BinMatrix：C++中的二进制矩阵操作与存储类

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"BinMatrix 是一个用于操作和存储二进制矩阵的开源 C++ 类库。它提供了多种矩阵运算功能，如逻辑或、逻辑与、矩阵乘法和矩阵乘方等。类的设计包括了四个抽象层次，使得在处理二进制矩阵时具有更高的灵活性和效率。" 在计算机科学中，二进制矩阵是用二进制值（0 或 1）表示的矩阵，常用于数据表示、图像处理、编码理论和计算机图形学等领域。BinMatrix 类的出现，是为了方便程序员在 C++ 中处理这类特殊矩阵，提供了一种高效且灵活的方法。首先，BinMatrix 类是最基础的层次，它存储一个 NxN 的方形二进制矩阵，并有一个属性 propNot 用于表示矩阵中的每个元素是否进行了 NOT 操作。这允许用户在不改变原始矩阵的情况下进行逻辑取反操作。接下来，BinMatrixA 类（即“BinMatrix 绝对”）扩展了 BinMatrix 的功能，支持矩阵的排列。它提供接口来设置排列，使得用户可以对矩阵进行不同方式的重排。内部，BinMatrixA 使用两个名为 permut1 和 permut2 的排列矩阵，以及一个 BinMatrixP 对象来存储原始数据。这种排列方式可以表示为 permut1 * M * permut2，其中 M 是 BinMatrixP 对象中的矩阵。然后是 BinMatrixP 类（即“BinMatrix 排列”），它允许用户选择特定背景下的行和列。这里的背景可能是一个全零矩阵或者全一矩阵，这在处理某些特定问题时非常有用，比如矩阵的子集操作或特定条件的矩阵变换。通过这样的多层次设计，BinMatrix 类库不仅提供了基本的二进制矩阵操作，还支持了矩阵的排列和组合，从而在各种应用场景下都能保持高效和灵活性。这对于开发涉及二进制数据处理的软件，尤其是那些需要执行复杂矩阵运算的算法，如图像处理、密码学或并行计算等，都是非常有益的。此外，由于 BinMatrix 是开源的，开发者可以查看其源代码，了解实现细节，甚至可以根据需求对其进行定制和扩展。开源软件的社区特性意味着用户可以得到持续的更新和支持，同时也可以贡献自己的改进，共同推动这个工具的发展。 BinMatrix 是一个强大的工具，它简化了 C++ 开发者在处理二进制矩阵时的工作，提供了丰富的操作选项和高效的矩阵处理能力，对于需要进行二进制数据运算的项目来说，是一个值得考虑的库。

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//set values for A and B

A.opMult(B);

This will set a union of all used rows of SmallMatrix inside p.m_pointers. Also it will

store all selected rows inside p.m_pointers . After, this each time we call setValue()

from BinMatrixP, it will actualize union of pointers between A and B, and according

about this pointers, insertSmallRow will avoid to use rows written inside pointer lists

from p.m_pointers. If p.m_pointers contains a pointer from row R to r (R ---> r) and

we want set a value inside row R , which not point to any row from SmallMatrix, if r

is available inside SmallMatrix, we will use this.

For set only a policy for a matrix, we can do :

PointerPolicy p(BSPointerPolicy::sameRelaxNext);

BinMatrix A(20);

A.setPointerPolicy(p);

//set values for A

BinMatrixR

BinMatrixR store all data. A object of BinMatrixR can contain many other

BinMatrixR objects. “BinMatrixR” come from “Binary Matrix Recursive”. A

BinMatrixR can be of 3 main matrix types :

• pSparse, for sparse matrix

• pEnd, for a dense matrix

• pBinpart, for contain submatrices

For indicate, that a matrix is of one or other type, we have variable prop :

Prop prop;

Size of a matrix is stored inside variable N, which have 2 associated convenient

variables :

• hN = N/2

• log2N = log

(N)

Also, have many functions for set a row or columns with values :

• void setCopyRow(int rowFrom,int rowTo);

• void setCopyCol(int colFrom,int colTo);

• void setRowValue(int row, bool value);

• void setColValue(int col, bool value);

• void setZoneValue(int rowMin,int rowMaxP,int colMin,int colMaxP,bool value);

• void setRowZerosOnes(int row, const OrdIntValSet& ones);

• void setColZerosOnes(int col, const OrdIntValSet& ones);

OrdIntValSet is a class for store intervals of integers. Places indicate in <ones> will

be 1, and rest will be 0.

In function setZoneValue(...) we indicate margins for rows and columns. Rows have

values : rowMin <= row < rowMaxP. Same is for columns.

Similary to BinMatrix, BinMatrixR also have many static functions for operate

between objects :

• static void opOr(BinMatrixR& A, const BinMatrixR& B);

• static void opAnd(BinMatrixR &A, const BinMatrixR &B);

• static void opXor(BinMatrixR &A, const BinMatrixR &B);

• static void opXnor(BinMatrixR &A, const BinMatrixR &B);

• static void opMult(BinMatrixR& A,BinMatrixR& B);

We also have protected functions for convert between types, see then :

• void convertToEnd();

• void convertEndToSparse();

• void convertSparseToBinpart();

• void convertBinpartToSparse(bool knowRest=false,bool _rest=false);

Only a pSparse can be converted to a pEnd. This is because a pEnd have a minimal

size inside BinMatrixR and this is a 64x64, so it's not possible to convert a pBinpart

to a pEnd, because a pBinpart always have a size at least 2 times bigger as a pEnd

matrix.

