Advanced 15th Course Python Module NumPy

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NumPy NumPy is the foundation package for high performance scientific computing and data analysis. Some of the functions are as follows:

• • Ndarray, a fast and space-saving multidimensional array with vector arithmetic operations and complex broadcast capabilities.
  • A standard mathematical function for fast operation of the entire set of data (without writing loops).
  • Tools for reading and writing disk data, and tools for manipulating memory-mapped files.
  • Linear algebra, random number generation, and Fourier transform functions.
  • Tools for integrating code written in C, C + +, Fortran, and other languages.

First, import the NumPy library: import NumPy as NP

A NumPy functions and properties:

Type	Type code	Description
int8, Uint8	I1, U1	Signed and unsigned 8-bit integer (1 bytes)
Int16, UInt16	I2, U2	Signed and unsigned 16-bit integer (2 bytes)
Int32, UInt32	I4, U4	Signed and unsigned 32-bit integer (4 bytes)
Int64, UInt64	i8, U8	Signed and unsigned 64-bit integer (8 bytes)
Float16	F2	Semi-precision floating-point number
Float32	F4, F	Single-precision floating-point number
Float64	F8, D	Double-precision floating-point number
float128	F16, G	Extended precision floating point number
Complex64	C8	Plural with two 32-bit representations, respectively
complex128	C16	Plural with two 64-bit representations, respectively
complex256	C32	Plural with two 128-bit representations, respectively
bool	?	Boolean type
Object	O	Python Object
String	Sn	Fixed-length strings, 1 bytes per character, such as S10
Unicode	Un	Fixed-length Unicode, the number of bytes determined by the system, such as U10

Table 2.1.a.1 NumPy Types

Generating functions	Role
Np.array (x) Np.array (x, Dtype)	Convert input data to a Ndarray Convert input data to a type of Ndarray
Np.asarray (Array)	Convert input data to a new (copy) Ndarray
Np.ones (N) Np.ones (N, Dtype) Np.ones_like (Ndarray)	Generates an n-length one-dimensional all-one ndarray Generating an N-length type is a one-dimensional all-one ndarray of Dtype Create a ndarray with the same shape as the parameter
Np.zeros (N) Np.zeros (N, Dtype) Np.zeros_like (Ndarray)	Generates an n-length one-dimensional full 0 Ndarray Generates an n-length type bit dtype one-dimensional full 0 Ndarray Similar to Np.ones_like (Ndarray)
Np.empty (N) Np.empty (N, Dtype) Np.empty (Ndarray)	Generates an uninitialized one-dimensional ndarray of N-length Generates an n-length type that is an uninitialized one-dimensional ndarray of Dtype Similar to Np.ones_like (Ndarray)
Np.eye (N) Np.identity (N)	Create an n * N unit Matrix (diagonal is 1, the remainder is 0)
Np.arange (num) Np.arange (begin, end) Np.arange (begin, end, step)	Generate a one-dimensional ndarray from 0 to num-1 steps 1 Generate a one-dimensional ndarray from begin to end-1 steps 1 Build a one-dimensional ndarray that steps from begin to End-step are step
Np.mershgrid (Ndarray, Ndarray,...)	Generate a Ndarray * Ndarray * ... The Multidimensional Ndarray
Np.where (Cond, Ndarray1, Ndarray2)	Depending on the condition cond, select Ndarray1 or Ndarray2 to return a new Ndarray
NP.IN1D (Ndarray, [x, y,...])	Checks if the elements in the Ndarray are equal to [x, y,...] Returns a bool array in one of the
Matrix functions	Description
Np.diag (Ndarray) Np.diag ([x, y,...])	Returns a diagonal (or non-diagonal) element of a square matrix as a one-dimensional array Converts a one-dimensional array to a square (non-diagonal element is 0)
Np.dot (Ndarray, Ndarray)	Matrix multiplication
Np.trace (Ndarray)	Computes the and of the diagonal elements
Sort function	Description
Np.sort (Ndarray)	Sort, return copy
Np.unique (Ndarray)	Returns the elements in Ndarray, excludes duplicate elements, and sorts
NP.INTERSECT1D (Ndarray1, Ndarray2) NP.UNION1D (Ndarray1, Ndarray2) NP.SETDIFF1D (Ndarray1, Ndarray2) NP.SETXOR1D (Ndarray1, Ndarray2)	Returns the intersection of the two and sorts. Returns the combination of the two and sorts. Returns the difference between the two. Returns the symmetry difference between the two
Unary calculation function	Description
Np.abs (Ndarray) Np.fabs (Ndarray)	Calculate absolute Value Calculate absolute value (non-plural)
Np.mean (Ndarray)	Averaging
NP.SQRT (Ndarray)	Calculate x^0.5
Np.square (Ndarray)	Calculate x^2
Np.exp (Ndarray)	Calculate e^x
Log, log10, log2, log1p	Log with natural logarithm, bottom 10 log, bottom 2 log, bottom (1+x)
Np.sign (Ndarray)	Calculate positive and negative numbers: 1 (positive), 0 (0), 1 (negative)
Np.ceil (Ndarray) Np.floor (Ndarray) Np.rint (Ndarray)	Calculates the smallest integer greater than or equal to the value Calculates the largest integer less than or equal to the value Rounding to the nearest integer, preserving Dtype
NP.MODF (Ndarray)	Returns the decimal and integer parts of an array as two independent arrays
Np.isnan (Ndarray)	Returns a bool array that determines whether it is Nan
Np.isfinite (Ndarray) Np.isinf (Ndarray)	Returns a Boolean array that determines whether it is a poor (non-INF, non-Nan) Returns an array of type bool that determines whether it is infinite
Cos, cosh, sin, sinh, tan, Tanh	General type and hyperbolic trigonometric functions
Arccos, Arccosh, Arcsin, Arcsinh, Arctan, Arctanh	Inverse trigonometric function and hyperbolic type inverse trigonometric function
Np.logical_not (Ndarray)	Calculates the true value of not x for each element, equivalent to-ndarray
Multivariate computational functions	Description
Np.add (Ndarray, Ndarray) Np.subtract (Ndarray, Ndarray) Np.multiply (Ndarray, Ndarray) Np.divide (Ndarray, Ndarray) Np.floor_divide (Ndarray, Ndarray) Np.power (Ndarray, Ndarray) Np.mod (Ndarray, Ndarray)	Add Subtraction Multiplication Division Circle Divide Method (discard remainder) Sub-party Die-finding
Np.maximum (Ndarray, Ndarray) Np.fmax (Ndarray, Ndarray) Np.minimun (Ndarray, Ndarray) Np.fmin (Ndarray, Ndarray)	To find the maximum value Maximum value (Ignore Nan) To find the minimum value Minimum value (Ignore Nan)
Np.copysign (Ndarray, Ndarray)	Assigning the symbol in Parameter 2 to parameter 1
Np.greater (Ndarray, Ndarray) Np.greater_equal (Ndarray, Ndarray) Np.less (Ndarray, Ndarray) Np.less_equal (Ndarray, Ndarray) Np.equal (Ndarray, Ndarray) Np.not_equal (Ndarray, Ndarray)	> >= < <= == !=
Logical_and (Ndarray, Ndarray) Logical_or (Ndarray, Ndarray) Logical_xor (Ndarray, Ndarray)	& | ^
Np.dot (Ndarray, Ndarray)	Calculating the matrix inner product of two Ndarray
Np.ix_ ([x,y,m,n],...)	Generates an indexer for fancy indexing (fancy index)
File read/write	Description
Np.save (String, Ndarray)	Save Ndarray to file named [String].npy] (no compression)
Np.savez (String, Ndarray1, Ndarray2, ...)	Save all Ndarray compression to a file named [String].npy]
Np.savetxt (sring, Ndarray, FMT, newline= ' \ n ')	Write Ndarray to file in FMT format
Np.load (String)	Reads the file contents of a filename string and translates it into a Ndarray object (or Dictionary object)
Np.loadtxt (String, delimiter)	Reads the file contents of the filename string, converting it to ndarray with delimiter as a delimiter

table 2.1.a.2 NP common functionsB Numpy.ndarray functions and properties:

