Class Matrix

Two-dimensional container of doubles.

Inheritance
Object
Matrix
LowerTriangularMatrix
PositiveDefiniteMatrix
UpperTriangularMatrix
Inherited Members
Namespace: Microsoft.ML.Probabilistic.Math
Assembly: Microsoft.ML.Probabilistic.dll
Syntax
[Serializable]
[DataContract]
public class Matrix : IList<double>, ICollection<double>, IReadOnlyList<double>, IReadOnlyCollection<double>, IEnumerable<double>, IEnumerable, ICloneable, SettableTo<Matrix>, CanSetAllElementsTo<double>

Constructors

Matrix()

Default constructor just used for serialization.

Declaration
protected Matrix()

Matrix(Matrix)

Copy constructor.

Declaration
public Matrix(Matrix that)
Parameters
Type Name Description
Matrix that

Matrix(Double[,])

Construct a matrix from data in a 2D array.

Declaration
[Construction(new string[]{"ToArray"})]
public Matrix(double[, ] data)
Parameters
Type Name Description
Double[,] data

2D array of elements.
Remarks

The 2D array is copied into new storage. The size of the matrix is taken from the array.

Matrix(Int32, Int32)

Construct a zero matrix of the given dimensions.

Declaration
public Matrix(int rows, int cols)
Parameters
Type Name Description
Int32 rows

Number of rows >= 0.
Int32 cols

Number of columns >= 0.

Matrix(Int32, Int32, Double[])

Construct a matrix by referencing an array.

Declaration
public Matrix(int nRows, int nCols, double[] data)
Parameters
Type Name Description
Int32 nRows

Number of rows.
Int32 nCols

Number of columns.
Double[] data

Storage for the matrix elements.

Fields

cols

Declaration
[DataMember]
protected readonly int cols
Field Value
Type Description
Int32

data

Declaration
[DataMember]
protected double[] data
Field Value
Type Description
Double[]

rows

Declaration
[DataMember]
protected readonly int rows
Field Value
Type Description
Int32

Properties

Cols

The number of columns of the matrix.

Declaration
public int Cols { get; }
Property Value
Type Description
Int32

Count

Number of elements in the matrix

Declaration
public int Count { get; }
Property Value
Type Description
Int32

Item[Int32]

Gets and sets an element.

Declaration
public double this[int index] { get; set; }
Parameters
Type Name Description
Int32 index
Property Value
Type Description
Double

Item[Int32, Int32]

Gets and sets an element.

Declaration
public double this[int row, int col] { get; set; }
Parameters
Type Name Description
Int32 row
Int32 col
Property Value
Type Description
Double

Rows

The number of rows of the matrix.

Declaration
public int Rows { get; }
Property Value
Type Description
Int32

SourceArray

Gets/sets the matrix's source array

Declaration
[IgnoreDataMember]
public double[] SourceArray { get; set; }
Property Value
Type Description
Double[]

Methods

CheckCompatible(Matrix, String)

Checks that a given matrix is the same size as this matrix. Throws an exception if not with the given string

Declaration
protected void CheckCompatible(Matrix that, string paramName)
Parameters
Type Name Description
Matrix that

The matrix to check
String paramName

CheckSymmetry(String)

Checks this matrix for symmetry

Declaration
[Conditional("DEBUG")]
public void CheckSymmetry(string paramName)
Parameters
Type Name Description
String paramName

Clone()

Fully clones this matrix

Declaration
public virtual object Clone()
Returns
Type Description
Object

Commutation(Int32, Int32)

Magnus and Neudecker's commutation matrix for a given size matrix

Declaration
public static Matrix Commutation(int rows, int cols)
Parameters
Type Name Description
Int32 rows
Int32 cols
Returns
Type Description
Matrix

The commutation matrix of size rowscols by rowscols

Contains(Double)

Returns true if this matrix contains the given value

Declaration
public bool Contains(double item)
Parameters
Type Name Description
Double item
Returns
Type Description
Boolean

CopyTo(Double[], Int32)

Copies the values in this matrix to an array starting at a given index in the destination array

Declaration
public void CopyTo(double[] array, int index)
Parameters
Type Name Description
Double[] array
Int32 index

CopyTo(Double[,])

Copies matrix values to a two-dimensional array.

