linear_algebra.matrix.ldl | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

46b633fd

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

2a0ce625

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -33,7 +33,7 @@ decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a d
 -/
 
 
-variable {𝕜 : Type _} [IsROrC 𝕜]
+variable {𝕜 : Type _} [RCLike 𝕜]
 
 variable {n : Type _} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
 
@@ -123,7 +123,7 @@ theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL
   · simp only [LDL.diag, hij, diagonal_apply_ne, Ne.def, not_false_iff, mul_mul_apply]
     rw [conj_transpose, transpose_map, transpose_transpose, dot_product_mul_vec,
       (LDL.lowerInv_orthogonal hS fun h : j = i => hij h.symm).symm, ← inner_conj_symm,
-      mul_vec_transpose, EuclideanSpace.inner_piLp_equiv_symm, ← IsROrC.star_def, ←
+      mul_vec_transpose, EuclideanSpace.inner_piLp_equiv_symm, ← RCLike.star_def, ←
       star_dot_product_star, dot_product_comm, star_star]
     rfl
 #align LDL.diag_eq_lower_inv_conj LDL.diag_eq_lowerInv_conj

2a0ce625

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 -/
-import Mathbin.Analysis.InnerProductSpace.GramSchmidtOrtho
-import Mathbin.LinearAlgebra.Matrix.PosDef
+import Analysis.InnerProductSpace.GramSchmidtOrtho
+import LinearAlgebra.Matrix.PosDef
 
 #align_import linear_algebra.matrix.ldl from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"

2a0ce625

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.ldl
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.InnerProductSpace.GramSchmidtOrtho
 import Mathbin.LinearAlgebra.Matrix.PosDef
 
+#align_import linear_algebra.matrix.ldl from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
 /-! # LDL decomposition
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

2a0ce625

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -65,7 +65,7 @@ theorem LDL.lowerInv_eq_gramSchmidtBasis :
           (@gramSchmidtBasis 𝕜 (n → 𝕜) _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) n _ _ _
             (Pi.basisFun 𝕜 n)))ᵀ :=
   by
-  ext (i j)
+  ext i j
   rw [LDL.lowerInv, Basis.coePiBasisFun.toMatrix_eq_transpose, coe_gramSchmidtBasis]
   rfl
 #align LDL.lower_inv_eq_gram_schmidt_basis LDL.lowerInv_eq_gramSchmidtBasis
@@ -118,7 +118,7 @@ theorem LDL.lowerInv_triangular {i j : n} (hij : i < j) : LDL.lowerInv hS i j =
 by some lower triangular matrix and get a diagonal matrix. -/
 theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL.lowerInv hS)ᴴ :=
   by
-  ext (i j)
+  ext i j
   by_cases hij : i = j
   ·
     simpa only [hij, LDL.diag, diagonal_apply_eq, LDL.diagEntries, Matrix.mul_assoc,

2a0ce625

bump to nightly-2023-06-18-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

3b5e23dc

Diff

@@ -48,6 +48,7 @@ open scoped Matrix
 
 variable {S : Matrix n n 𝕜} [Fintype n] (hS : S.PosDef)
 
+#print LDL.lowerInv /-
 /-- The inverse of the lower triangular matrix `L` of the LDL-decomposition. It is obtained by
 applying Gram-Schmidt-Orthogonalization w.r.t. the inner product induced by `Sᵀ` on the standard
 basis vectors `pi.basis_fun`. -/
@@ -55,7 +56,9 @@ noncomputable def LDL.lowerInv : Matrix n n 𝕜 :=
   @gramSchmidt 𝕜 (n → 𝕜) _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) n _ _ _
     (Pi.basisFun 𝕜 n)
 #align LDL.lower_inv LDL.lowerInv
+-/
 
+#print LDL.lowerInv_eq_gramSchmidtBasis /-
 theorem LDL.lowerInv_eq_gramSchmidtBasis :
     LDL.lowerInv hS =
       ((Pi.basisFun 𝕜 n).toMatrix
@@ -66,7 +69,9 @@ theorem LDL.lowerInv_eq_gramSchmidtBasis :
   rw [LDL.lowerInv, Basis.coePiBasisFun.toMatrix_eq_transpose, coe_gramSchmidtBasis]
   rfl
 #align LDL.lower_inv_eq_gram_schmidt_basis LDL.lowerInv_eq_gramSchmidtBasis
+-/
 
