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matrix-ts

Matrix overview

A constrained matrix type. Allows for matrix/vector operations that won’t fail due to incompatible shapes

Added in v1.0.0

Table of contents

Constructors

from2dVectors

Signature

export declare const from2dVectors: <M, N, A>(ks: V.Vec<M, V.Vec<N, A>>) => Mat<M, N, A>

Added in v1.0.0

fromNestedReadonlyArrays

Signature

export declare const fromNestedReadonlyArrays: <M extends number, N extends number>(
  m: M,
  n: N
) => <A>(as: readonly (readonly A[])[]) => O.Option<Mat<M, N, A>>

Added in v1.0.0

fromNestedTuples

Signature

export declare const fromNestedTuples: {
  <A>(t: []): Mat<0, 0, A>
  <A>(t: [[A]]): Mat<1, 1, A>
  <A>(t: [[A, A]]): Mat<1, 2, A>
  <A>(t: [[A], [A]]): Mat<2, 1, A>
  <A>(t: [[A, A], [A, A]]): Mat<2, 2, A>
  <A>(t: [[A, A, A]]): Mat<1, 3, A>
  <A>(t: [[A], [A], [A]]): Mat<3, 1, A>
  <A>(t: [[A, A, A], [A, A, A]]): Mat<2, 3, A>
  <A>(t: [[A, A], [A, A], [A, A]]): Mat<3, 2, A>
  <A>(t: [[A, A, A], [A, A, A], [A, A, A]]): Mat<3, 3, A>
  <A>(t: [[A, A, A, A]]): Mat<1, 4, A>
  <A>(t: [[A], [A], [A], [A]]): Mat<4, 1, A>
  <A>(t: [[A, A, A, A], [A, A, A, A]]): Mat<2, 4, A>
  <A>(t: [[A, A], [A, A], [A, A], [A, A]]): Mat<4, 2, A>
  <A>(t: [[A, A, A, A], [A, A, A, A], [A, A, A, A]]): Mat<3, 4, A>
  <A>(t: [[A, A, A], [A, A, A], [A, A, A], [A, A, A]]): Mat<4, 3, A>
  <A>(t: [[A, A, A, A], [A, A, A, A], [A, A, A, A], [A, A, A, A]]): Mat<4, 4, A>
  <A>(t: [[A, A, A, A, A]]): Mat<1, 5, A>
  <A>(t: [[A], [A], [A], [A], [A]]): Mat<5, 1, A>
  <A>(t: [[A, A, A, A, A], [A, A, A, A, A]]): Mat<2, 5, A>
  <A>(t: [[A, A], [A, A], [A, A], [A, A], [A, A]]): Mat<5, 2, A>
  <A>(t: [[A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A]]): Mat<3, 5, A>
  <A>(t: [[A, A, A], [A, A, A], [A, A, A], [A, A, A], [A, A, A]]): Mat<5, 3, A>
  <A>(t: [[A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A]]): Mat<4, 5, A>
  <A>(t: [[A, A, A, A], [A, A, A, A], [A, A, A, A], [A, A, A, A], [A, A, A, A]]): Mat<5, 4, A>
  <A>(t: [[A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A]]): Mat<5, 5, A>
  <A>(t: [[A, A, A, A, A, A]]): Mat<1, 6, A>
  <A>(t: [[A], [A], [A], [A], [A], [A]]): Mat<6, 1, A>
  <A>(t: [[A, A, A, A, A, A], [A, A, A, A, A, A]]): Mat<2, 6, A>
  <A>(t: [[A, A], [A, A], [A, A], [A, A], [A, A], [A, A]]): Mat<6, 2, A>
  <A>(t: [[A, A, A, A, A, A], [A, A, A, A, A, A], [A, A, A, A, A, A]]): Mat<3, 6, A>
  <A>(t: [[A, A, A], [A, A, A], [A, A, A], [A, A, A], [A, A, A], [A, A, A]]): Mat<6, 3, A>
  <A>(t: [[A, A, A, A, A, A], [A, A, A, A, A, A], [A, A, A, A, A, A], [A, A, A, A, A, A]]): Mat<4, 6, A>
  <A>(t: [[A, A, A, A], [A, A, A, A], [A, A, A, A], [A, A, A, A], [A, A, A, A], [A, A, A, A]]): Mat<6, 4, A>
  <A>(t: [[A, A, A, A, A, A], [A, A, A, A, A, A], [A, A, A, A, A, A], [A, A, A, A, A, A], [A, A, A, A, A, A]]): Mat<
    5,
    6,
    A
  >
  <A>(t: [[A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A], [A, A, A, A, A]]): Mat<
    6,
    5,
    A
  >
  <A>(
    t: [
      [A, A, A, A, A, A],
      [A, A, A, A, A, A],
      [A, A, A, A, A, A],
      [A, A, A, A, A, A],
      [A, A, A, A, A, A],
      [A, A, A, A, A, A]
    ]
  ): Mat<6, 6, A>
}