Declaration
public void CopyTo(double[, ] values)
Parameters
Type Name Description
Double[,] values

An array whose GetLength(0) >= Rows and GetLength(1) >= Cols.

Determinant()

Determinant of a square matrix

Declaration
public double Determinant()
Returns
Type Description
Double

The determinant

Diagonal()

Creates a vector from the diagonal values in the matrix

Declaration
public Vector Diagonal()
Returns
Type Description
Vector

DiagonalOfProduct(Matrix, Matrix)

The diagonal elements of a matrix product.

Declaration
public static Vector DiagonalOfProduct(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

A matrix of size n by m.
Matrix b

A matrix of size m by n.
Returns
Type Description
Vector

v[i] = sum_k a[i,k]*b[k,i]

EigenvaluesInPlace(Double[], Double[])

Compute the eigenvalues of a square matrix, destroying the contents of the matrix.

Declaration
public void EigenvaluesInPlace(double[] eigenvaluesReal, double[] eigenvaluesImag)
Parameters
Type Name Description
Double[] eigenvaluesReal

On output, the real part of the eigenvalues.
Double[] eigenvaluesImag

On output, the imaginary part of the eigenvalues.

EnumerateDiagonal()

Enumerator which yields the diagonal elements of the matrix

Declaration
public IEnumerable<double> EnumerateDiagonal()
Returns
Type Description
IEnumerable<Double>

Equals(Object)

Object comparator.

Declaration
public override bool Equals(object obj)
Parameters
Type Name Description
Object obj

An object - must be an IntMatrix.
Returns
Type Description
Boolean

True if objects are equal.
Overrides

EqualsAll(Double)

Tests if all elements are equal to a given value.

Declaration
public bool EqualsAll(double value)
Parameters
Type Name Description
Double value

The value to test against.
Returns
Type Description
Boolean

True if all elements are equal to value.

FromArray(Double[,])

Construct a matrix from data in a 2D array.

Declaration
public static Matrix FromArray(double[, ] data)
Parameters
Type Name Description
Double[,] data

2D array of elements.
Returns
Type Description
Matrix
Remarks

The 2D array is copied into new storage. The size of the matrix is taken from the array.

FromDiagonal(Vector)

Creates a new diagonal matrix with diagonal values specified in the given vector

Declaration
public static Matrix FromDiagonal(Vector diag)
Parameters
Type Name Description
Vector diag
Returns
Type Description
Matrix

GetColumn(Int32)

Returns the specified column as an array of doubles

Declaration
public double[] GetColumn(int col)
Parameters
Type Name Description
Int32 col
Returns
Type Description
Double[]

GetEnumerator()

Gets a typed enumerator for this matrix

Declaration
public IEnumerator<double> GetEnumerator()
Returns
Type Description
IEnumerator<Double>

GetHashCode()

Hash code generator.

Declaration
public override int GetHashCode()
Returns
Type Description
Int32

The hash code for the instance.
Overrides

GetRow(Int32)

Returns the specified row as an array of doubles

Declaration
public double[] GetRow(int row)
Parameters
Type Name Description
Int32 row
Returns
Type Description
Double[]

Identity(Int32)

Creates an identity matrix of the specified size

Declaration
public static Matrix Identity(int dimension)
Parameters
Type Name Description
Int32 dimension
Returns
Type Description
Matrix

IdentityScaledBy(Int32, Double)

Creates an identity matrix of the specified size, scaled by the specified value

Declaration
public static Matrix IdentityScaledBy(int dimension, double scale)
Parameters
Type Name Description
Int32 dimension
Double scale
Returns
Type Description
Matrix

IndexOf(Double)

Returns the first index of the given item if it exists in the matrix, otherwise returns -1

Declaration
public int IndexOf(double item)
Parameters
Type Name Description
Double item
Returns
Type Description
Int32

Inner(Matrix)

Inner product of matrices.

Declaration
public double Inner(Matrix A)
Parameters
Type Name Description
Matrix A

A matrix with the same size as this.
Returns
Type Description
Double

sum_ij A[i,j]*this[i,j].

Inverse()

Return the inverse of this matrix - not implemented yet

Declaration
public Matrix Inverse()
Returns
Type Description
Matrix

IsPositiveDefinite()

Tests for positive-definiteness.

