png files into Excel to be displayed as diagrams.
GitHub Repo
https://github.com/Seba-Toso/Guessit-App
Seba-Toso/Guessit-App
Finished|http://imgfz.com/i/wtWe8Ox.png|http://imgfz.com/i/6r3yxpI.png|http://imgfz.com/i/BgFjO3P.png|I had to make a game in which you can enter a number of up to 2 digits. Then, the device will launch numbers trying to "guess" my number. With each round, it must be indicated if the device number is less or greater than mine. Once the chosen number has been reached, it will be show it in the final screen with the round count.|This app was made using React-Native, expo as skeleton and expo vector icons. The handling of the app states was done with the useState hook. For the numbers released by the app, Math.random and Math.floor were used to ensure rounding down.|Tenía que hacer un juego en el que se pueda introducir un número de hasta 2 dígitos. Luego, el dispositivo lanzará números tratando de "adivinar" mi número. Con cada ronda, se debe indicar si el número de dispositivo es menor o mayor que el mío. Una vez alcanzado el número elegido, se mostrará en la pantalla final con el recuento de rondas.| Esta aplicación se creó con React-Native, expo como esqueleto e íconos vectoriales de expo. El manejo de los estados de la aplicación se realizó con el enlace useState. Para los números publicados por la aplicación, se usaron Math.random y Math.floor para garantizar el redondeo a la baja.
GitHub Repo
https://github.com/ekncarcc/OSG
ekncarcc/OSG
Welcome to the OpenSceneGraph (OSG). For up-to-date information on the project, in-depth details on how to compile and run libraries and examples, see the documentation on the OpenSceneGraph website: http://www.openscenegraph.org/index.php/documentation For support subscribe to our public mailing list or forum, details at: http://www.openscenegraph.org/index.php/support For the impatient, we've included quick build instructions below, these are are broken down is three parts: 1) General notes on building the OpenSceneGraph 2) OSX release notes 3) iOS release notes If details below are not sufficient then head over to the openscenegraph.org to the Documentation/GettingStarted and Documentation/PlatformSpecifics sections for more indepth instructions. Robert Osfield. Project Lead. 12th August 2015. -- Section 1. How to build the OpenSceneGraph ========================================== The OpenSceneGraph uses the CMake build system to generate a platform-specific build environment. CMake reads the CMakeLists.txt files that you'll find throughout the OpenSceneGraph directories, checks for installed dependenciesand then generates the appropriate build system. If you don't already have CMake installed on your system you can grab it from http://www.cmake.org, use version 2.4.6 or later. Details on the OpenSceneGraph's CMake build can be found at: http://www.openscenegraph.org/projects/osg/wiki/Build/CMake Under unices (i.e. Linux, IRIX, Solaris, Free-BSD, HP-Ux, AIX, OSX) use the cmake or ccmake command-line utils. Note that cmake . defaults to building Release to ensure that you get the best performance from your final libraries/applications. cd OpenSceneGraph cmake . make sudo make install Alternatively, you can create an out-of-source build directory and run cmake or ccmake from there. The advantage to this approach is that the temporary files created by CMake won't clutter the OpenSceneGraph source directory, and also makes it possible to have multiple independent build targets by creating multiple build directories. In a directory alongside the OpenSceneGraph use: mkdir build cd build cmake ../OpenSceneGraph make sudo make install Under Windows use the GUI tool CMakeSetup to build your VisualStudio files. The following page on our wiki dedicated to the CMake build system should help guide you through the process: http://www.openscenegraph.org/index.php/documentation/platform-specifics/windows Under OSX you can either use the CMake build system above, or use the Xcode projects that you will find in the OpenSceneGraph/Xcode directory. See release notes on OSX CMake build below. For further details on compilation, installation and platform-specific information read "Getting Started" guide: http://www.openscenegraph.org/index.php/documentation/10-getting-started Section 2. Release notes on OSX build, by Eric Sokolowsky, August 5, 2008 ========================================================================= There are several ways to compile OpenSceneGraph under OSX. The recommended way is to use CMake 2.6 to generate Xcode projects, then use Xcode to build the library. The default project will be able to build Debug or Release libraries, examples, and sample applications. Here are some key settings to consider when using CMake: BUILD_OSG_EXAMPLES - By default this is turned off. Turn this setting on to compile many great example programs. CMAKE_OSX_ARCHITECTURES - Xcode can create applications, executables, libraries, and frameworks that can be run on more than one architecture. Use this setting to indicate the architectures on which to build OSG. Possibilities include ppc, ppc64, i386, and x86_64. Building OSG using either of the 64-bit options (ppc64 and x86_64) has its own caveats below. OSG_BUILD_APPLICATION_BUNDLES - Normally only executable binaries are created for the examples and sample applications. Turn this option on if you want to create real OSX .app bundles. There are caveats