+#print LDL.invertibleLowerInv /-
 noncomputable instance LDL.invertibleLowerInv : Invertible (LDL.lowerInv hS) :=
   by
   rw [LDL.lowerInv_eq_gramSchmidtBasis]
@@ -76,29 +81,39 @@ noncomputable instance LDL.invertibleLowerInv : Invertible (LDL.lowerInv hS) :=
         (Pi.basisFun 𝕜 n))
   infer_instance
 #align LDL.invertible_lower_inv LDL.invertibleLowerInv
+-/
 
+#print LDL.lowerInv_orthogonal /-
 theorem LDL.lowerInv_orthogonal {i j : n} (h₀ : i ≠ j) :
     ⟪LDL.lowerInv hS i, Sᵀ.mulVec (LDL.lowerInv hS j)⟫ₑ = 0 :=
   @gramSchmidt_orthogonal 𝕜 _ _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) _ _ _ _ _ _ _ h₀
 #align LDL.lower_inv_orthogonal LDL.lowerInv_orthogonal
+-/
 
+#print LDL.diagEntries /-
 /-- The entries of the diagonal matrix `D` of the LDL decomposition. -/
 noncomputable def LDL.diagEntries : n → 𝕜 := fun i =>
   ⟪star (LDL.lowerInv hS i), S.mulVec (star (LDL.lowerInv hS i))⟫ₑ
 #align LDL.diag_entries LDL.diagEntries
+-/
 
+#print LDL.diag /-
 /-- The diagonal matrix `D` of the LDL decomposition. -/
 noncomputable def LDL.diag : Matrix n n 𝕜 :=
   Matrix.diagonal (LDL.diagEntries hS)
 #align LDL.diag LDL.diag
+-/
 
+#print LDL.lowerInv_triangular /-
 theorem LDL.lowerInv_triangular {i j : n} (hij : i < j) : LDL.lowerInv hS i j = 0 := by
   rw [←
     @gramSchmidt_triangular 𝕜 (n → 𝕜) _ (_ : _) (inner_product_space.of_matrix hS.transpose) n _ _ _
       i j hij (Pi.basisFun 𝕜 n),
     Pi.basisFun_repr, LDL.lowerInv]
 #align LDL.lower_inv_triangular LDL.lowerInv_triangular
+-/
 
+#print LDL.diag_eq_lowerInv_conj /-
 /-- Inverse statement of **LDL decomposition**: we can conjugate a positive definite matrix
 by some lower triangular matrix and get a diagonal matrix. -/
 theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL.lowerInv hS)ᴴ :=
@@ -115,12 +130,16 @@ theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL
       star_dot_product_star, dot_product_comm, star_star]
     rfl
 #align LDL.diag_eq_lower_inv_conj LDL.diag_eq_lowerInv_conj
+-/
 
+#print LDL.lower /-
 /-- The lower triangular matrix `L` of the LDL decomposition. -/
 noncomputable def LDL.lower :=
   (LDL.lowerInv hS)⁻¹
 #align LDL.lower LDL.lower
+-/
 
+#print LDL.lower_conj_diag /-
 /-- **LDL decomposition**: any positive definite matrix `S` can be
 decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a diagonal matrix.  -/
 theorem LDL.lower_conj_diag : LDL.lower hS ⬝ LDL.diag hS ⬝ (LDL.lower hS)ᴴ = S :=
@@ -130,4 +149,5 @@ theorem LDL.lower_conj_diag : LDL.lower hS ⬝ LDL.diag hS ⬝ (LDL.lower hS)ᴴ
     Matrix.mul_inv_eq_iff_eq_mul_of_invertible]
   exact LDL.diag_eq_lowerInv_conj hS
 #align LDL.lower_conj_diag LDL.lower_conj_diag
+-/

2a0ce625

bump to nightly-2023-06-18-05

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

cd92954f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.ldl
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.Matrix.PosDef
 
 /-! # LDL decomposition
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves the LDL-decomposition of matricies: Any positive definite matrix `S` can be
 decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a diagonal matrix.

46b633fd

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -37,7 +37,6 @@ variable {𝕜 : Type _} [IsROrC 𝕜]
 
 variable {n : Type _} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
 
--- mathport name: «expr⟪ , ⟫ₑ»
 local notation "⟪" x ", " y "⟫ₑ" => @inner 𝕜 _ _ ((PiLp.equiv 2 _).symm x) ((PiLp.equiv _ _).symm y)
 
 open Matrix

46b633fd

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -42,7 +42,7 @@ local notation "⟪" x ", " y "⟫ₑ" => @inner 𝕜 _ _ ((PiLp.equiv 2 _).symm
 
 open Matrix
 
-open Matrix
+open scoped Matrix
 
 variable {S : Matrix n n 𝕜} [Fintype n] (hS : S.PosDef)

46b633fd

bump to nightly-2023-04-28-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

1df38d74

Diff

@@ -61,7 +61,7 @@ theorem LDL.lowerInv_eq_gramSchmidtBasis :
             (Pi.basisFun 𝕜 n)))ᵀ :=
   by
   ext (i j)
-  rw [LDL.lowerInv, Basis.CoePiBasisFun.toMatrix_eq_transpose, coe_gramSchmidtBasis]
+  rw [LDL.lowerInv, Basis.coePiBasisFun.toMatrix_eq_transpose, coe_gramSchmidtBasis]
   rfl
 #align LDL.lower_inv_eq_gram_schmidt_basis LDL.lowerInv_eq_gramSchmidtBasis

46b633fd

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.ldl
-! leanprover-community/mathlib commit 9f0d61b4475e3c3cba6636ab51cdb1f3949d2e1d
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -50,13 +50,14 @@ variable {S : Matrix n n 𝕜} [Fintype n] (hS : S.PosDef)
 applying Gram-Schmidt-Orthogonalization w.r.t. the inner product induced by `Sᵀ` on the standard
 basis vectors `pi.basis_fun`. -/
 noncomputable def LDL.lowerInv : Matrix n n 𝕜 :=
-  @gramSchmidt 𝕜 (n → 𝕜) _ (InnerProductSpace.ofMatrix hS.transpose) n _ _ _ (Pi.basisFun 𝕜 n)
+  @gramSchmidt 𝕜 (n → 𝕜) _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) n _ _ _
+    (Pi.basisFun 𝕜 n)
 #align LDL.lower_inv LDL.lowerInv
 
 theorem LDL.lowerInv_eq_gramSchmidtBasis :
     LDL.lowerInv hS =
       ((Pi.basisFun 𝕜 n).toMatrix
-          (@gramSchmidtBasis 𝕜 (n → 𝕜) _ (InnerProductSpace.ofMatrix hS.transpose) n _ _ _
+          (@gramSchmidtBasis 𝕜 (n → 𝕜) _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) n _ _ _
             (Pi.basisFun 𝕜 n)))ᵀ :=
   by
   ext (i j)
@@ -69,18 +70,14 @@ noncomputable instance LDL.invertibleLowerInv : Invertible (LDL.lowerInv hS) :=
   rw [LDL.lowerInv_eq_gramSchmidtBasis]
   haveI :=
     Basis.invertibleToMatrix (Pi.basisFun 𝕜 n)
-      (@gramSchmidtBasis 𝕜 (n → 𝕜) _ (inner_product_space.of_matrix hS.transpose) n _ _ _
+      (@gramSchmidtBasis 𝕜 (n → 𝕜) _ (_ : _) (inner_product_space.of_matrix hS.transpose) n _ _ _
         (Pi.basisFun 𝕜 n))
   infer_instance
 #align LDL.invertible_lower_inv LDL.invertibleLowerInv
 
 theorem LDL.lowerInv_orthogonal {i j : n} (h₀ : i ≠ j) :
     ⟪LDL.lowerInv hS i, Sᵀ.mulVec (LDL.lowerInv hS j)⟫ₑ = 0 :=
-  show
-    @inner 𝕜 (n → 𝕜) (InnerProductSpace.ofMatrix hS.transpose).toHasInner (LDL.lowerInv hS i)
-        (LDL.lowerInv hS j) =
-      0
-    by apply gramSchmidt_orthogonal _ _ h₀
+  @gramSchmidt_orthogonal 𝕜 _ _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) _ _ _ _ _ _ _ h₀
 #align LDL.lower_inv_orthogonal LDL.lowerInv_orthogonal
 
 /-- The entries of the diagonal matrix `D` of the LDL decomposition. -/
@@ -95,8 +92,8 @@ noncomputable def LDL.diag : Matrix n n 𝕜 :=
 
 theorem LDL.lowerInv_triangular {i j : n} (hij : i < j) : LDL.lowerInv hS i j = 0 := by
   rw [←
-    @gramSchmidt_triangular 𝕜 (n → 𝕜) _ (inner_product_space.of_matrix hS.transpose) n _ _ _ i j hij
-      (Pi.basisFun 𝕜 n),
+    @gramSchmidt_triangular 𝕜 (n → 𝕜) _ (_ : _) (inner_product_space.of_matrix hS.transpose) n _ _ _
+      i j hij (Pi.basisFun 𝕜 n),
     Pi.basisFun_repr, LDL.lowerInv]
 #align LDL.lower_inv_triangular LDL.lowerInv_triangular

9f0d61b4

bump to nightly-2023-03-18-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

24261a71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.ldl
-! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
+! leanprover-community/mathlib commit 9f0d61b4475e3c3cba6636ab51cdb1f3949d2e1d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -37,9 +37,8 @@ variable {𝕜 : Type _} [IsROrC 𝕜]
 
 variable {n : Type _} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
 
--- mathport name: «expr⟪ , ⟫»
-local notation "⟪" x ", " y "⟫" =>
-  @inner 𝕜 (n → 𝕜) (PiLp.innerProductSpace fun _ => 𝕜).toHasInner x y
+-- mathport name: «expr⟪ , ⟫ₑ»
+local notation "⟪" x ", " y "⟫ₑ" => @inner 𝕜 _ _ ((PiLp.equiv 2 _).symm x) ((PiLp.equiv _ _).symm y)
 
 open Matrix
 
@@ -51,8 +50,7 @@ variable {S : Matrix n n 𝕜} [Fintype n] (hS : S.PosDef)
 applying Gram-Schmidt-Orthogonalization w.r.t. the inner product induced by `Sᵀ` on the standard
 basis vectors `pi.basis_fun`. -/
 noncomputable def LDL.lowerInv : Matrix n n 𝕜 :=
-  @gramSchmidt 𝕜 (n → 𝕜) _ (InnerProductSpace.ofMatrix hS.transpose) n _ _ _ fun k =>
-    Pi.basisFun 𝕜 n k
+  @gramSchmidt 𝕜 (n → 𝕜) _ (InnerProductSpace.ofMatrix hS.transpose) n _ _ _ (Pi.basisFun 𝕜 n)
 #align LDL.lower_inv LDL.lowerInv
 
 theorem LDL.lowerInv_eq_gramSchmidtBasis :
@@ -77,7 +75,7 @@ noncomputable instance LDL.invertibleLowerInv : Invertible (LDL.lowerInv hS) :=
 #align LDL.invertible_lower_inv LDL.invertibleLowerInv
 
 theorem LDL.lowerInv_orthogonal {i j : n} (h₀ : i ≠ j) :
-    ⟪LDL.lowerInv hS i, Sᵀ.mulVec (LDL.lowerInv hS j)⟫ = 0 :=
+    ⟪LDL.lowerInv hS i, Sᵀ.mulVec (LDL.lowerInv hS j)⟫ₑ = 0 :=
   show
     @inner 𝕜 (n → 𝕜) (InnerProductSpace.ofMatrix hS.transpose).toHasInner (LDL.lowerInv hS i)
         (LDL.lowerInv hS j) =
@@ -87,7 +85,7 @@ theorem LDL.lowerInv_orthogonal {i j : n} (h₀ : i ≠ j) :
 
 /-- The entries of the diagonal matrix `D` of the LDL decomposition. -/
 noncomputable def LDL.diagEntries : n → 𝕜 := fun i =>
-  ⟪star (LDL.lowerInv hS i), S.mulVec (star (LDL.lowerInv hS i))⟫
+  ⟪star (LDL.lowerInv hS i), S.mulVec (star (LDL.lowerInv hS i))⟫ₑ
 #align LDL.diag_entries LDL.diagEntries
 
