Subclass of numpy.matrix behaving as matrices in matlab.

## Project description

## Introduction

This is my module about matrix operation. It imitates matlab grammar. If you love matlab as well as python, then this is your choice. It will be a good experience to operating matrices matlab-like.

Sugar: one can use single index to refer to the elements in a matrix. (see following examples)

## Organization

mymat:

- mymat
- matshow
- matdemo
- test_mat
- linalg
- denoise

## Feature

- Current Version:
- fix some bugs.
- Demonstrate Gauss elimination with tkinter.
- Define LinearEquation class

>>> import mymat.matdemo >>> mymat.matdemo.main()

- Main Feature(>0.1.x):
- MyMat, PyMat is now the subclass of MatBase
- improve some essential methods, fix some bugs
- the index can be in reserved order, such as A[3:1:-1,1]
- see numerical experiment in mat_demo (improved)
- add more methods (introduced below) and A[is,js]=[] now is legal
- fix some bugs, make the codes more robust

finally, another improvement is that when create a matrix, we use following codes to set dtype (may temporarily)

- if data.dtype != np.complex128 and data.dtype != object:
- kwargs.setdefault(‘dtype’, np.float64)

- Main Feature(0.0.x):
- introduce operator | and & to concatenate matrices
- in setitem, the index is allowed to be out of range as matlab with the help of update method (see below)
- correct the codes of delete, improve the codes of many method
- add poly/expm (Tylor approximation) method to calculate p(A) and e^A
- add totex method, transforming a matrix to its tex-form
- the default dtype of MyMat is float64(complex128 when it is complex), but the integer matrix is int32. so, don’t forget to convert the dtype if neccessary. But this is temporary.

### Grammar

#### basic grammar

import:

>>> import mymat >>> A = mymat.MyMat([]) # use import mymat.pymat to import PyMat

operators (Python left, Matlab right):

A*B := A*B (B*A := B*A) A/B := A/B == A*B.I (B/A := B/A == B*A.I) A ** B := A .* B (B ** A := B .* A) A//B := A./B (B//A := B./A) A<<B := A.^B (B<<A := B.^A) A^B := A^B A|B := [A,B] A&B :=[A;B]

We use matlab-type index, instead of python-type index, for example:

>>> A=TestMat(5) [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]: M(5 X 5) >>> A[[3,4,7,10]] # with single index as in matlab [11, 16, 7, 22]: M(1 X 4) >>> A[[2,3],1:4] [6, 7, 8, 9; 11, 12, 13, 14]: M(2 X 4) >>> A[[1,3],[2,4]] # use A.get(([1,3],[2,4])) to get matrix([2, 14]) [2, 4; 12, 14]: M(2 X 2) >>> A[3:1:-1,:] # reversing order [11, 12, 13, 14, 15; 6, 7, 8, 9, 10; 1, 2, 3, 4, 5]: M(3 X 5)

Use delete method to delete some rows or columns, as in matlab:

>>> A=H(7) >>> B=A.delete([1,3],slice(3)) # <=> B=A.copy(); B[[1,3],[1,2,3]]=[] >>> B.shape (5, 4)

Linear equation:

>>> le = LinearEquation(A, b) >>> print(le.totex()) # print tex of a linear equation

#### Demonstration and Visualization

demonstration and numerical experiment:

>>> import mymat >>> import mymat.matdemo # see Gauss elimination >>> A=mymat.MyMat('1,1,1,6;0,4,-1,5;2,-2,1,1') # or A=mymat.MyMat('1&1&1&6\\0&4&-1&5\\2&-2&1&1') just copying the latex codes >>> mymat.matdemo.guassDemo(A) # show the process of getting the echelon form of A >>> mymat.matdemo.denoiseDemo([n:noised signal(row vector)]) # see a denoising experiment

draw a matrix:

>>> import mymat.matshow # draw a matrix on axes(require matplotlib) >>> ms = mymat.matshow.MatrixShow(A); ms.show()

#### Methods and Functions

other methods:

__call__: A(ind) == A[ind] delete(ind1=row, ind2=col): delete row-rows and col-columns proj(ind1=row, ind2=col): =0 out of A[row, col], for example A.proj(ind1=COLON, ind2=[2,3])=[2,3] where A=[1,2,3,4] repmat((ind1, ind2)|ind): repeat matrix as in Matlab (like tile) just: cut matrix to a certain size, and supplement zeros if the size is too large. cat: as concatenate equal: (A == B == C).all() apply: A.apply(lambda x:x+1) == A+1 plus: A.plus(n) == A + nI robinson: A.robinson(j, x) == A[j<-x], namely A[:,j]=x used in Cramer rule echelon: get the echelon form (include the corresponding column indexes) tril, triu, diag are similar to matlab row(col)_transform1/2/3: elementary row (column) transforms (Gauss tranforms) comat: get the co-matrix (similar with delete) cofactor: A.cofactor(i,j)=Aij get the cofactor based on comat rho: the spectral radius totex: to tex form of matrix tolineq: to tex form of linear equations wrt augment matrix argmin, argmax

class methods:

MyMat.zeros, MyMat.ones, MyMat.random, MyMat.randint, MyMat.eye

functions and variables:

ind2ind: the most essential function times: translate single index to double index compind: get complementary index (called in proj) COLON: slice(None), COLON2=(COLON,COLON)

matrices:

FM: Fourier matrix FIM: Fourier inverse matrix FUM: Fourier unitary matrix Ho: Horsehold matrix Ref: reflection matrix H: Hilbert matrix Elm1,Elm2,Elm3: elementary matrices (3 types)

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