Ndarray.ndim	Get the dimension of Ndarray
Ndarray.shape	Get the length of each dimension of Ndarray
Ndarray.dtype	Gets the data type of the element in the Ndarray
Ndarray. T	Simple Transpose matrix Ndarray

table 2.1.b.1 Ndarray Properties

Function	Description
Ndarray.astype (Dtype)	The conversion type, which occurs if the conversion fails TypeError
Ndarray.copy ()	Copying a copy of Ndarray (new memory space)
Ndarray.reshape ((n,m,...))	Convert Ndarray to n*m* ... The multidimensional Ndarray (not copy)
Ndarray.transpose ((Xindex,yindex,...))	Xindex,yindex by Dimension Index ... Matrix transpose, dependent on shape, cannot be used for one-dimensional matrices (not copy)
Ndarray.swapaxes (Xindex,yindex)	Swap dimensions (not copy)
Calculation function	Description
Ndarray.mean (axis=0)	Averaging
Ndarray.sum (axis= 0)	Sum
Ndarray.cumsum (axis=0) Ndarray.cumprod (axis=0)	Accumulation Tired Ride
NDARRAY.STD () Ndarray.var ()	Variance Standard deviation
Ndarray.max () Ndarray.min ()	Maximum Value Minimum value
Ndarray.argmax () Ndarray.argmin ()	Index of Maximum value Minimum value Index
Ndarray.any () Ndarray.all ()	If there is at least one true Whether all is true
Ndarray.dot (Ndarray)	Calculating the inner product of matrices
Sort function	Description
Ndarray.sort (axis=0)	Sort, return source data

table 2.1.b.2 Ndarray functions

Ndarray[n]	Select N+1 Element
NDARRAY[N:M]	Select N+1 to M elements
ndarray[:]	Select all elements
Ndarray[n:]	Select N+1 to last element
NDARRAY[:N]	Select No. 0 to nth element
ndarray[Bool_ndarray] Note: Bool_ndarray represents a bool type of Ndarray	Select the element that is true
Ndarray[[x,y,m,n]] ...	Select the order and sequence of Ndarray for X, Y, M, n
NDARRAY[N,M] NDARRAY[N][M]	Select the m+1 element of line n+1
Ndarray[n,m,...] Ndarray[n][m] ....	Select N rows n columns .... The Elements

table 2.1.b.3 Ndarray index/Slice modeC Numpy.random functions and properties: with normal distribution (average 0, standard deviation 1)

function	description
Seed () Seed (int) Seed (ndarray)	determine random number generation seed
Permutation (int) Permutation (Ndarray) td>	Returns the random arrangement of a one-dimensional sequence from 0~9 Returns the random arrangement of a sequence
Shuffle (ndarray)	for a sequence in-place random order
rand (int) Randint (begin,end,num=1)	Produce an int uniformly distributed sample value Randomly selects num integers from a given begin and end
randn (N, M, ...)	Generate a n*m* ... Ndarray
Normal (size= (n,m,...))	Generate a n*m* ... Ndarray  of the Normal (Gaussian) distribution;
Beta (ndarray1,ndarray2)	generates a sample value for the beta distribution, and the parameter must be greater than 0
chisquare ()	generates sample values for Chi-square distribution
gamma ()	produces a gamma distribution of sample values
uniform ()	produces sample values that are evenly distributed in [0,1]

2.1.c.1 Random Common functions

D Numpy.linalg functions and properties:

Function	Description
Det (Ndarray)	Computed matrix column type
Eig (Ndarray)	The eigenvalues and eigen vectors of the matrix are calculated
INV (Ndarray) PINV (Ndarray)	Calculating the inverse of a square matrix Moore-penrose pseudo-inverse of a square matrix
QR (Ndarray)	calculate QR Decomposition
SVD (Ndarray)	Compute singular value decomposition SVD
Solve (Ndarray)	Solving a linear equation Group ax = b, where A is a phalanx
LSTSQ (Ndarray)	The least squares solution for calculating ax=b

2.1.d.1 Linalg Common functions

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Advanced 15th Course Python Module NumPy