Declaration
public bool IsPositiveDefinite()
Returns
Type Description
Boolean

True if the matrix is positive-definite, i.e. all eigenvalues > 0.

Kronecker(Matrix)

Kronecker product with another matrix.

Declaration
public Matrix Kronecker(Matrix A)
Parameters
Type Name Description
Matrix A
Returns
Type Description
Matrix

The Kronecker product

MaxDiff(Matrix)

Returns the maximum absolute difference between matrix elements.

Declaration
public double MaxDiff(Matrix that)
Parameters
Type Name Description
Matrix that

The second matrix.
Returns
Type Description
Double

max(abs(this[i,j] - that[i,j])).
Matching infinities or NaNs do not count.
If this and that are not the same size, returns infinity.
Remarks

This routine is typically used instead of Equals, since Equals is susceptible to roundoff errors.

MaxDiff(Matrix, Double)

Returns the maximum relative difference between matrix elements.

Declaration
public double MaxDiff(Matrix that, double rel)
Parameters
Type Name Description
Matrix that

The second matrix.
Double rel

An offset to avoid division by zero.
Returns
Type Description
Double

max(abs(this[i,j] - that[i,j])/(abs(this[i,j]) + rel)).
Matching infinities or NaNs do not count.
If this and that are not the same size, returns infinity.
Remarks

This routine is typically used instead of Equals, since Equals is susceptible to roundoff errors.

Median()

Returns the median of the values in the matrix

Declaration
public double Median()
Returns
Type Description
Double

Outer()

Returns the product of this matrix and its transpose

Declaration
public PositiveDefiniteMatrix Outer()
Returns
Type Description
PositiveDefiniteMatrix

OuterTranspose()

Returns the transpose of this matrix times this matrix

Declaration
public PositiveDefiniteMatrix OuterTranspose()
Returns
Type Description
PositiveDefiniteMatrix

Parse(String)

Parse a string (in the format produced by ToString) to recover a Matrix

Declaration
public static Matrix Parse(string s)
Parameters
Type Name Description
String s

The string to parse
Returns
Type Description
Matrix

A matrix

PredivideBy(LowerTriangularMatrix)

Gets the solution to AX=B, where A is a lower triangular matrix. Equivalent to the left-division X = A\B.

Declaration
public Matrix PredivideBy(LowerTriangularMatrix A)
Parameters
Type Name Description
LowerTriangularMatrix A

A lower triangular matrix with A.Rows == this.Rows. Cannot be this.
Returns
Type Description
Matrix

this
Remarks

this is used as the right-hand side matrix B, and it also receives the solution. Throws an exception if A is singular.

PredivideBy(PositiveDefiniteMatrix)

Premultiply this matrix by the inverse of the given positive definite matrix

Declaration
public Matrix PredivideBy(PositiveDefiniteMatrix A)
Parameters
Type Name Description
PositiveDefiniteMatrix A
Returns
Type Description
Matrix

PredivideBy(UpperTriangularMatrix)

Gets the solution to AX=B, where A is an upper triangular matrix and B is a matrix of right-hand sides. It is equivalent to the left-division X = A\B.

Declaration
public Matrix PredivideBy(UpperTriangularMatrix A)
Parameters
Type Name Description
UpperTriangularMatrix A

An upper triangular matrix with A.Rows == this.Rows. Cannot be this.
Returns
Type Description
Matrix

this
Remarks

this is used as the right-hand side matrix B, and it also receives the solution. Throws an exception if A is singular.

PredivideByTranspose(LowerTriangularMatrix)

Gets the solution to A'X=B, where A is a lower triangular matrix. Equivalent to the left-division X = A'\B.

Declaration
public Matrix PredivideByTranspose(LowerTriangularMatrix A)
Parameters
Type Name Description
LowerTriangularMatrix A

A lower triangular matrix with A.Cols == this.Rows. Cannot be this.
Returns
Type Description
Matrix

this
Remarks

this is used as the right-hand side matrix B, and it also receives the solution. Throws an exception if A is singular.

QuadraticForm(Vector)

Evaluates the product x'Ax (where ' is transposition).

Declaration
public double QuadraticForm(Vector x)
Parameters
Type Name Description
Vector x

A vector whose length equals Rows.
Returns
Type Description
Double

The above product.
Remarks

this must be a square matrix with Rows == x.Count.

