# 2.2.3.9.16 matrixbase::DotMultiply

## Description

Multiply two matrices element by element.

## Syntax

BOOL DotMultiply( matrixbase & mb )

## Parameters

mb
[input] matrix which is multiplied with this matrix.

## Return

Returns TRUE on success and FALSE on Failure.

## Examples

EX1

void matrixbase_DotMultiply_ex1()
{
matrix<double> mat1 = {
{1,  2,  3},
{4,  5,  6}
};
matrix<double> mat2 = {
{ 1, 0, -1},
{-1, 0,  1}
};

int rc = mat1.DotMultiply( mat2 );  // Multiply mat1 by mat2
if(!rc)
printf("  Error: DotDivide failed. rc=%d\n");
else{
printf("The matrix is:\n");
for(int ii=0; ii< mat1.GetNumRows(); ii++){
for(int jj=0; jj< mat1.GetNumCols(); jj++)
printf("%g  ", mat1[ii][jj]);
printf("\r\n");
}
}
}

EX2

// Element-wise multiplication of two matrices
void matrixbase_DotMultiply_ex2()
{
int rc;

matrix<double> mat1 = {
{1,  2,  3},
{4,  5,  6}
};

matrix<double> mat2 = {
{ 1, 0, -1},
{-1, 0,  1}
};

MatrixPage MatPg1;
MatPg1.Create("Origin");
MatrixLayer MatLy1 = MatPg1.Layers(0);
Matrix Mat1(MatLy1);
Mat1 = mat1;
printf("  The original matrix is %s.\n",Mat1.GetName());

MatrixPage MatPg2;
MatPg2.Create("Origin");
MatrixLayer MatLy2 = MatPg2.Layers(0);
Matrix Mat2(MatLy2);
Mat2 = mat1;  // Mat2 contents are initially identical to the original mat1

MatrixPage MatPg3;
MatPg3.Create("Origin");
MatrixLayer MatLy3 = MatPg3.Layers(0);
Matrix Mat3(MatLy3);
Mat3 = mat2; // This is used to multiply on Mat2

rc=mat1.DotMultiply( mat2 );  // Multiply mat2 to mat1
if(!rc)
printf("  Error: DotMultiply on %s by %s failed.\n",
Mat2.GetName(),Mat3.GetName());
else
{
Mat2 = mat1;
printf("  The result of multiplication by %s is %s.\n",
Mat3.GetName(),Mat2.GetName());
}
}

EX3

// Element-wise multiplication of two matrices - Error case
void matrixbase_DotMultiply_ex3()
{
matrix<double> mat1 = {
{1,  2,  3},
{4,  5,  6}
};

matrix<double> mat2 = {
{ 1, 0, -1}
};

MatrixPage MatPg1;
MatPg1.Create("Origin");
MatrixLayer MatLy1 = MatPg1.Layers(0);
Matrix Mat1(MatLy1);
Mat1 = mat1;
printf("  The original matrix is %s.\n",Mat1.GetName());

MatrixPage MatPg2;
MatPg2.Create("Origin");
MatrixLayer MatLy2 = MatPg2.Layers(0);
Matrix Mat2(MatLy2);
Mat2 = mat1;  // Mat2 contents are initially identical to the original mat1

MatrixPage MatPg3;
MatPg3.Create("Origin");
MatrixLayer MatLy3 = MatPg3.Layers(0);
Matrix Mat3(MatLy3);
Mat3 = mat2; // This is used to multiply on Mat2

int rc=mat1.DotMultiply( mat2 );    // Multiply mat2 to mat1 - they have different shapes
// No changes result on mat1. And rc will equal to 0.
if(!rc)
printf("  Error: DotMultiply on %s by %s failed.\n",
Mat2.GetName(),Mat3.GetName());
else
{
Mat2 = mat1;
printf("  The result of multiplication by %s is %s.\n",
Mat3.GetName(),Mat2.GetName());
}
}

EX4

#define MAKEMAT(X) MatrixLayer MatLy##X;MatLy##X.Create();Matrix Mat##X(MatLy##X)

void matrixbase_DotMultiply_ex4()

{
matrix mat1 = {
{1, 2, 3},
{1, 2, 3},
{1, 2, 3}
};
matrix mat2 = {
{2, 3, 4},
{3, 4, 5},
{4, 5, 6}
};

MAKEMAT(1); MAKEMAT(2); MAKEMAT(3); MAKEMAT(4);
MAKEMAT(5); MAKEMAT(6); MAKEMAT(7);

Mat1=mat1; Mat2=mat2;

Mat3=mat1*mat2;
printf("%s = %s * %s <== proper multiplication of 2    matrices\n",Mat3.GetName(),Mat1.GetName(),Mat2.GetName());

Mat4=mat1*10;
printf("%s = 10 * %s <== scalr multiplication of a   matrix\n",Mat4.GetName(),Mat1.GetName());

Mat5=mat1;
Mat5.DotMultiply(mat2);
printf("%s = DotMultiply(%s,%s) <== element-wise multiplication of 2 matrices\n",Mat5.GetName(),Mat1.GetName(),Mat2.GetName());

Mat6=mat1;
Mat6.Cross(mat2);
printf("%s = Cross(%s,%s) <== cross product of 2 matrices\n",Mat6.GetName(),Mat1.GetName(),Mat2.GetName());

mat1.CumulativeProduct(Mat7);
printf("%s = CumulativeProduct(%s) <== cumulative product of a matrix\n",Mat7.GetName(),Mat1.GetName());
}

## Remark

Multiply two matrices element by element placing the result in this matrix. The underlying base type of the matrix passed as an argument must be "less than or equal" to the underlying base type of this matrix. The matrices must have the same size.

Note

The following is a summary of various matrix operations:

1) Multiplication:

1-1) * ... Proper multiplication of 2 matrices (mat1*mat2)

1-2) * ... Scaler multiplication of a matrix (mat1*A or A*mat1)

1-3) DotMultiply ... Element-wise multiplication of 2 matrices

1-4) Cross ... Cross product of 2 matrices

1-5) CumulativeProduct ... cumulative product of a matrix

2) Division:

2-1) / ... Not defined for 2 matrices. For proper division, multiply Inverse(mat1)

2-2) / ... Scaler division of a matrix (mat1/A)

2-3) DotDivide ... Element-wise division of 2 matrices

3-1) + ... Element-wise addition of 2 matrices

3-2) + ... Scaler addition of a matrix (mat1+A or A+mat1)

3-3) SumColumns ... Summation of each column in a matrix

3-4) CumulativeSum ... Cumulative product of a matrix

4) Subtraction:

4-1) - ... Element-wise subtraction of 2 matrices

4-2) - ... Scaler subtraction of a matrix (mat1-A or A-mat1)

4-3) Difference ... Difference of adjacent 2 rows in a matrix (1st order differential)

5) Power:

5-1) ^ (or pow) ... Not defined as element-wise power of 2 matrices

5-2) ^ (or pow) ... Not defined as scaler power of a matrix

5-3) DotPower ... Element-wise power of 2 matrices

To depict the differences of above multiplications, try the EX3.