Added in v1.0.0

fromVectorAsColumn

Signature

export declare const fromVectorAsColumn: <N, A>(v: V.Vec<N, A>) => Mat<N, 1, A>

Added in v1.0.0

fromVectorAsRow

Signature

export declare const fromVectorAsRow: <N, A>(v: V.Vec<N, A>) => Mat<1, N, A>

Added in v1.0.0

identity

Constructs the identity matrix

Signature

export declare const identity: <A>(R: Rng.Ring<A>) => <M extends number>(m: M) => Mat<M, M, A>

Added in v1.0.0

makeBy

Signature

export declare const makeBy: <M extends number, N extends number, A>(
  m: M,
  n: N,
  f: (a: [number, number]) => A
) => Mat<M, N, A>

Added in v1.0.0

outerProduct

Signature

export declare const outerProduct: <A>(
  R: Rng.Ring<A>
) => <M extends number, N extends number>(v1: V.Vec<M, A>, v2: V.Vec<N, A>) => Mat<M, N, A>

Added in v1.0.0

randMatrix

Signature

export declare const randMatrix: <M extends number, N extends number, A>(
  m: M,
  n: N,
  make: IO.IO<A>
) => IO.IO<Mat<M, N, A>>

Added in v1.0.0

repeat

Signature

export declare const repeat: <A>(a: A) => <M extends number, N extends number>(m: M, n: N) => Mat<M, N, A>

Added in v1.0.0

vand

Constructs a Vandermonde matrix from a vector. Note: Terms is inclusive of the first column of ones. So a quadratic Vandermonde matrix has 3 terms.

Signature

export declare const vand: <N extends number>(terms: N) => <M extends number>(t: V.Vec<M, number>) => Mat<M, N, number>

Added in v1.1.0

Destructors

shape

Signature

export declare const shape: <M extends number, N extends number, A>(m: Mat<M, N, A>) => [M, N]

Added in v1.0.0

toNestedArrays

Signature

export declare const toNestedArrays: <M, N, A>(m: Mat<M, N, A>) => A[][]

Added in v1.0.0

toNestedReadonlyArrays

Signature

export declare const toNestedReadonlyArrays: <M, N, A>(m: Mat<M, N, A>) => readonly (readonly A[])[]

Added in v1.0.0

Instance Operations

foldMap

Signature

export declare const foldMap: <M>(M: Mn.Monoid<M>) => <N, O, A>(f: (a: A) => M) => (fa: Mat<N, O, A>) => M

Added in v1.0.0

foldMapWithIndex

Signature

export declare const foldMapWithIndex: <M>(
  M: Mn.Monoid<M>
) => <N, O, A>(f: (i: [number, number], a: A) => M) => (fa: Mat<N, O, A>) => M

Added in v1.0.0

map

Signature

export declare const map: <M, N, A, B>(f: (a: A) => B) => (v: Mat<M, N, A>) => Mat<M, N, B>

Added in v1.0.0

mapWithIndex

Signature

export declare const mapWithIndex: <M, N, A, B>(
  f: (ij: [number, number], a: A) => B
) => (v: Mat<M, N, A>) => Mat<M, N, B>

Added in v1.0.0

reduce

Signature

export declare const reduce: <M, N, A, B>(b: B, f: (b: B, a: A) => B) => (fa: Mat<M, N, A>) => B

Added in v1.0.0

reduceRight

Signature

export declare const reduceRight: <M, N, B, A>(b: A, f: (b: B, a: A) => A) => (fa: Mat<M, N, B>) => A

Added in v1.0.0

reduceRightWithIndex

Signature

export declare const reduceRightWithIndex: <M, N, B, A>(
  b: A,
  f: (i: [number, number], b: B, a: A) => A
) => (fa: Mat<M, N, B>) => A