 /-- The diagonal matrix `D` of the LDL decomposition. -/
@@ -109,12 +107,12 @@ theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL
   ext (i j)
   by_cases hij : i = j
   ·
-    simpa only [hij, LDL.diag, diagonal_apply_eq, LDL.diagEntries, Matrix.mul_assoc, inner,
-      Pi.star_apply, IsROrC.star_def, starRingEnd_self_apply]
+    simpa only [hij, LDL.diag, diagonal_apply_eq, LDL.diagEntries, Matrix.mul_assoc,
+      EuclideanSpace.inner_piLp_equiv_symm, star_star]
   · simp only [LDL.diag, hij, diagonal_apply_ne, Ne.def, not_false_iff, mul_mul_apply]
     rw [conj_transpose, transpose_map, transpose_transpose, dot_product_mul_vec,
       (LDL.lowerInv_orthogonal hS fun h : j = i => hij h.symm).symm, ← inner_conj_symm,
-      mul_vec_transpose, EuclideanSpace.inner_eq_star_dotProduct, ← IsROrC.star_def, ←
+      mul_vec_transpose, EuclideanSpace.inner_piLp_equiv_symm, ← IsROrC.star_def, ←
       star_dot_product_star, dot_product_comm, star_star]
     rfl
 #align LDL.diag_eq_lower_inv_conj LDL.diag_eq_lowerInv_conj

3fc0b254

bump to nightly-2023-03-15-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

4e269297

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.ldl
-! leanprover-community/mathlib commit 0fc5496584478976b86f17941b3ff25ad7c4ebd6
+! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -113,7 +113,7 @@ theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL
       Pi.star_apply, IsROrC.star_def, starRingEnd_self_apply]
   · simp only [LDL.diag, hij, diagonal_apply_ne, Ne.def, not_false_iff, mul_mul_apply]
     rw [conj_transpose, transpose_map, transpose_transpose, dot_product_mul_vec,
-      (LDL.lowerInv_orthogonal hS fun h : j = i => hij h.symm).symm, ← inner_conj_sym,
+      (LDL.lowerInv_orthogonal hS fun h : j = i => hij h.symm).symm, ← inner_conj_symm,
       mul_vec_transpose, EuclideanSpace.inner_eq_star_dotProduct, ← IsROrC.star_def, ←
       star_dot_product_star, dot_product_comm, star_star]
     rfl

0fc54965

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

46b633fd

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -105,7 +105,7 @@ theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS * S * (LDL.low
   · simp only [diag, diagEntries, EuclideanSpace.inner_piLp_equiv_symm, star_star, hij,
     diagonal_apply_eq, Matrix.mul_assoc]
     rfl
-  · simp only [LDL.diag, hij, diagonal_apply_ne, Ne.def, not_false_iff, mul_mul_apply]
+  · simp only [LDL.diag, hij, diagonal_apply_ne, Ne, not_false_iff, mul_mul_apply]
     rw [conjTranspose, transpose_map, transpose_transpose, dotProduct_mulVec,
       (LDL.lowerInv_orthogonal hS fun h : j = i => hij h.symm).symm, ← inner_conj_symm,
       mulVec_transpose, EuclideanSpace.inner_piLp_equiv_symm, ← RCLike.star_def, ←

46b633fd

chore: Rename IsROrC to RCLike (#10819)

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

43618f93

Diff

@@ -30,7 +30,7 @@ decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a d
 -/
 
 
-variable {𝕜 : Type*} [IsROrC 𝕜]
+variable {𝕜 : Type*} [RCLike 𝕜]
 variable {n : Type*} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
 
 section set_options
@@ -108,7 +108,7 @@ theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS * S * (LDL.low
   · simp only [LDL.diag, hij, diagonal_apply_ne, Ne.def, not_false_iff, mul_mul_apply]
     rw [conjTranspose, transpose_map, transpose_transpose, dotProduct_mulVec,
       (LDL.lowerInv_orthogonal hS fun h : j = i => hij h.symm).symm, ← inner_conj_symm,
-      mulVec_transpose, EuclideanSpace.inner_piLp_equiv_symm, ← IsROrC.star_def, ←
+      mulVec_transpose, EuclideanSpace.inner_piLp_equiv_symm, ← RCLike.star_def, ←
       star_dotProduct_star, dotProduct_comm, star_star]
     rfl
 #align LDL.diag_eq_lower_inv_conj LDL.diag_eq_lowerInv_conj

