BinMatrix:BinMatrix是用于操作和存储二进制矩阵的类-开源

BinMatrix

version 3

Introduction.

BinMatrix is a class for store a binary matrix and operate between them.

Each BinMatrix-object represent a binary matrix. This matrix always is quadratic,

which size is stored inside member variable N. So, matrix have size NxN.

We have 4 levels of abstraction for a matrix, which main entry is BinMatrix :

- BinMatrix. Only maintain a variable for tell if the underling values are taking as

permute matrices are called permut1 and permut2, and a matrix BinMatrixA, are in

form : permut1 * M * permut2, in which M have values from BinMatrixP object.

- BinMatrixP. “BinMatrix Permutated”. Within this class, we can select rows and

columns to use over a specific background (examples are a background of zeros, or a

background of ones or a background of a lower triangle). Values from cells which

rows and columns are selected are looked at the “small matrix” or main object of type

BinMatrixR, in which we store data. If a cell have either a row or columns not

selected, his values need to take from background.

- BinMatrixR. “BinMatrix Recursive”. In this matrix-object we store all data. It's

recursive because it can contain inside many smaller BinMatrix-objects. This matrix

BinMatrixA object. Also, BinMatrix need to have a constructor, for tell him that we

send a antisimetric data, so BinMatrix will automatically search for a triangular (it is

not a general case). A good idea in case of triangulars, is add a capability to

BinMatrixP to select diagonal rows instead of regular rows and columns. In this way,

it will spare more memory.

If you not use operation NOT, not use permutation and not use selected rows

capability, because you know its a very dense matrix, you can also directly construct

a BinMatrixR matrix, instead of a BinMatrix.

A diagram image :

Versioned background.

pSparse with differents background (zero-background or ones-background, ...). I take

pRowColumns concept outside of BinMatrixR, it will become BinMatrixP, because

only have sense in general to select rows and columns in a total way. BinMatrixR will

become very much simple.

In this third version, we do something still different to the version 2. For example

how we select rows and columns, store in memory. Also add a level of permutations

(BinMatrixA) because triangulars only have sense if we can permutate (in general

rows and columns not will have a perfect order). Also, in version 2 we handle inside

BinMatrixR, not quadratic matrices, and this let make a code more unreadibily and

more long to program. In version 3, this always are quadratic and size is a power of 2,

so it is very much easy to handle. A not quadratic matrix can be partitioned from a

It is the main interface for all other matrix classes. Only maintain a variable for tell if

the underling values are taking as original, or we take as a NOT operation in front

(NOT(0)=1, NOT(1)=0, for each cell). This variable is propNot. This class will set

and obtain values from a BinMatrixA object. A setNot() will only change propNot.

If propNot==false , we not have applied a NOT operation, but if it is true, we applied

a NOT operation. In cases of operations between 2 matrices, in some cases will force

propNot to be true or false, changing underling matrix objects to reflect this.

Main operations.

We have 2 main operations : one for set values, and another for get values :

We have defined this functions for this :

Recommended is use of form opOr, because all operations have this, in case of 2

operands. Also it is pendent to do a

In which we store result inside C.

- Hadamard product. It is realize a operation AND between 2 matrices to return a

Always , it will take A and B to realize A XOR B and put result into A.

- Multiplication. It realize a multiplication wetween two matrices. Supported

functions are :

- Power. It realize a power of a matrix M : C = M^p. Here C is result. We only have

defined cased in which C will be same matrix M : M = M^p. Functions are :

- setTransposed(). Set this matrix to his transposed version. We not have a

propTransposed value, but this operations is very quicky, in time O(1)...O(log(N)),

because change background inside BinMatrixP is O(1), and transpose BinMatrixR

underling matrices of type BinMatrixE can be transposed in time O(1) and sparse

matrices also. Only in case we have a big matrix with many BinMatrixR submatrices,

this time can be increased to O(log(N)).

- setToZeros(). Simply set this matrix to a zero matrix.

- Get a inverse matrix : First check if this matrix have a inverse matrix, calling to

haveInverse() , and after, if have inverse, get the transposed matrix with

setTransposed(). Transposed matrix are same as inversed matrix in case of binary

matrix. For example, you want to get a inversed matrix of A, into B, we can do :

First function set randPoints cells to value value. This is recommend for not dense

matrices, because it not guaranty to not repeat a same cells.

For set random dense matrices, use second or third function. Your only can use in

second function, denominators which are powers of 2 (like 2,4,8,16,...). For example,

your will set random values in which ones are 3 times more often in average as zeros.

So the probability of have a one is 3/4. For have this, call second function with :

A.setRandomValues(3,4);

If you want only a 3/8 of ones (and 5/8 of ones), then use :

A.setRandomValues(3,8);

If you not like to think about denominators, you can also use a third function, and if