Added in v1.0.0

reduceWithIndex

Signature

export declare const reduceWithIndex: <M, N, A, B>(
  b: B,
  f: (i: [number, number], b: B, a: A) => B
) => (fa: Mat<M, N, A>) => B

Added in v1.0.0

sequence

Signature

export declare function sequence<F extends URIS4>(
  F: Apl.Applicative4<F>
): <S, R, E, A, M, N>(ta: Mat<M, N, Kind4<F, S, R, E, A>>) => Kind4<F, S, R, E, Mat<M, N, A>>
export declare function sequence<F extends URIS3>(
  F: Apl.Applicative3<F>
): <R, E, A, M, N>(ta: Mat<M, N, Kind3<F, R, E, A>>) => Kind3<F, R, E, Mat<M, N, A>>
export declare function sequence<F extends URIS2>(
  F: Apl.Applicative2<F>
): <E, A, M, N>(ta: Mat<M, N, Kind2<F, E, A>>) => Kind2<F, E, Mat<M, N, A>>
export declare function sequence<F extends URIS>(
  F: Apl.Applicative1<F>
): <A, M, N>(ta: Mat<M, N, Kind<F, A>>) => Kind<F, Mat<M, N, A>>

Added in v1.0.0

traverse

Signature

export declare function traverse<F extends URIS4>(
  F: Apl.Applicative4<F>
): <S, R, E, A, B>(f: (a: A) => Kind4<F, S, R, E, B>) => <M, N>(ta: Mat<M, N, A>) => Kind4<F, S, R, E, Mat<M, N, B>>
export declare function traverse<F extends URIS3>(
  F: Apl.Applicative3<F>
): <R, E, A, B>(f: (a: A) => Kind3<F, R, E, B>) => <M, N>(ta: Mat<M, N, A>) => Kind3<F, R, E, Mat<M, N, B>>
export declare function traverse<F extends URIS2>(
  F: Apl.Applicative2<F>
): <E, A, B>(f: (a: A) => Kind2<F, E, B>) => <M, N>(ta: Mat<M, N, A>) => Kind2<F, E, Mat<M, N, B>>
export declare function traverse<F extends URIS>(
  F: Apl.Applicative1<F>
): <A, B>(f: (a: A) => Kind<F, B>) => <M, N>(ta: Mat<M, N, A>) => Kind<F, Mat<M, N, B>>

Added in v1.0.0

traverseWithIndex

Signature

export declare function traverseWithIndex<F extends URIS4>(
  F: Apl.Applicative4<F>
): <S, R, E, A, B>(
  f: (i: [number, number], a: A) => Kind4<F, S, R, E, B>
) => <M, N>(ta: Mat<M, N, A>) => Kind4<F, S, R, E, Mat<M, N, B>>
export declare function traverseWithIndex<F extends URIS3>(
  F: Apl.Applicative3<F>
): <R, E, A, B>(
  f: (i: [number, number], a: A) => Kind3<F, R, E, B>
) => <M, N>(ta: Mat<M, N, A>) => Kind3<F, R, E, Mat<M, N, B>>
export declare function traverseWithIndex<F extends URIS2>(
  F: Apl.Applicative2<F>
): <E, A, B>(f: (i: [number, number], a: A) => Kind2<F, E, B>) => <M, N>(ta: Mat<M, N, A>) => Kind2<F, E, Mat<M, N, B>>
export declare function traverseWithIndex<F extends URIS>(
  F: Apl.Applicative1<F>
): <A, B>(f: (i: [number, number], a: A) => Kind<F, B>) => <M, N>(ta: Mat<M, N, A>) => Kind<F, Mat<M, N, B>>

Added in v1.0.0

Instances

Foldable

Signature

export declare const Foldable: Fl.Foldable3<'Mat'>

Added in v1.0.0

FoldableWithIndex

Signature

export declare const FoldableWithIndex: FlI.FoldableWithIndex3<'Mat', [number, number]>

Added in v1.0.0

Functor

Signature

export declare const Functor: Fun.Functor3<'Mat'>

Added in v1.0.0

FunctorWithIndex

Signature

export declare const FunctorWithIndex: FunI.FunctorWithIndex3<'Mat', [number, number]>

Added in v1.0.0

URI

Signature

export declare const URI: 'Mat'

Added in v1.0.0

URI (type alias)

