Pointwise Operations

Hereinafter the following convention is used:

– small Greek letters are used to denote scalars;
– small Latin letters are used to denote vectors;
– capital Latin letters are used to denote matrices.

This topic contains the following sections:

Addition
Subtraction
Multiplication
Division
See Also

Addition

Pointwise addition operation is identical to simple addition, as it allows summing each element of the given matrix with a scalar or with the corresponding element of the other matrix.

Operation	Description	Performance
matrix-scalar pointwise addition	Adds the given scalar to each element of the matrix: In place: PointwiseAddInPlace(Double) Returning result: PointwiseAdd(Double) Out of place: PointwiseAdd(Double, Matrix)
matrix-matrix pointwise addition	Adds each element of the given matrix to the corresponding element of the defined matrix. This operation is identical to simple matrix-matrix addition. given: then: In place: PointwiseAddInPlace(Matrix) Returning result: PointwiseAdd(Matrix) Out of place: PointwiseAdd(Matrix, Matrix)

Operation

Description

Performance

matrix-scalar pointwise addition

Adds the given scalar to each element of the matrix:

In place:

method PointwiseAddInPlace(Double)

Returning result:

method PointwiseAdd(Double)

Out of place:

method PointwiseAdd(Double, Matrix)

matrix-matrix pointwise addition

Adds each element of the given matrix to the corresponding element of the defined matrix. This operation is identical to simple matrix-matrix addition.

given:

then:

In place:

method PointwiseAddInPlace(Matrix)

Returning result:

method PointwiseAdd(Matrix)

Out of place:

method PointwiseAdd(Matrix, Matrix)

Subtraction

Pointwise subtraction allows calculating the difference between each element of the given matrix and a scalar or between each element of the given matrix and the corresponding element of the other defined matrix.

Operation	Description	Performance
matrix-scalar pointwise subtraction	Subtracts the given scalar from each element of the matrix: In place: PointwiseSubtractInPlace(Double) Returning result: PointwiseSubtract(Double) Out of place: PointwiseSubtract(Double, Matrix) Subtracts each element of the vector from the given scalar: In place: PointwiseLeftSubtractInPlace(Double) Returning result: PointwiseLeftSubtract(Double) Out of place: PointwiseLeftSubtract(Double, Matrix)
matrix-matrix pointwise subtraction	Subtracts each element of the other matrix from the corresponding element of the given matrix: then: In place: PointwiseSubtractInPlace(Matrix) Returning result: PointwiseSubtract(Matrix) Out of place: PointwiseSubtract(Matrix, Matrix) Subtracts each element of the matrix from the corresponding element of another matrix: In place: PointwiseLeftSubtractInPlace(Matrix) Returning result: PointwiseLeftSubtract(Matrix) Out of place: PointwiseLeftSubtract(Matrix, Matrix)

Operation

Description

Performance

matrix-scalar pointwise subtraction

Subtracts the given scalar from each element of the matrix:

In place:

method PointwiseSubtractInPlace(Double)

Returning result:

method PointwiseSubtract(Double)

Out of place:

method PointwiseSubtract(Double, Matrix)

Subtracts each element of the vector from the given scalar:

In place:

method PointwiseLeftSubtractInPlace(Double)

Returning result:

method PointwiseLeftSubtract(Double)

Out of place:

method PointwiseLeftSubtract(Double, Matrix)

matrix-matrix pointwise subtraction

Subtracts each element of the other matrix from the corresponding element of the given matrix:

then:

In place:

method PointwiseSubtractInPlace(Matrix)

Returning result:

method PointwiseSubtract(Matrix)

Out of place:

method PointwiseSubtract(Matrix, Matrix)

Subtracts each element of the matrix from the corresponding element of another matrix:

In place:

method PointwiseLeftSubtractInPlace(Matrix)

Returning result:

method PointwiseLeftSubtract(Matrix)

Out of place:

method PointwiseLeftSubtract(Matrix, Matrix)

Multiplication

Pointwise multiplication provides multiplying each element of the given matrix by a scalar or by the corresponding element of another given matrix.

Operation	Description	Performance
matrix-scalar pointwise multiplication	Multiplies each element of the matrix by the given scalar: In place: PointwiseMultiplyInPlace(Double) Returning result: PointwiseMultiply(Double) Out of place: PointwiseMultiply(Double, Matrix)
matrix-matrix pointwise multiplication	Multiplies each element of the given matrix by the corresponding element of another given matrix: Given two matrices: the result will be: In place: PointwiseMultiplyInPlace(Matrix) Returning result: PointwiseMultiply(Matrix) Out of place: PointwiseMultiply(Matrix, Matrix)

Operation

Description

Performance

matrix-scalar pointwise multiplication

Multiplies each element of the matrix by the given scalar:

In place:

method PointwiseMultiplyInPlace(Double)

Returning result:

method PointwiseMultiply(Double)

Out of place:

method PointwiseMultiply(Double, Matrix)

matrix-matrix pointwise multiplication

Multiplies each element of the given matrix by the corresponding element of another given matrix:

Given two matrices:

the result will be:

In place:

method PointwiseMultiplyInPlace(Matrix)

Returning result:

method PointwiseMultiply(Matrix)

Out of place:

method PointwiseMultiply(Matrix, Matrix)

Division

Division of each element of the matrix by a scalar or by the corresponding element of the second matrix.

Operation	Description	Performance
matrix-scalar pointwise division	Divides each element of this matrix by the given scalar: In place: PointwiseDivideInPlace(Double) Returning result: PointwiseDivide(Double) Out of place: PointwiseDivide(Double, Matrix) Divides a given scalar by each element of this matrix: In place: PointwiseLeftDivideInPlace(Double) Returning result: PointwiseLeftDivide(Double) Out of place: PointwiseLeftDivide(Double, Matrix)
matrix-matrix pointwise division	Divides each element of this matrix by the corresponding element of the other matrix: Given two matrices: the result will be: In place: PointwiseDivideInPlace(Matrix) Returning result: PointwiseDivide(Matrix) Out of place: PointwiseDivide(Matrix, Matrix) Divides each element of the second matrix by the corresponding element of this matrix: In place: PointwiseLeftDivideInPlace(Matrix) Returning result: PointwiseLeftDivide(Matrix) Out of place: PointwiseLeftDivide(Matrix, Matrix)

Operation

Description

Performance

matrix-scalar pointwise division

Divides each element of this matrix by the given scalar: