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@tdajs/normal-form

Index

Reduction Classes

Elementary Operations Interfaces

Normal Form Interfaces

Elementary Operations Functions

Other Functions

Utility Functions

Elementary Operations Functions

exchangeCols

  • exchangeCols(j: number, k: number, mat: number[][], options?: Options): [result: number[][], E: number[][], Einv: number[][]]

  • Performs the elementary column operation to exchanges the j-th and k-th columns of a matrix.

    Parameters

    • j: number
    • k: number

      index of the column to be exchanged

    • mat: number[][]

      matrix to perform the operation on

    • Optional options: Options

      optional arguments; see Options for more details

    Returns [result: number[][], E: number[][], Einv: number[][]]

    array of three matrices. The first matrix is the resultant matrix and the last two are the corresponding elementary matrix and its inverse (if changeBase: true is set in the options).

exchangeRows

  • exchangeRows(i: number, k: number, mat: number[][], options?: Options): [result: number[][], E: number[][], Einv: number[][]]

  • Performs the elementary row operation to exchanges the i-th and k-th rows of a matrix.

    Parameters

    • i: number

      index of the row to be exchanged

    • k: number

      index of the row to be exchanged

    • mat: number[][]

      matrix to perform the operation on

    • Optional options: Options

      optional arguments; see Options for more details

    Returns [result: number[][], E: number[][], Einv: number[][]]

    array of three matrices. The first matrix is the resultant matrix and the last two are the corresponding elementary matrix and its inverse (if changeBase: true is set in the options).

multiplyCol

  • multiplyCol(j: number, q: number, mat: number[][], options?: Options): [result: number[][], E: number[][], Einv: number[][]]

  • Performs the elementary column operation to multiply the entries of the i-th column by q of a matrix.

    Parameters

    • j: number

      index of the column to be multiplied

    • q: number

      (integer) multiplier

    • mat: number[][]

      matrix to perform the operation on

    • Optional options: Options

      optional arguments; see Options for more details

    Returns [result: number[][], E: number[][], Einv: number[][]]

    array of three matrices. The first matrix is the resultant matrix and the last two are the corresponding elementary matrix and its inverse (if changeBase: true is set in the options).

multiplyRow

  • multiplyRow(i: number, q: number, mat: number[][], options?: Options): [result: number[][], E: number[][], Einv: number[][]]

  • Performs the elementary row operation to multiply the entries of the i-th row by q of a matrix.

    Parameters

    • i: number

      index of the row to be multiplied

    • q: number

      (integer) multiplier (q=+1, -1)

    • mat: number[][]

      matrix to perform the operation on

    • Optional options: Options

      optional arguments; see Options for more details

    Returns [result: number[][], E: number[][], Einv: number[][]]

    array of three matrices. The first matrix is the resultant matrix and the last two are the corresponding elementary matrix and its inverse (if changeBase: true is set in the options).

replaceCol

  • replaceCol(j: number, k: number, q: number, mat: number[][], options?: Options): [result: number[][], E: number[][], Einv: number[][]]

  • Performs the elementary column operation to replace the j-th column by q * the k-th column of a matrix.

    Parameters

    • j: number
    • k: number

      index of the other column

    • q: number

      (integer) mutiplier

    • mat: number[][]

      matrix to perform the operation on

    • Optional options: Options

      optional arguments; see Options for more details

    Returns [result: number[][], E: number[][], Einv: number[][]]

    array of three matrices. The first matrix is the resultant matrix and the last two are the corresponding elementary matrix and its inverse (if changeBase: true is set in the options).

replaceRow

  • replaceRow(i: number, k: number, q: number, mat: number[][], options?: Options): [result: number[][], E: number[][], Einv: number[][]]

  • Performs the elementary row operation to replace the i-th row by q * the k-th row of a matrix.

    Parameters

    • i: number

      index of the row to be replaced

    • k: number

      index of the other row

    • q: number

      (integer) mutiplier

    • mat: number[][]

      matrix to perform the operation on

    • Optional options: Options

      optional arguments; see Options for more details

    Returns [result: number[][], E: number[][], Einv: number[][]]

    array of three matrices. The first matrix is the resultant matrix and the last two are the corresponding elementary matrix and its inverse (if changeBase: true is set in the options).

Other Functions

findAntiPivot

  • findAntiPivot(__namedParameters: [number, number], mat: number[][], offset: number): number[]

  • Parameters

    • __namedParameters: [number, number]
    • mat: number[][]
    • offset: number

    Returns number[]

findPivot

  • findPivot(mat: number[][], offset: number): number[]

  • Parameters

    • mat: number[][]
    • offset: number

    Returns number[]

improvePivot

  • improvePivot(pivot: number[], antiPivot: number[], mat: number[][], offset?: number): number[][]

  • Parameters

    • pivot: number[]
    • antiPivot: number[]
    • mat: number[][]
    • offset: number = 0

    Returns number[][]

isZero

  • isZero(mat: number[][], offset?: number): boolean

  • Parameters

    • mat: number[][]
    • offset: number = 0

    Returns boolean

Utility Functions

changeBasis

  • changeBasis(oldBasis: string[], basechangeMat: number[][]): string[]

  • Transforms an old basis to a new basis by post multiplying by the basechange matrix.

    Parameters

    • oldBasis: string[]

      vector of basis elements

    • basechangeMat: number[][]

      basechange matrix

    Returns string[]

    vector of new basis

idMat

  • idMat(size: number): number[][]

  • Generates a copy of the identity matrix of a given size.

    Parameters

    • size: number

    Returns number[][]

    an identity matrix

mat2Tex

  • mat2Tex(mat: number[][]): string

  • Generates a string that MathJax/KaTex can use to print a matrix.

    Parameters

    • mat: number[][]

      matrix to be printed

    Returns string

    Latex/KaTex ready string

multiplyMat

  • multiplyMat(A: number[][], B: number[][]): number[][]

  • Post multiplies the matrix A by the matrix B, provided they are of compatible dimensions.

    Parameters

    • A: number[][]
    • B: number[][]

    Returns number[][]

    a new copy of the product matrix

vec2Tex

  • vec2Tex(vec: number[]): string

  • Generates a string that MathJax/KaTex can use to print a vector.

    Parameters

    • vec: number[]

      vector to be printed

    Returns string

    Latex/KaTex ready string

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