46b633fd

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -31,7 +31,6 @@ decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a d
 
 
 variable {𝕜 : Type*} [IsROrC 𝕜]
-
 variable {n : Type*} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
 
 section set_options

46b633fd

chore: Matrix.mulVec and Matrix.vecMul get infix notation (#10297)

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Notation.20for.20mul_vec.20and.20vec_mul

Co-authored-by: Martin Dvorak <mdvorak@ista.ac.at>

deb48fab

Diff

@@ -77,13 +77,13 @@ noncomputable instance LDL.invertibleLowerInv : Invertible (LDL.lowerInv hS) :=
 #align LDL.invertible_lower_inv LDL.invertibleLowerInv
 
 theorem LDL.lowerInv_orthogonal {i j : n} (h₀ : i ≠ j) :
-    ⟪LDL.lowerInv hS i, Sᵀ.mulVec (LDL.lowerInv hS j)⟫ₑ = 0 :=
+    ⟪LDL.lowerInv hS i, Sᵀ *ᵥ LDL.lowerInv hS j⟫ₑ = 0 :=
   @gramSchmidt_orthogonal 𝕜 _ _ (_ : _) (InnerProductSpace.ofMatrix hS.transpose) _ _ _ _ _ _ _ h₀
 #align LDL.lower_inv_orthogonal LDL.lowerInv_orthogonal
 
 /-- The entries of the diagonal matrix `D` of the LDL decomposition. -/
 noncomputable def LDL.diagEntries : n → 𝕜 := fun i =>
-  ⟪star (LDL.lowerInv hS i), S.mulVec (star (LDL.lowerInv hS i))⟫ₑ
+  ⟪star (LDL.lowerInv hS i), S *ᵥ star (LDL.lowerInv hS i)⟫ₑ
 #align LDL.diag_entries LDL.diagEntries
 
 /-- The diagonal matrix `D` of the LDL decomposition. -/

46b633fd

refactor: remove PiLp.equiv (#6501)

This removes the (PiLp.equiv 2 fun i => α i) abbreviation, replacing it with its implementation (WithLp.equiv 2 (∀ i, α i)). The same thing is done for PiLp.linearEquiv.

bfb6bb73

Diff

@@ -38,7 +38,8 @@ section set_options
 
 set_option linter.uppercaseLean3 false
 set_option quotPrecheck false
-local notation "⟪" x ", " y "⟫ₑ" => @inner 𝕜 _ _ ((PiLp.equiv 2 _).symm x) ((PiLp.equiv _ _).symm y)
+local notation "⟪" x ", " y "⟫ₑ" =>
+  @inner 𝕜 _ _ ((WithLp.equiv 2 _).symm x) ((WithLp.equiv _ _).symm y)
 
 open Matrix

46b633fd

refactor(LinearAlgebra/Matrix/PosDef): Generalize to StarOrderedRing (#6489)

I assume this is mathematically sound, though right now we can't generalize many dependencies due to the reliance of InnerProductSpace.

ee8a9190

Diff

@@ -42,7 +42,7 @@ local notation "⟪" x ", " y "⟫ₑ" => @inner 𝕜 _ _ ((PiLp.equiv 2 _).symm
 
 open Matrix
 
-open scoped Matrix
+open scoped Matrix ComplexOrder
 
 variable {S : Matrix n n 𝕜} [Fintype n] (hS : S.PosDef)

46b633fd

refactor(Data/Matrix): Eliminate ⬝ notation in favor of HMul (#6487)

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

38c07226

Diff

@@ -99,7 +99,7 @@ theorem LDL.lowerInv_triangular {i j : n} (hij : i < j) : LDL.lowerInv hS i j =
 