Signature

export type URI = typeof URI

Added in v1.0.0

getAdditiveAbelianGroup

Signature

export declare const getAdditiveAbelianGroup: <A>(
  R: Rng.Ring<A>
) => <M extends number, N extends number>(m: M, n: N) => TC.AbelianGroup<Mat<M, N, A>>

Added in v1.0.0

getBimodule

Signature

export declare const getBimodule: <A>(
  R: Rng.Ring<A>
) => <M extends number, N extends number>(m: M, n: N) => TC.Bimodule<Mat<M, N, A>, A, A>

Added in v1.0.0

getSquareMonoidProduct

Signature

export declare const getSquareMonoidProduct: <A>(R: Rng.Ring<A>) => <M extends number>(m: M) => Mn.Monoid<Mat<M, M, A>>

Added in v1.1.0

Matrix Operations

get

Signature

export declare const get: (i: number, j: number) => <M, N, A>(m: Mat<M, N, A>) => O.Option<A>

Added in v1.0.0

lift2

Signature

export declare const lift2: <A, B>(f: (x: A, y: A) => B) => <M, N>(x: Mat<M, N, A>, y: Mat<M, N, A>) => Mat<M, N, B>

Added in v1.0.0

linMap

Transform a vector x into vector b by matrix A

Ax = b

Efficiency: 2mn flops (for numeric Ring)

Signature

export declare const linMap: <R>(
  R: Rng.Ring<R>
) => <M, N1, N2 extends N1>(A: Mat<M, N1, R>, x: V.Vec<N2, R>) => V.Vec<M, R>

Added in v1.0.0

linMapR

Transform a row-vector x into vector b by matrix A

xA = b

Efficiency: 2mn flops (for numeric Ring)

Signature

export declare const linMapR: <R>(
  R: Rng.Ring<R>
) => <M extends number, N1 extends number, N2 extends N1>(x: V.Vec<N1, R>, A: Mat<N2, M, R>) => V.Vec<M, R>

Added in v1.1.0

mul

Multiply two matricies with matching inner dimensions

(A ∈ R_mn) (B ∈ R_np) = C ∈ R_mp

Efficiency: 2mpn flops (for numeric Ring)

Signature

export declare const mul: <A>(
  R: Rng.Ring<A>
) => <M extends number, N1 extends number, N2 extends N1, P extends number>(
  x: Mat<M, N1, A>,
  y: Mat<N2, P, A>
) => Mat<M, P, A>

Added in v1.0.0

trace

The sum of the diagonal elements

Efficiency: m flops (for numeric Ring)

Signature

export declare const trace: <A>(R: Rng.Ring<A>) => <M extends number>(fa: Mat<M, M, A>) => A

Added in v1.0.0

transpose

Signature

export declare const transpose: <M extends number, N extends number, A>(v: Mat<M, N, A>) => Mat<N, M, A>

Added in v1.0.0

updateAt

Signature

export declare const updateAt: <A>(
  i: number,
  j: number,
  a: A
) => <M extends number, N extends number>(A: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.1.0

Model

Mat (interface)

Signature

export interface Mat<M, N, A> extends V.Vec<M, V.Vec<N, A>> {
  _rows: M
  _cols: N
}

Added in v1.0.0

Sub-Matrix

appendColumn

Add a column at the end of a matrix. Due to the limitations of the typesystem, the length parameter must be passed explicitly, and will be the number of columns of the returned matrix.

Signature

export declare const appendColumn: <M extends number, A>(
  c0: V.Vec<M, A>
) => <P extends number, N extends number>(m: Mat<M, N, A>) => Mat<M, P, A>

Added in v1.1.0

cropColumns

Crops a matrix to be square by removing excess columns. Returns O.none if there are more columns than rows.

Signature

export declare const cropColumns: <M extends number, N extends number, A>(m: Mat<M, N, A>) => O.Option<Mat<M, M, A>>

Added in v1.1.0

cropRows

Crops a matrix to be square by removing excess rows. Returns O.none if there are more columns than rows.

Signature

export declare const cropRows: <M extends number, N extends number, A>(m: Mat<M, N, A>) => O.Option<Mat<N, N, A>>

Added in v1.1.0

getSubColumn

Used to extract a sub-column from a matrix, and returns a new generic P that represents the length of the sub-column.

