Merge pull request #13732 from gajomi/structuredmatrixprinting

General method for modifying printing of elements in arrays

base/abstractarray.jl

@@ -706,6 +706,9 @@ end
 
 get(A::AbstractArray, I::RangeVecIntList, default) = get!(similar(A, typeof(default), map(length, I)...), A, I, default)
 
+## structured matrix methods ##
+replace_in_print_matrix(A::AbstractMatrix,i::Integer,j::Integer,s::AbstractString) = s
+replace_in_print_matrix(A::AbstractVector,i::Integer,j::Integer,s::AbstractString) = s
 
 ## Concatenation ##
 

base/linalg/bidiag.jl

@@ -40,6 +40,16 @@ function getindex{T}(A::Bidiagonal{T}, i::Integer, j::Integer)
     i == j ? A.dv[i] : (A.isupper && (i == j-1)) || (!A.isupper && (i == j+1)) ? A.ev[min(i,j)] : zero(T)
 end
 
+
+## structured matrix methods ##
+function Base.replace_in_print_matrix(A::Bidiagonal,i::Integer,j::Integer,s::AbstractString)
+    if A.isupper
+        i==j || i==j-1 ? s : Base.replace_with_centered_mark(s)
+    else
+        i==j || i==j+1 ? s : Base.replace_with_centered_mark(s)
+    end
+end
+
 #Converting from Bidiagonal to dense Matrix
 full{T}(M::Bidiagonal{T}) = convert(Matrix{T}, M)
 function convert{T}(::Type{Matrix{T}}, A::Bidiagonal)

base/linalg/diagonal.jl

@@ -51,6 +51,13 @@ function unsafe_setindex!(D::Diagonal, v, i::Int, j::Int)
     D
 end
 
+
+## structured matrix methods ##
+function Base.replace_in_print_matrix(A::Diagonal,i::Integer,j::Integer,s::AbstractString)
+    i==j ? s : Base.replace_with_centered_mark(s)
+end
+
+
 ishermitian{T<:Real}(D::Diagonal{T}) = true
 ishermitian(D::Diagonal) = all(D.diag .== real(D.diag))
 issym(D::Diagonal) = true

base/linalg/triangular.jl

@@ -159,6 +159,16 @@ function setindex!(A::UnitLowerTriangular, x, i::Integer, j::Integer)
     return A
 end
 
+
+## structured matrix methods ##
+function Base.replace_in_print_matrix(A::UpperTriangular,i::Integer,j::Integer,s::AbstractString)
+    i<=j ? s : Base.replace_with_centered_mark(s)
+end
+function Base.replace_in_print_matrix(A::LowerTriangular,i::Integer,j::Integer,s::AbstractString)
+    i>=j ? s : Base.replace_with_centered_mark(s)
+end
+
+
 istril(A::LowerTriangular) = true
 istril(A::UnitLowerTriangular) = true
 istriu(A::UpperTriangular) = true

base/linalg/tridiag.jl

@@ -196,6 +196,12 @@ end
 getindex( a::ZeroOffsetVector, i) = a.data[i+1]
 setindex!(a::ZeroOffsetVector, x, i) = a.data[i+1]=x
 
+
+## structured matrix methods ##
+function Base.replace_in_print_matrix(A::SymTridiagonal,i::Integer,j::Integer,s::AbstractString)
+    i==j-1||i==j||i==j+1 ? s : Base.replace_with_centered_mark(s)
+end
+
 #Implements the inverse using the recurrence relation between principal minors
 # a, b, c are assumed to be the subdiagonal, diagonal, and superdiagonal of
 # a tridiagonal matrix.
@@ -375,6 +381,12 @@ function getindex{T}(A::Tridiagonal{T}, i::Integer, j::Integer)
     end
 end
 