to creating .app bundles, see below. OSG_WINDOWING_SYSTEM - You have the choice to use Carbon or X11 when building applications on OSX. Under Leopard and later, X11 applications, when started, will automatically launch X11 when needed. However, full-screen X11 applications will still show the menu bar at the top of the screen. Since many parts of the Carbon user interface are not 64-bit, X11 is the only supported option for OSX applications compiled for ppc64 or x86_64. There is an Xcode directory in the base of the OSG software distribution, but its future is limited, and will be discontinued once the CMake project generator completely implements its functionality. APPLICATION BUNDLES (.app bundles) The example programs when built as application bundles only contain the executable file. They do not contain the dependent libraries as would a normal bundle, so they are not generally portable to other machines. They also do not know where to find plugins. An environmental variable OSG_LIBRARY_PATH may be set to point to the location where the plugin .so files are located. OSG_FILE_PATH may be set to point to the location where data files are located. Setting OSG_FILE_PATH to the OpenSceneGraph-Data directory is very useful when testing OSG by running the example programs. Many of the example programs use command-line arguments. When double-clicking on an application (or using the equivalent "open" command on the command line) only those examples and applications that do not require command-line arguments will successfully run. The executable file within the .app bundle can be run from the command-line if command-line arguments are needed. 64-BIT APPLICATION SUPPORT OpenSceneGraph will not compile successfully when OSG_WINDOWING_SYSTEM is Carbon and either x86_64 or ppc64 is selected under CMAKE_OSX_ARCHITECTURES, as Carbon is a 32bit only API. A version of the osgviewer library written in Cocoa is needed. However, OSG may be compiled under 64-bits if the X11 windowing system is selected. However, Two parts of the OSG default distribution will not work with 64-bit X11: the osgviewerWX example program and the osgdb_qt (Quicktime) plugin. These must be removed from the Xcode project after Cmake generates it in order to compile with 64-bit architectures. The lack of the latter means that images such as jpeg, tiff, png, and gif will not work, nor will animations dependent on Quicktime. A new ImageIO-based plugin is being developed to handle the still images, and a QTKit plugin will need to be developed to handle animations. Section 3. Release notes on iOS build, by Thomas Hoghart ========================================================= * Run CMake with either OSG_BUILD_PLATFORM_IPHONE or OSG_BUILD_PLATFORM_IPHONE_SIMULATOR set: $ mkdir build-iOS ; cd build-iOS $ ccmake -DOSG_BUILD_PLATFORM_IPHONE_SIMULATOR=YES -G Xcode .. * Check that CMAKE_OSX_ARCHITECTURE is i386 for the simulator or armv6;armv7 for the device * Disable DYNAMIC_OPENSCENEGRAPH, DYNAMIC_OPENTHREADS This will give us the static build we need for iPhone. * Disable OSG_GL1_AVAILABLE, OSG_GL2_AVAILABLE, OSG_GL3_AVAILABLE, OSG_GL_DISPLAYLISTS_AVAILABLE, OSG_GL_VERTEX_FUNCS_AVAILABLE * Enable OSG_GLES1_AVAILABLE *OR* OSG_GLES2_AVAILABLE *OR* OSG_GLES3_AVAILABLE (GLES3 will enable GLES2 features) * Ensure OSG_WINDOWING_SYSTEM is set to IOS * Change FREETYPE include and library paths to an iPhone version (OpenFrameworks has one bundled with its distribution) * Ensure that CMake_OSX_SYSROOT points to your iOS SDK. * Generate the Xcode project * Open the Xcode project $ open OpenSceneGraph.xcodeproj * Under Sources -> osgDB, select FileUtils.cpp and open the 'Get Info' panel, change File Type to source.cpp.objcpp Here's an example for the command-line: $ cmake -G Xcode \ -D OSG_BUILD_PLATFORM_IPHONE:BOOL=ON \ -D CMAKE_CXX_FLAGS:STRING="-ftree-vectorize -fvisibility-inlines-hidden -mno-thumb -arch armv6 -pipe -no-cpp-precomp -miphoneos-version-min=3.1 -mno-thumb" \ -D BUILD_OSG_APPLICATIONS:BOOL=OFF \ -D OSG_BUILD_FRAMEWORKS:BOOL=OFF \ -D OSG_WINDOWING_SYSTEM:STRING=IOS \ -D OSG_BUILD_PLATFORM_IPHONE:BOOL=ON \ -D CMAKE_OSX_ARCHITECTURES:STRING="armv6;armv7" \ -D CMAKE_OSX_SYSROOT:STRING=/Developer/Platforms/iPhoneOS.platform/Developer/SDKs/iPhoneOS4.2.sdk \ -D OSG_GL1_AVAILABLE:BOOL=OFF \ -D OSG_GL2_AVAILABLE:BOOL=OFF \ -D OSG_GLES1_AVAILABLE:BOOL=ON \ -D OSG_GL_DISPLAYLISTS_AVAILABLE:BOOL=OFF \ -D OSG_GL_FIXED_FUNCTION_AVAILABLE:BOOL=ON \ -D OSG_GL_LIBRARY_STATIC:BOOL=OFF \ -D OSG_GL_MATRICES_AVAILABLE:BOOL=ON \ -D OSG_GL_VERTEX_ARRAY_FUNCS_AVAILABLE:BOOL=ON \ -D OSG_GL_VERTEX_FUNCS_AVAILABLE:BOOL=OFF \ -D DYNAMIC_OPENSCENEGRAPH:BOOL=OFF \ -D DYNAMIC_OPENTHREADS:BOOL=OFF . Known issues: * When Linking final app against ive plugin, you need to add -lz to the 'Other linker flags' list. * Apps and exes don't get created * You can only select Simulator, or Device projects. In the XCode project you will see both types but the sdk they link will be the same.
GitHub Repo
https://github.com/fravezzimattia/img-to-vector
fravezzimattia/img-to-vector
img-to-svg is a Python CLI that converts JPG/PNG images into scalable SVG vectors. It supports color and black-and-white modes, quality presets, interactive or non-interactive usage, PNG transparency handling, and two engines: vtracer (recommended) and a legacy internal algorithm.
GitHub Repo
https://github.com/sayantann11/all-classification-templetes-for-ML