mymat 1.1.0

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)