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Docstrings for colrange/rowrange and friends (#372)
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‎src/generic/AbstractBandedMatrix.jl‎

Lines changed: 176 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -64,19 +64,193 @@ bandrange(A) = -bandwidth(A,1):bandwidth(A,2)
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67-
# start/stop indices of the i-th column/row, bounded by actual matrix size
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"""
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colstart(A, i::Integer)
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Return the starting row index of the filled bands in the i-th column,
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bounded by the actual matrix size.
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# Examples
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```jldoctest
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julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> BandedMatrices.colstart(A, 3)
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2
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julia> BandedMatrices.colstart(A, 4)
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3
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```
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"""
6889
@inline colstart(A, i::Integer) = max(i-bandwidth(A,2), 1)
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"""
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colstop(A, i::Integer)
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Return the stopping row index of the filled bands in the i-th column,
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bounded by the actual matrix size.
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# Examples
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```jldoctest
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julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> BandedMatrices.colstop(A, 3)
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3
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julia> BandedMatrices.colstop(A, 4)
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4
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```
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"""
69113
@inline colstop(A, i::Integer) = max(min(i+bandwidth(A,1), size(A, 1)), 0)
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"""
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rowstart(A, i::Integer)
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Return the starting column index of the filled bands in the i-th row,
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bounded by the actual matrix size.
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# Examples
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```jldoctest
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julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> BandedMatrices.rowstart(A, 2)
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2
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julia> BandedMatrices.rowstart(A, 3)
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3
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```
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"""
70137
@inline rowstart(A, i::Integer) = max(i-bandwidth(A,1), 1)
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"""
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rowstop(A, i::Integer)
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Return the stopping column index of the filled bands in the i-th row,
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bounded by the actual matrix size.
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# Examples
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```jldoctest
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julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> BandedMatrices.rowstop(A, 2)
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3
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julia> BandedMatrices.rowstop(A, 4)
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4
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```
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"""
71161
@inline rowstop(A, i::Integer) = max(min(i+bandwidth(A,2), size(A, 2)), 0)
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"""
164+
colrange(A, i::Integer)
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Return the range of rows in the `i`-th column that correspond to filled bands.
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# Examples
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```jldoctest
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julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> colrange(A, 1)
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1:1
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julia> colrange(A, 3)
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2:3
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```
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"""
74184
@inline colrange(A, i::Integer) = colstart(A,i):colstop(A,i)
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"""
187+
rowrange(A, i::Integer)
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Return the range of columns in the `i`-th row that correspond to filled bands.
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# Examples
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```jldoctest
193+
julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> rowrange(A, 1)
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1:2
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julia> rowrange(A, 4)
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4:4
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```
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"""
75207
@inline rowrange(A, i::Integer) = rowstart(A,i):rowstop(A,i)
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77209

78-
# length of i-the column/row
210+
"""
211+
collength(A, i::Integer)
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213+
Return the number of filled bands in the `i`-th column.
214+
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# Examples
216+
```jldoctest
217+
julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
223+
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julia> BandedMatrices.collength(A, 1)
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1
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227+
julia> BandedMatrices.collength(A, 2)
228+
2
229+
```
230+
"""
79231
@inline collength(A, i::Integer) = max(colstop(A, i) - colstart(A, i) + 1, 0)
232+
233+
"""
234+
rowlength(A, i::Integer)
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236+
Return the number of filled bands in the `i`-th row.
237+
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# Examples
239+
```jldoctest
240+
julia> A = BandedMatrix(0=>1:4, 1=>5:7)
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4×4 BandedMatrix{Int64} with bandwidths (0, 1):
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1 5 ⋅ ⋅
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⋅ 2 6 ⋅
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⋅ ⋅ 3 7
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⋅ ⋅ ⋅ 4
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julia> BandedMatrices.rowlength(A, 1)
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2
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250+
julia> BandedMatrices.rowlength(A, 4)
251+
1
252+
```
253+
"""
80254
@inline rowlength(A, i::Integer) = max(rowstop(A, i) - rowstart(A, i) + 1, 0)
81255

82256
@inline banded_colsupport(A, j::Integer) = colrange(A, j)

‎test/test_symbanded.jl‎

Lines changed: 29 additions & 27 deletions
Original file line numberDiff line numberDiff line change
@@ -310,33 +310,35 @@ end
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end
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end
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313-
@testset "Generalized eigenvalues $W{$T}($Ua,$Ub)($n,$wa-$wb)" for (T,W) in (
314-
(Float32, Symmetric),
315-
(Float64, Symmetric),
316-
(Float32, Hermitian),
317-
(Float64, Hermitian),
318-
(ComplexF32, Hermitian),
319-
(ComplexF64, Hermitian),
320-
),
321-
(Ua, Ub) in ((:L,:L), (:U,:U)),
322-
(wa, wb) in ((2, 3), (3, 2)), n in (4,)
323-
#
324-
function sbmatrix(W, T, U, w, n)
325-
r = U == :L ? (0:-1:-w+1) : (0:w-1)
326-
band(k) = k => ones(T, n - abs(k)) * 2.0^-abs(k)
327-
W(BandedMatrix(band.(r)...), U)
328-
end
329-
A = sbmatrix(W, T, Ua, wa, n)
330-
B = sbmatrix(W, T, Ub, wb, n)
331-
AM, BM = Matrix.((A,B))
332-
@test eigvals(A, B) ≈ eigvals(AM, BM)
333-
if VERSION >= v"1.9"
334-
Λ, V = eigen(A, B)
335-
VM = Matrix(V)
336-
Λ2, V2 = eigen(AM, BM)
337-
@test Λ ≈ Λ2
338-
@test VM' * AM * VM ≈ V2' * AM * V2
339-
@test VM' * AM * VM ≈ VM' * BM * VM * Diagonal(Λ)
313+
@testset "Generalized eigenvalues" begin
314+
@testset "$W{$T}($Ua,$Ub)($n,$wa-$wb)" for (T,W) in (
315+
(Float32, Symmetric),
316+
(Float64, Symmetric),
317+
(Float32, Hermitian),
318+
(Float64, Hermitian),
319+
(ComplexF32, Hermitian),
320+
(ComplexF64, Hermitian),
321+
),
322+
(Ua, Ub) in ((:L,:L), (:U,:U)),
323+
(wa, wb) in ((2, 3), (3, 2)), n in (4,)
324+
#
325+
function sbmatrix(W, T, U, w, n)
326+
r = U == :L ? (0:-1:-w+1) : (0:w-1)
327+
band(k) = k => ones(T, n - abs(k)) * 2.0^-abs(k)
328+
W(BandedMatrix(band.(r)...), U)
329+
end
330+
A = sbmatrix(W, T, Ua, wa, n)
331+
B = sbmatrix(W, T, Ub, wb, n)
332+
AM, BM = Matrix.((A,B))
333+
@test eigvals(A, B) ≈ eigvals(AM, BM)
334+
if VERSION >= v"1.9"
335+
Λ, V = eigen(A, B)
336+
VM = Matrix(V)
337+
Λ2, V2 = eigen(AM, BM)
338+
@test Λ ≈ Λ2
339+
@test VM' * AM * VM ≈ V2' * AM * V2
340+
@test VM' * AM * VM ≈ VM' * BM * VM * Diagonal(Λ)
341+
end
340342
end
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end
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