QuadraticForm(Vector, Vector)

Evaluates the product x'Ay (where ' is transposition).

Declaration
public double QuadraticForm(Vector x, Vector y)
Parameters
Type Name Description
Vector x

A vector whose length equals Rows.
Vector y

A vector whose length equals Cows.
Returns
Type Description
Double

The above product.

RowVector(Int32)

A row of the matrix.

Declaration
public Vector RowVector(int row)
Parameters
Type Name Description
Int32 row

An integer in [0,Rows-1].
Returns
Type Description
Vector

If colStride == 1, then a Vector object pointing at one row of this matrix. Otherwise a copy of the row.

Scale(Double)

Multiplies this matrix by a scalar.

Declaration
public Matrix Scale(double scale)
Parameters
Type Name Description
Double scale

The scalar.
Returns
Type Description
Matrix

this
Remarks

this receives the product. This method is a synonym for SetToProduct(this, scale)

ScaleCols(Vector)

Multiplies each column of this matrix by a different scalar.

Declaration
public Matrix ScaleCols(Vector colScale)
Parameters
Type Name Description
Vector colScale

The ith element scales column i.
Returns
Type Description
Matrix

this
Remarks

this receives the product.

ScaleRows(Vector)

Multiplies each row of this matrix by a different scalar.

Declaration
public Matrix ScaleRows(Vector rowScale)
Parameters
Type Name Description
Vector rowScale

The ith element scales row i.
Returns
Type Description
Matrix

this
Remarks

this receives the product.

SetAllElementsTo(Double)

Sets all elements to a given value.

Declaration
public void SetAllElementsTo(double value)
Parameters
Type Name Description
Double value

The new value.

SetDiagonal(Vector)

Sets the diagonal elements to the values specified in the given vector

Declaration
public Matrix SetDiagonal(Vector diag)
Parameters
Type Name Description
Vector diag
Returns
Type Description
Matrix

SetSubmatrix(Int32, Int32, Matrix)

Set a submatrix of this matrix to match another matrix.

Declaration
public void SetSubmatrix(int firstRow, int firstColumn, Matrix that)
Parameters
Type Name Description
Int32 firstRow

Index of the first row in this to copy to.
Int32 firstColumn

Index of the first column in this to copy to.
Matrix that

Size is at most this.Rows-thisRow by this.Cols-thisColumn.

SetSubmatrix(Int32, Int32, Matrix, Int32, Int32, Int32, Int32)

Sets a submatrix of this matrix to match another matrix.

Declaration
public void SetSubmatrix(int thisRow, int thisColumn, Matrix that, int thatRow, int thatColumn, int numRows, int numColumns)
Parameters
Type Name Description
Int32 thisRow

Index of the first row in this to copy to.
Int32 thisColumn

Index of the first column in this to copy to.
Matrix that

Size is at most this.Rows-firstRow by this.Cols-firstColumn.
Int32 thatRow

Index of the first row in that to copy.
Int32 thatColumn

Index of the first column in that to copy.
Int32 numRows

The number of rows to copy
Int32 numColumns

The number of columns to copy

SetTo(Matrix)

Copies values from another matrix.

Declaration
public void SetTo(Matrix that)
Parameters
Type Name Description
Matrix that

The second matrix, which must have the same size as this.

SetTo(Double[])

Copies values from an array.

Declaration
public void SetTo(double[] values)
Parameters
Type Name Description
Double[] values

An array whose length is at least this.Count.

SetTo(Double[], Int32)

Copies values from an array.

Declaration
public void SetTo(double[] values, int startIndex)
Parameters
Type Name Description
Double[] values

An array whose length is at least this.Count + startIndex.
Int32 startIndex

The index of the first value in values.

SetTo(Double[,])

Copies values from a two-dimensional array.

Declaration
public void SetTo(double[, ] values)
Parameters
Type Name Description
Double[,] values

An array whose GetLength(0) >= Rows and GetLength(1) >= Cols.

SetToDiagonal(Vector)

Sets this matrix to a diagonal matrix with diagonal values specified in the given vector

Declaration
public Matrix SetToDiagonal(Vector diag)
Parameters
Type Name Description
Vector diag
Returns
Type Description
Matrix

SetToDifference(Matrix, Matrix)

Sets this matrix to the difference of two matrices. Assumes compatible matrices.