Note: fromIncl is the inclusive column start-index, and toExcl is the exclusive column end-index. If toExcl is omitted, then the extracted sub-column will span to the last row of the matrix.

Note: In order to preserve type safety, P cannot be inferred, and must be passed directly as a type argument.

If P is unknown, it can be declared in the parent function as an arbitrary generic that has a numeric constraint.

See: Decomposition > QR as an example declaring an unknown length constraint

Signature

export declare const getSubColumn: (
  col: number,
  fromIncl: number,
  toExcl?: number | undefined
) => <P extends number, M extends number, N extends number, A>(m: Mat<M, N, A>) => O.Option<V.Vec<P, A>>

Added in v1.1.0

getSubMatrix

Used to extract a portion of a matrix, and returns new generics P and Q that represents the the rows / columns of the extracted sub-matrix.

Note: rowFromIncl and colFromIncl are the inclusive row / column start-indices, and rowToExcl and colToExcl are the exclusive row / column end-indices. If rowToExcl or colToExcl are omitted, the extracted sub-matrix will span to the final row / column.

Note: In order to preserve type safety, P and Q cannot be inferred, and must be passed directly as type arguments.

If P and Q are unknown, they can be declared in the parent function as arbitrary generics that have a numeric constraint.

See: Decomposition > QR as an example declaring unknown length constraints

Signature

export declare const getSubMatrix: <P extends number, Q extends number>(
  rowFromIncl: number,
  colFromIncl: number,
  rowToExcl?: number | undefined,
  colToExcl?: number | undefined
) => <M extends number, N extends number, A>(m: Mat<M, N, A>) => O.Option<Mat<P, Q, A>>

Added in v1.1.0

mapColumn

Map a particular column of a matrix

Signature

export declare const mapColumn: <A>(
  columnIndex: number,
  f: (a: A) => A
) => <M extends number, N extends number>(m: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.1.0

mapRow

Map a particular row of a matrix

Signature

export declare const mapRow: <A>(
  rowIndex: number,
  f: (a: A) => A
) => <M extends number, N extends number>(m: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.1.0

prependColumn

Add a column at the beginning of a matrix. Due to the limitations of the typesystem, the length parameter must be passed explicitly, and will be the number of columns of the returned matrix.

Signature

export declare const prependColumn: <M extends number, A>(
  c0: V.Vec<M, A>
) => <P extends number, N extends number>(m: Mat<M, N, A>) => Mat<M, P, A>

Added in v1.1.0

reduceByColumn

Reduce the columns of a matrix to a vector of opposite length

Signature

export declare const reduceByColumn: <M extends number, A, B>(
  f: (a: V.Vec<M, A>) => B
) => <N extends number>(A: Mat<M, N, A>) => V.Vec<N, B>

Added in v1.1.0

reduceByRow

Reduce the rows of a matrix to a vector of opposite length

Signature

export declare const reduceByRow: <N extends number, A, B>(
  f: (a: V.Vec<N, A>) => B
) => <M extends number>(m: Mat<M, N, A>) => V.Vec<M, B>

Added in v1.1.0

switchColumns

Signature

export declare const switchColumns: (
  i: number,
  j: number
) => <N extends number, M extends number, A>(vs: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.1.0

switchRows

Signature

export declare const switchRows: (i: number, j: number) => <A, N, M>(vs: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.0.0

updateSubColumn

Used to replace a sub-column of a matrix along with a generic P that is the length of the sub-column. If P is incompatible with matrix length N, or provided indices will result in an overflow, O.none is returned.

Note: fromRowIncl is the inclusive row start-index

Signature

export declare const updateSubColumn: <P extends number, A>(
  col: number,
  fromRowIncl: number,
  repl: V.Vec<P, A>
) => <M extends number, N extends number>(m: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.1.0

updateSubMatrix

Used to replace a portion of a matrix with generics P and Q that are the rows / columns of the replacement sub-matrix. If P is incompatible with matrix rows M, Q is incompatible with matrix columns N, or if provided indices will result in an overflow, O.none is returned.

Note: rowFromIncl and colFromIncl are the inclusive row / column start-indices

Signature

export declare const updateSubMatrix: <P extends number, Q extends number, A>(
  rowFromIncl: number,
  colFromIncl: number,
  repl: Mat<P, Q, A>
) => <M extends number, N extends number>(m: Mat<M, N, A>) => O.Option<Mat<M, N, A>>

Added in v1.1.0