 /-- Inverse statement of **LDL decomposition**: we can conjugate a positive definite matrix
 by some lower triangular matrix and get a diagonal matrix. -/
-theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL.lowerInv hS)ᴴ := by
+theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS * S * (LDL.lowerInv hS)ᴴ := by
   ext i j
   by_cases hij : i = j
   · simp only [diag, diagEntries, EuclideanSpace.inner_piLp_equiv_symm, star_star, hij,
@@ -120,7 +120,7 @@ noncomputable def LDL.lower :=
 
 /-- **LDL decomposition**: any positive definite matrix `S` can be
 decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a diagonal matrix.  -/
-theorem LDL.lower_conj_diag : LDL.lower hS ⬝ LDL.diag hS ⬝ (LDL.lower hS)ᴴ = S := by
+theorem LDL.lower_conj_diag : LDL.lower hS * LDL.diag hS * (LDL.lower hS)ᴴ = S := by
   rw [LDL.lower, conjTranspose_nonsing_inv, Matrix.mul_assoc,
     Matrix.inv_mul_eq_iff_eq_mul_of_invertible (LDL.lowerInv hS),
     Matrix.mul_inv_eq_iff_eq_mul_of_invertible]

46b633fd

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -30,9 +30,9 @@ decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a d
 -/
 
 
-variable {𝕜 : Type _} [IsROrC 𝕜]
+variable {𝕜 : Type*} [IsROrC 𝕜]
 
-variable {n : Type _} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
+variable {n : Type*} [LinearOrder n] [IsWellOrder n (· < ·)] [LocallyFiniteOrderBot n]
 
 section set_options

46b633fd

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.ldl
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
 import Mathlib.LinearAlgebra.Matrix.PosDef
 
+#align_import linear_algebra.matrix.ldl from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-! # LDL decomposition
 
 This file proves the LDL-decomposition of matrices: Any positive definite matrix `S` can be

46b633fd

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -64,7 +64,7 @@ theorem LDL.lowerInv_eq_gramSchmidtBasis :
             (Pi.basisFun 𝕜 n)))ᵀ := by
   letI := NormedAddCommGroup.ofMatrix hS.transpose
   letI := InnerProductSpace.ofMatrix hS.transpose
-  ext (i j)
+  ext i j
   rw [LDL.lowerInv, Basis.coePiBasisFun.toMatrix_eq_transpose, coe_gramSchmidtBasis]
   rfl
 #align LDL.lower_inv_eq_gram_schmidt_basis LDL.lowerInv_eq_gramSchmidtBasis
@@ -103,7 +103,7 @@ theorem LDL.lowerInv_triangular {i j : n} (hij : i < j) : LDL.lowerInv hS i j =
 /-- Inverse statement of **LDL decomposition**: we can conjugate a positive definite matrix
 by some lower triangular matrix and get a diagonal matrix. -/
 theorem LDL.diag_eq_lowerInv_conj : LDL.diag hS = LDL.lowerInv hS ⬝ S ⬝ (LDL.lowerInv hS)ᴴ := by
-  ext (i j)
+  ext i j
   by_cases hij : i = j
   · simp only [diag, diagEntries, EuclideanSpace.inner_piLp_equiv_symm, star_star, hij,
     diagonal_apply_eq, Matrix.mul_assoc]

46b633fd

chore: tidy various files (#5233)

697ac1d3

Diff

@@ -13,7 +13,7 @@ import Mathlib.LinearAlgebra.Matrix.PosDef
 
 /-! # LDL decomposition
 
-This file proves the LDL-decomposition of matricies: Any positive definite matrix `S` can be
+This file proves the LDL-decomposition of matrices: Any positive definite matrix `S` can be
 decomposed as `S = LDLᴴ` where `L` is a lower-triangular matrix and `D` is a diagonal matrix.
 
 ## Main definitions

46b633fd

feat: port LinearAlgebra.Matrix.LDL (#5061)

depends on: #4920
depends on: #5058
depends on: #5059
depends on: #5060

b4efa00f

`linear_algebra.matrix.ldl` ⟷ `Mathlib.LinearAlgebra.Matrix.LDL`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 996

linear_algebra.matrix.ldl ⟷ Mathlib.LinearAlgebra.Matrix.LDL

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 996

`linear_algebra.matrix.ldl` ⟷ `Mathlib.LinearAlgebra.Matrix.LDL`