LMatrix Structure

Represents a lower triangular matrix.

Inheritance Hierarchy

SystemObject
SystemValueType
Austra.LibraryLMatrix

Namespace: Austra.Library
Assembly: Austra.Library (in Austra.Library.dll) Version: 2.7.0+b25929339ea1019e260029cf0ebd18b3a0ce2443

Syntax

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public readonly struct LMatrix : IFormattable, 
	IEquatable<LMatrix>, IEqualityOperators<LMatrix, LMatrix, bool>, 
	IEqualityOperators<LMatrix, RMatrix, bool>, IEqualityOperators<LMatrix, Matrix, bool>, 
	IAdditionOperators<LMatrix, LMatrix, LMatrix>, IAdditionOperators<LMatrix, RMatrix, Matrix>, 
	IAdditionOperators<LMatrix, double, LMatrix>, ISubtractionOperators<LMatrix, LMatrix, LMatrix>, 
	ISubtractionOperators<LMatrix, RMatrix, Matrix>, ISubtractionOperators<LMatrix, double, LMatrix>, 
	IMultiplyOperators<LMatrix, Matrix, Matrix>, IMultiplyOperators<LMatrix, DVector, DVector>, 
	IMultiplyOperators<LMatrix, double, LMatrix>, IDivisionOperators<LMatrix, double, LMatrix>, 
	IUnaryNegationOperators<LMatrix, LMatrix>, IMatrix

The LMatrix type exposes the following members.

Constructors

	Name	Description
	LMatrix(DVector)	Creates a diagonal matrix given its diagonal.
	LMatrix(Int32)	Creates an empty square matrix.
	LMatrix(Int32, NormalRandom)	Creates a squared matrix with a standard normal distribution.
	LMatrix(Int32, Int32)	Creates an empty rectangular matrix.
	LMatrix(Int32, Random)	Creates a square lower matrix filled with a uniform distribution generator.
	LMatrix(Int32, Int32, NormalRandom)	Creates a matrix filled with a standard normal distribution.
	LMatrix(Int32, Int32, Double)	Creates a matrix with a given number of rows and columns, and its internal array.
	LMatrix(Int32, Int32, Random)	Creates a matrix filled with a uniform distribution generator.
	LMatrix(Int32, Random, Double, Double)	Creates a square matrix filled with a uniform distribution generator.
	LMatrix(Int32, Int32, Random, Double, Double)	Creates a matrix filled with a uniform distribution generator.

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Properties

	Name	Description
	Cols	Gets the number of columns.
	IsInitialized	Has the matrix been properly initialized?
	IsSquare	Checks if the matrix is a square one.
	Item	Gets the value at a single cell.
	Rows	Gets the number of rows.

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Methods

	Name	Description
	AMax	Gets the cell with the maximum absolute value.
	AMin	Gets the cell with the minimum absolute value.
	Clone	Creates an identical lower triangular matrix.
	Contains	Checks if the matrix contains the given value.
	Determinant	Gets the determinant of the matrix.
	Diagonal	Gets the main diagonal.
	Equals(LMatrix)	Checks if the provided argument is a matrix with the same values.
	Equals(Object)	Checks if the provided argument is a matrix with the same values. (Overrides ValueTypeEquals(Object))
	GetHashCode	Returns the hashcode for this matrix. (Overrides ValueTypeGetHashCode)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	Identity	Creates an identity matrix given its size.
	Inverse	Calculates the inverse of the matrix.
	Maximum	Gets the cell with the maximum value.
	Minimum	Gets the cell with the minimum value.
	MultiplyAdd(DVector, DVector)	Transforms a vector and adds an offset.
	MultiplyAdd(DVector, DVector, Double)	Transforms a vector and adds an offset.
	MultiplySubtract(DVector, DVector)	Transforms a vector and subtracts an offset.
	MultiplySubtract(DVector, DVector, Double)	Transforms a vector and subtracts an offset.
	MultiplyTranspose	Multiplies this matrix by the transposed argument.
	Redim(Int32)	Creates a new matrix with different dimensions.
	Redim(Int32, Int32)	Creates a new matrix with different dimensions.
	Solve(DVector)	Solves the equation Ax = b for x.
	Solve(DVector, DVector)	Solves the equation Ax = b for x.
	Square	Multiplies this matrix by its own transposed.
	Stats	Gets statistics on the matrix cells.
	Sum	Calculates the sum of the matrix cells.
	ToString	Gets a textual representation of this matrix. (Overrides ValueTypeToString)
	ToString(String, IFormatProvider)	Gets a textual representation of this matrix.
	Trace	Calculates the trace of a matrix.
	Transpose	Transposes the matrix.

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Operators

	Name	Description
	Addition(Double, LMatrix)	Adds a scalar value to a lower triangular matrix.
	Addition(LMatrix, LMatrix)	Sums two lower matrices with the same size.
	Addition(LMatrix, RMatrix)	Adds a lower-triangular matrix and an upper-triangular one.
	Addition(LMatrix, Double)	Adds a scalar value to a lower triangular matrix.
	Division(DVector, LMatrix)	Solves the equation m*x = v for the vector x.
	Division(LMatrix, Double)	Divides a matrix by a scalar value.
	Division(Matrix, LMatrix)	Solves the equation m2*x = m1 for the matrix x.
	Equality(LMatrix, LMatrix)	Checks two matrices for equality.
	Equality(LMatrix, Matrix)	Checks two matrices for equality.
	Equality(LMatrix, RMatrix)	Checks two matrices for equality.
	(LMatrix to Matrix)	Explicit conversion from a triangular matrix to a rectangular one.
	(LMatrix to Double)	Explicit conversion from a matrix to a onedimensional array.
	(Matrix to LMatrix)	Implicit conversion from a rectangular to a lower triangular matrix.
	Inequality(LMatrix, LMatrix)	Checks two matrices for inequality.
	Inequality(LMatrix, Matrix)	Checks two matrices for inequality.
	Inequality(LMatrix, RMatrix)	Checks two matrices for inequality.
	Multiply(Double, LMatrix)	Multiplies a lower triangular matrix by a scalar value.
	Multiply(LMatrix, DVector)	Transform a vector using a matrix.
	Multiply(LMatrix, LMatrix)	Multiplies two lower-triangular matrices.
	Multiply(LMatrix, Matrix)	Multiplies a lower triangular matrix by a rectangular one.
	Multiply(LMatrix, RMatrix)	Multiplies a lower-triangular matrix with an upper-triangular one.
	Multiply(LMatrix, Double)	Multiplies a lower triangular matrix by a scalar value.
	Multiply(Matrix, LMatrix)	Multiplies a rectangular matrix by a lower triangular one.
	Multiply(RMatrix, LMatrix)	Multiplies an upper-triangular matrix with a lower-triangular one.
	Subtraction(Double, LMatrix)	Subtracts a lower triangular matrix from a scalar value.
	Subtraction(LMatrix, LMatrix)	Subtracts two lower matrices with the same size.
	Subtraction(LMatrix, RMatrix)	Subtracts an upper triangular matrix from a lower triangular one.
	Subtraction(LMatrix, Double)	Subtracts a scalar value from a lower triangular matrix.
	UnaryNegation(LMatrix)	Negates a lower matrix.

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Remarks

Having a separate type for lower-triangular matrices is not a matter of storage, but of semantics. For instance, the Cholesky factorization always returns either a lower or upper triangular matrix, so it's important for the API to make clear which type of matrix is returning.

Lower-triangular matrices may have a different number of rows and columns.

Reference

Austra.Library Namespace