Declaration
public Matrix SetToDifference(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix, which must have the same size as this.
Matrix b

Second matrix, which must have the same size as this.
Returns
Type Description
Matrix

this
Remarks

this receives the difference, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToDifference(Matrix, Double, Matrix)

Sets this matrix to a - bScale*b

Declaration
public Matrix SetToDifference(Matrix a, double bScale, Matrix b)
Parameters
Type Name Description
Matrix a
Double bScale
Matrix b
Returns
Type Description
Matrix

SetToEigenvectorsOfSymmetric(Matrix)

Set the columns to the eigenvectors of a symmetric matrix, modifying the input matrix to contain its eigenvalues on the diagonal. The input matrix = this'modifiedthis.

Declaration
public void SetToEigenvectorsOfSymmetric(Matrix symmetricMatrix)
Parameters
Type Name Description
Matrix symmetricMatrix

A symmetric matrix, modified on return to contain its eigenvalues on the diagonal

SetToElementwiseProduct(Matrix, Matrix)

The element-wise product of two matrices.

Declaration
public Matrix SetToElementwiseProduct(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix, which must have the same size as this.
Matrix b

Second matrix, which must have the same size as this.
Returns
Type Description
Matrix

this
Remarks

this[i,j] = a[i,j] * b[i,j]. this receives the product, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToElementwiseRatio(Matrix, Matrix)

The element-wise ratio of two matrices.

Declaration
public Matrix SetToElementwiseRatio(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix, which must have the same size as this.
Matrix b

Second matrix, which must have the same size as this.
Returns
Type Description
Matrix

this
Remarks

this[i,j] = a[i,j] / b[i,j]. this receives the ratio, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToIdentity()

Sets the matrix to the identity.

Declaration
public Matrix SetToIdentity()
Returns
Type Description
Matrix

The mutated matrix.
Remarks

The matrix must be square.

SetToIdentityScaledBy(Double)

Sets the matrix to the identity times a number.

Declaration
public Matrix SetToIdentityScaledBy(double scale)
Parameters
Type Name Description
Double scale
Returns
Type Description
Matrix

The mutated matrix.
Remarks

The matrix must be square.

SetToKronecker(Matrix, Matrix)

Set this matrix to the Kronecker product of two matrices

Declaration
public void SetToKronecker(Matrix A, Matrix B)
Parameters
Type Name Description
Matrix A
Matrix B

SetToLeastSquares(Matrix, Matrix)

Solve Y = X*A

Declaration
public double SetToLeastSquares(Matrix Y, Matrix X)
Parameters
Type Name Description
Matrix Y

Portrait matrix
Matrix X

Portrait matrix
Returns
Type Description
Double

The smallest squared singular value of X. This is useful for detecting an ill-conditioned problem.

SetToOuter(Matrix)

Modify this to be the product of a matrix and its transpose (A*A').

Declaration
public Matrix SetToOuter(Matrix A)
Parameters
Type Name Description
Matrix A

Matrix. Cannot be this.
Returns
Type Description
Matrix

this
Remarks

this receives A*A' and must already be the correct size. If this and A occupy overlapping portions of the same source array, the results are undefined.

SetToOuter(Vector, Vector)

Returns the outer product of two vectors.

Declaration
public Matrix SetToOuter(Vector a, Vector b)
Parameters
Type Name Description
Vector a

First vector, of length this.Rows.
Vector b

Second vector, of length this.Cols.
Returns
Type Description
Matrix

this
Remarks

this receives the product, and must already be the correct size. If this and a/b occupy overlapping portions of the same source array, the results are undefined.

SetToOuterTranspose(Matrix)

Modify this to be the product A'*A.

Declaration
public Matrix SetToOuterTranspose(Matrix A)
Parameters
Type Name Description
Matrix A

Matrix. Cannot be this.
Returns
Type Description
Matrix

this
Remarks

this receives A'*A and must already be the correct size. If this and A occupy overlapping portions of the same source array, the results are undefined.

SetToProduct(Matrix, Matrix)

Modify this to be the product of two matrices.