BinMatrixE

This is a class used for matrices types pEnd from BinMatrixR. BinMatrixE also

maintain a variable N for indicate a size NxN , but this size will be always same. At

this moment (January 2015), BinMatrixE::bmes = 64, so also N=64 and size of this

matrix always is 64x64. If in a future memory bus and bytes in computer are

standarized with 128 bits, we can change this in variable bmes and changing “typedef

uint64_t uint64” to uint128.

We maintain 2 integer arrays for store all data :

• uint64 orig[64];

• uint64 trans[64];

orig store values by rows. So orig[i] is a 64 bit integer, representing row i, and bit j of

orig[i] means column j, so if bit j of orig[i] is a 1, so value of cell (i,j) is true. If this

value is 0, cell (i,j) is false.

So this matrix is represented with :

orig[0],bit 0 orig[0],bit 1 orig[0],bit 2

..........................

orig[0],bit 61 orig[0],bit 62 orig[0],bit 63

orig[1],bit 0 orig[1],bit 1 orig[1],bit 2 orig[1],bit 61 orig[1],bit 62 orig[1],bit 63

orig[2],bit 0 orig[2],bit 1 orig[2],bit 2 orig[2],bit 61 orig[2],bit 62 orig[2],bit 63

........................... ......................... .................................

orig[61],bit 0 orig[61],bit 1 orig[61],bit 2

.....................

orig[61],bit 61 orig[61],bit 62 orig[61],bit 63

orig[62],bit 0 orig[62],bit 1 orig[62],bit 2

orig[62],bit 61 orig[62],bit 62 orig[62],bit 63

orig[63],bit 0 orig[63],bit 1 orig[63],bit 2

orig[63],bit 61 orig[63],bit 62 orig[63],bit 63

trans can also represent data of this matrix. Name come from “transposed”

trans store values by columns. So trans[j] is a 64 bit integer, representing column j,

and bit i of trans[j] means column i, so if bit i of trans[j] is a 1, so value of cell (i,j) is

true. If this value is 0, cell (i,j) is false.

This matrix is represented with :

trans[0],bit 0 trans[1],bit 0 trans[2],bit 0

..........................

trans[61],bit 0 trans[62],bit 0 trans[63],bit 0

trans[0],bit 1 trans[1],bit 1 trans[2],bit 1 trans[61],bit 1 trans[62],bit 1 trans[63],bit 1

trans[0],bit 2 trans[1],bit 2 trans[2],bit 2 trans[61],bit 2 trans[62],bit 2 trans[63],bit 2

........................... ......................... .................................

trans[0],bit 61 trans[1],bit 61 trans[2],bit 61

.....................

trans[61],bit 61 trans[62],bit 61 trans[63],bit 61

trans[0],bit 62 trans[1],bit 62 trans[2],bit 62

trans[61],bit 62 trans[62],bit 62 trans[63],bit 62

trans[0],bit 63 trans[1],bit 63 trans[2],bit 63

trans[61],bit 63 trans[62],bit 63 trans[63],bit 63

One idea for a develpment of BinMatrixE is to make free the simultan existence of

orig and trans. We can create one or two variables like origValid and transValid. In

all functions we need to guaranty either orig or trans are valid, or both, in this way

always origValid || transValid = true.

We have some protected functions for convert a “orig-array” to a “trans-array” and

viceversa :

• void origToTrans();

• void transToOrig();

BinMatrixE have several functions for set values :

• void setValue(int a, int b, bool value);//for set a value at (a,b)

• void setRandomValues(int randPoints, bool value = true);//for set randPoints

cells to value value

• void setRandomValues(int p,int q,int w,int h);//for set random ones over zeros in

which we have a probability of p/q to have a 1 in a cell and a 1-p/q for have a 0. Area for

fill random ones is (0,0)-(w-1,h-1).

• void setAllValue(bool value);//set all cells to value value

• void setRowValue(int row, bool value);//set row row to value value

• void setColValue(int col, bool value);//set column col to value value

• void setRowsValue(int rowMin, int rowMaxP, bool value);//set from row rowMin

until row rowMaxP-1 all rows to value value

• void setColsValue(int colMin, int colMaxP, bool value);//set from column

colMin until column colMaxP-1 all columns to value value

• void setZoneValue(int rowMin, int rowMaxP, int colMin, int colMaxP, bool

value);//set a area enclosed between (rowMin,colMin)-(rowMaxP-1,colMaxP-1) to value value

• void setRowZerosOnes(int row, const OrdIntValSet& ones);//set all cells

(row,i)

∀i∈ones

to value true, rest (in same row) set to value false (0).

• void setColZerosOnes(int col, const OrdIntValSet& ones);//same, but for column

col and intervals of rows

For set a value in this matrix, we change a bit :

void BinMatrixE::setValue(int a, int b, bool value)

{

...

if (value) {

orig[a] |= uint64(1)<<b;

trans[b] |= uint64(1)<<a;

}

else {

orig[a] &= ~(uint64(1)<<b);

trans[b] &= ~(uint64(1)<<a);

}

...

For set a value in row value, we need to change a bit from orig[a]. This bit is bit b

from orig[a]. We use a OR-operation for set a true on this bit :

orig[a] |= uint64(1)<<b;

For example, if orig[a] have a 64 bit ended with :

...010010100

If we want to change (a,1) (1 is 0 based), we make a or with a number which just

have a 1 at bit 1 :

...010010100

...000000010 ( = 1<<b = 1<<1 )

----------------

...010010110

If we want to set a cell to 0, we use a AND with a integer which have all 1 except bit

b, for example we change cell (a,2) to 0, so change bit 2 of row a :

...010010100

AND

...111111011 ( = ~(1<<b) = ~(1<<2) )

--------------

...010010000

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