+
+## structured matrix methods ##
+function Base.replace_in_print_matrix(A::Tridiagonal,i::Integer,j::Integer,s::AbstractString)
+    i==j-1||i==j||i==j+1 ? s : Base.replace_with_centered_mark(s)
+end
+
 #tril and triu
 
 istriu(M::Tridiagonal) = all(M.dl .== 0)

base/show.jl

@@ -1126,6 +1126,17 @@ function alignment(
     return a
 end
 
+"""
+Unexported convenience function used in body of `replace_in_print_matrix`
+methods. By default returns a string of the same width as original with a
+centered cdot, used in printing of structural zeros of structured matrices.
+Accept keyword args `c` for alternate single character marker.
+"""
+function replace_with_centered_mark(s::AbstractString;c::Char = '⋅')
+    N = length(s)
+    return join(setindex!([utf8(" ") for i=1:N],string(c),ceil(Int,N/2)))
+end
+
 """
 `print_matrix_row(io, X, A, i, cols, sep)` produces the aligned output for
 a single matrix row X[i, cols] where the desired list of columns is given.
@@ -1135,8 +1146,7 @@ is specified as string sep.
 """
 function print_matrix_row(io::IO,
     X::AbstractVecOrMat, A::Vector,
-    i::Integer, cols::AbstractVector, sep::AbstractString
-)
+    i::Integer, cols::AbstractVector, sep::AbstractString)
     for k = 1:length(A)
         j = cols[k]
         if isassigned(X,Int(i),Int(j)) # isassigned accepts only `Int` indices
@@ -1149,7 +1159,8 @@ function print_matrix_row(io::IO,
         end
         l = repeat(" ", A[k][1]-a[1]) # pad on left and right as needed
         r = repeat(" ", A[k][2]-a[2])
-        print(io, l, sx, r)
+        prettysx = replace_in_print_matrix(X,i,j,sx)
+        print(io, l, prettysx, r)
         if k < length(A); print(io, sep); end
     end
 end

test/show.jl

@@ -339,9 +339,20 @@ end
 # Issue 14121
 @test_repr "(A'x)'"
 
+
 # issue #14481
 @test_repr "in(1,2,3)"
 @test_repr "<(1,2,3)"
 @test_repr "+(1,2,3)"
 @test_repr "-(1,2,3)"
 @test_repr "*(1,2,3)"
+
+# test structured zero matrix printing for select structured types
+A = reshape(1:16,4,4)
+@test replstr(Diagonal(A)) == "4x4 Diagonal{$Int}:\n 1  ⋅   ⋅   ⋅\n ⋅  6   ⋅   ⋅\n ⋅  ⋅  11   ⋅\n ⋅  ⋅   ⋅  16"
+@test replstr(Bidiagonal(A,true)) == "4x4 Bidiagonal{$Int}:\n 1  5   ⋅   ⋅\n ⋅  6  10   ⋅\n ⋅  ⋅  11  15\n ⋅  ⋅   ⋅  16"
+@test replstr(Bidiagonal(A,false)) == "4x4 Bidiagonal{$Int}:\n 1  ⋅   ⋅   ⋅\n 2  6   ⋅   ⋅\n ⋅  7  11   ⋅\n ⋅  ⋅  12  16"
+@test replstr(SymTridiagonal(A+A')) == "4x4 SymTridiagonal{$Int}:\n 2   7   ⋅   ⋅\n 7  12  17   ⋅\n ⋅  17  22  27\n ⋅   ⋅  27  32"
+@test replstr(Tridiagonal(diag(A,-1),diag(A),diag(A,+1))) == "4x4 Tridiagonal{$Int}:\n 1  5   ⋅   ⋅\n 2  6  10   ⋅\n ⋅  7  11  15\n ⋅  ⋅  12  16"
+@test replstr(UpperTriangular(A)) == "4x4 UpperTriangular{$Int,Array{$Int,2}}:\n 1  5   9  13\n ⋅  6  10  14\n ⋅  ⋅  11  15\n ⋅  ⋅   ⋅  16"
+@test replstr(LowerTriangular(A)) == "4x4 LowerTriangular{$Int,Array{$Int,2}}:\n 1  ⋅   ⋅   ⋅\n 2  6   ⋅   ⋅\n 3  7  11   ⋅\n 4  8  12  16"