Declaration
public Matrix SetToProduct(Matrix A, Matrix B)
Parameters
Type Name Description
Matrix A

First matrix. Cannot be this.
Matrix B

Second matrix. Cannot be this.
Returns
Type Description
Matrix
Remarks

A and B must have compatible dimensions. this receives the product, and must already be the correct size. If this and A/B occupy overlapping portions of the same source array, the results are undefined.

SetToProduct(Matrix, Double)

Gets a matrix times a scalar.

Declaration
public Matrix SetToProduct(Matrix m, double s)
Parameters
Type Name Description
Matrix m

A matrix, which must have the same size as this. Can be the same object as this.
Double s

A scalar.
Returns
Type Description
Matrix
Remarks

this receives the product, and must already be the correct size.
If this and m occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToRightSingularVectors(Matrix)

Set the columns to the right singular vectors of a matrix, modifying the input matrix to contain its left singular vectors scaled by the singular values.

Declaration
public void SetToRightSingularVectors(Matrix A)
Parameters
Type Name Description
Matrix A

A portrait matrix with the same number of columns as this, modified on return to contain its left singular vectors (as columns) scaled by the singular values
Remarks

this must be a square matrix.

SetToSubmatrix(Matrix, Int32, Int32)

Sets the matrix to a submatrix of another.

Declaration
public Matrix SetToSubmatrix(Matrix that, int firstRow, int firstColumn)
Parameters
Type Name Description
Matrix that

Size must be at least this.Rows+firstRow by this.Cols+firstColumn.
Int32 firstRow

Index of the first row in that to copy.
Int32 firstColumn

Index of the first column in that to copy.
Returns
Type Description
Matrix

this

SetToSum(Matrix, Matrix)

Sets this matrix to sum of two other matrices. Assumes compatible matrices.

Declaration
public Matrix SetToSum(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix, which must have the same size as this.
Matrix b

Second matrix, which must have the same size as this.
Returns
Type Description
Matrix

this
Remarks

this[i,j] = a[i,j] + b[i,j]. this receives the sum, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToSum(Double, Matrix, Double, Matrix)

The sum of two matrices with scale factors.

Declaration
public Matrix SetToSum(double aScale, Matrix a, double bScale, Matrix b)
Parameters
Type Name Description
Double aScale

A scale factor.
Matrix a

First matrix, which must have the same size as this.
Double bScale

A scale factor.
Matrix b

Second matrix, which must have the same size as this.
Returns
Type Description
Matrix

this
Remarks

this[i,j] = aScalea[i,j] + bScaleb[i,j].

SetToSumWithOuter(Matrix, Double, Vector, Vector)

Returns a matrix plus the scaled outer product of two vectors.

Declaration
public Matrix SetToSumWithOuter(Matrix m, double scale, Vector a, Vector b)
Parameters
Type Name Description
Matrix m

A matrix with the same size as this. Can be this.
Double scale
Vector a

A vector with a.Count == this.Rows
Vector b

A vector with b.Count == this.Cols
Returns
Type Description
Matrix

this[i,j] = m[i,j] + scale*a[i]*b[j]

SetToTranspose(Matrix)

Sets the matrix to the transpose of another.

Declaration
public Matrix SetToTranspose(Matrix that)
Parameters
Type Name Description
Matrix that

The matrix to transpose. Can be the same object as this. that.Count must equal this.Count.
Returns
Type Description
Matrix

this
Remarks

this receives the transposed matrix, and must already be the correct size. If this and that are different objects but occupy overlapping portions of the same source array, the results are undefined.

Symmetrize()

Set a[i,j] to the average (a[i,j]+a[j,i])/2

Declaration
public void Symmetrize()

SymmetryError()

max | this[i,j] - this[j,i] |

Declaration
public double SymmetryError()
Returns
Type Description
Double

ToArray()

Creates a 2-D arrays from this matrix

Declaration
public double[, ] ToArray()
Returns
Type Description
Double[,]

ToString()

ToString override

Declaration
public override string ToString()
Returns
Type Description
String
Overrides

ToString(String)

Convert the matrix to a string, using a specified number format

Declaration
public string ToString(string format)
Parameters
Type Name Description
String format

The format string for each matrix entry
Returns
Type Description
String

A string

Trace()

Trace of a square matrix.

