Documentation

Mathlib.Tactic.Matrix.OfLists

Matrices from lists of rows #

ofLists reads a list of rows as a Matrix, and the results here transport the list operations to the matrix ones.

Main results #

Implementation notes #

The definitions recurse on the dimensions, so on literals they reduce in the kernel to the vecCons form of the !![…] notation, and a literal in that notation is definitionally an ofLists term.

source
def Mathlib.Tactic.Matrix.ofList {α : Type u_1} [Zero α] (n : ℕ) :
List α → Fin n → α

Construct a vector from the first n elements of a list, padded with 0.

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Instances For
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    @[simp]
    theorem Mathlib.Tactic.Matrix.ofList_apply {α : Type u_1} [Zero α] (n : ℕ) (l : List α) (i : Fin n) :
    ofList n l i = l.getD (↑i) 0
    source
    def Mathlib.Tactic.Matrix.ofListsFun {α : Type u_1} [Zero α] (m n : ℕ) :
    List (List α) → Fin m → Fin n → α

    The first n elements of the first m lists as a function of two indices, padded with 0.

    Equations
    Instances For
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      def Mathlib.Tactic.Matrix.ofLists {α : Type u_1} [Zero α] (m n : ℕ) (rows : List (List α)) :
      Matrix (Fin m) (Fin n) α

      Construct a matrix from the first n elements of the first m lists, padded with 0.

      Equations
      Instances For
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        @[simp]
        theorem Mathlib.Tactic.Matrix.ofLists_apply {α : Type u_1} [Zero α] (m n : ℕ) (rows : List (List α)) (i : Fin m) :
        ofLists m n rows i = ofList n (rows.getD ↑i [])
        source
        @[simp]
        theorem Mathlib.Tactic.Matrix.ListMatrix.dotProduct_eq {α : Type u_1} [Mul α] [AddCommMonoid α] (n : ℕ) (l₁ l₂ : List α) :
        dotProduct n l₁ l₂ = ofList n l₁ ⬝ᵥ ofList n l₂
        source
        @[simp]
        theorem Mathlib.Tactic.Matrix.ofLists_transpose {α : Type u_1} [Zero α] (m n : ℕ) (rows : List (List α)) :
        ofLists n m (ListMatrix.transpose n rows) = (ofLists m n rows).transpose
        source
        theorem Mathlib.Tactic.Matrix.ofLists_mul {α : Type u_1} [Mul α] [AddCommMonoid α] (l m n : ℕ) (A B : List (List α)) :
        ofLists l m A * ofLists m n B = ofLists l n (ListMatrix.mul l m n A B)
        source
        theorem Mathlib.Tactic.Matrix.toArray_ofLists {α : Type u_1} [Zero α] {m n : ℕ} {rows : List (List α)} (hrows : ∀ row ∈ rows, row.length = n) (hl : rows.flatten.toArray.size = m * n) :
        (ofLists m n rows).toArray = rows.flatten.toArray

        The row-major array of the entries of the matrix of m rows of n entries is the array of their concatenation.