Declaration
public double Trace()
Returns
Type Description
Double

The trace.

TraceOfProduct(Matrix, Matrix)

The sum of diagonal elements of a matrix product.

Declaration
public static double TraceOfProduct(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

A matrix of size n by m.
Matrix b

A matrix of size m by n.
Returns
Type Description
Double

sum_i sum_k a[i,k]*b[k,i]

Transpose()

Transposes the matrix.

Declaration
public Matrix Transpose()
Returns
Type Description
Matrix

The transposed matrix.

Operators

Addition(Matrix, Matrix)

Returns the sum of two matrices. Assumes compatible matrices.

Declaration
public static Matrix operator +(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix.
Matrix b

Second matrix.
Returns
Type Description
Matrix

Their sum.

Division(Matrix, Double)

Divides every element of a matrix by a scalar.

Declaration
public static Matrix operator /(Matrix m, double s)
Parameters
Type Name Description
Matrix m

A matrix.
Double s

A scalar.
Returns
Type Description
Matrix

A new matrix with the ratio.

Equality(Matrix, Matrix)

Equality operator.

Declaration
public static bool operator ==(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix.
Matrix b

Second Matrix.
Returns
Type Description
Boolean

True if the matrices have the same size and element values.

Inequality(Matrix, Matrix)

Inequality operator.

Declaration
public static bool operator !=(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix.
Matrix b

Second matrix.
Returns
Type Description
Boolean

True if matrices are not equal.

Multiply(Matrix, Matrix)

Matrix product.

Declaration
public static Matrix operator *(Matrix A, Matrix B)
Parameters
Type Name Description
Matrix A

First matrix.
Matrix B

Second matrix.
Returns
Type Description
Matrix

A new matrix with their product.

Multiply(Matrix, Vector)

Premultiplies a vector by a matrix (i.e. A*x).

Declaration
public static Vector operator *(Matrix A, Vector x)
Parameters
Type Name Description
Matrix A

A matrix.
Vector x

A vector.
Returns
Type Description
Vector

A new vector with the product.

Multiply(Matrix, Double)

Multiplies every element of a matrix by a scalar.

Declaration
public static Matrix operator *(Matrix m, double s)
Parameters
Type Name Description
Matrix m

A matrix.
Double s

A scalar.
Returns
Type Description
Matrix

A new matrix with the product.

Multiply(Vector, Matrix)

Postmultiplies a vector by a matrix (i.e. x*A).

Declaration
public static Vector operator *(Vector x, Matrix A)
Parameters
Type Name Description
Vector x

A vector.
Matrix A

A matrix.
Returns
Type Description
Vector

The new vector with the product.

Subtraction(Matrix, Matrix)

Returns the difference of two matrices. Assumes compatible matrices.

Declaration
public static Matrix operator -(Matrix a, Matrix b)
Parameters
Type Name Description
Matrix a

First matrix.
Matrix b

Second matrix.
Returns
Type Description
Matrix

Their difference.

UnaryNegation(Matrix)

Returns the negation of a matrix.

Declaration
public static Matrix operator -(Matrix a)
Parameters
Type Name Description
Matrix a

The matrix to negate.
Returns
Type Description
Matrix

The negation -a.

Explicit Interface Implementations

ICollection<Double>.Add(Double)

Declaration
void ICollection<double>.Add(double item)
Parameters
Type Name Description
Double item

ICollection<Double>.Clear()

Declaration
void ICollection<double>.Clear()

ICollection<Double>.IsReadOnly

Declaration
bool ICollection<double>.IsReadOnly { get; }
Returns
Type Description
Boolean

ICollection<Double>.Remove(Double)

Declaration
bool ICollection<double>.Remove(double item)
Parameters
Type Name Description
Double item
Returns
Type Description
Boolean

IList<Double>.Insert(Int32, Double)

Declaration
void IList<double>.Insert(int index, double item)
Parameters
Type Name Description
Int32 index
Double item

IList<Double>.RemoveAt(Int32)

Declaration
void IList<double>.RemoveAt(int index)
Parameters
Type Name Description
Int32 index

IEnumerable.GetEnumerator()

Gets an enumerator for this matrix

Declaration
IEnumerator IEnumerable.GetEnumerator()
Returns
Type Description
IEnumerator

Implements

Extension Methods