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LICENSE.md

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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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Contains code that is modified from Julia's Base code, which is distributted
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Contains code that is modified from Julia's Base code, which is distributed
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with the following license:
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Copyright (c) 2009-2018: Jeff Bezanson, Stefan Karpinski, Viral B. Shah, and other contributors:
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NEWS.md

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- Fix several bugs and performance enhancements
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#### 0.7.1
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- `F` was renamed `DFunction` for dynamic funtion
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- `F` was renamed `DFunction` for dynamic function
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- `Fun`s are now subtypes of `Function`
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- Support `f^k` for polynomial `f` and real `k`
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- Fix several bugs and performance enhancements
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#### 0.6.0
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- Adds support for Julia v0.6
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- Replaces FixedSizeArrays.jl dependancy with StaticArrays.jl
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- Replaces FixedSizeArrays.jl dependency with StaticArrays.jl
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- Auto-vectorization `f([1,2,3])` is removed in favour of broadcasting `f.([1,2,3])`
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docs/src/usage/constructors.md

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julia> g = abs(f);
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julia> space(g) isa ContinuousSpace # Piecewise continous functions
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julia> space(g) isa ContinuousSpace # Piecewise continuous functions
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true
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julia> domain(g) isa PiecewiseSegment # Segments interspersed by the roots of f

docs/src/usage/spaces.md

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A key tool for solving differential equations are the ultraspherical spaces, encoded as `Ultraspherical(λ)` for `λ ≠ 0`,
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which can be defined by the span of derivatives of Chebyshev polynomials, or alternatively as polynomials orthogonal with respect to the weight ``(1-x^2)^{λ - \frac{1}{2}}`` for ``-1 ≤ x ≤ 1``.
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Note that `Ultraspherical(1)` corresponds to the Chebyshev basis of the second kind: ``\mathop{U}_k(x) = \frac{\sin((k+1)\arccos{x})}{\sin(\arccos{x})}``. The relationship with Chebyshev polynomials follows from trigonemetric identities: ``\mathop{T}_k'(x) = k \mathop{U}_{k-1}(x)``.
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Note that `Ultraspherical(1)` corresponds to the Chebyshev basis of the second kind: ``\mathop{U}_k(x) = \frac{\sin((k+1)\arccos{x})}{\sin(\arccos{x})}``. The relationship with Chebyshev polynomials follows from trigonometric identities: ``\mathop{T}_k'(x) = k \mathop{U}_{k-1}(x)``.
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Converting between ultraspherical polynomials (with integer orders) is extremely efficient: it requires ``\mathop{O}(n)`` operations, where ``n`` is the number of coefficients.
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examples/Eigenvalue.jl

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# If the solutions are not relatively constant near the boundary then one should push
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# the boundaries further out.
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# For problems with different contraints or boundary conditions,
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# For problems with different constraints or boundary conditions,
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# `B` can be any zero functional constraint, e.g., `DefiniteIntegral()`.
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include("Eigenvalue_anharmonic.jl")

examples/Eigenvalue_anharmonic.jl

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SEg = ApproxFun.SymmetricEigensystem(L, B);
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# We construct `n × n` matrix representations of the opertors that we diagonalize
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# We construct `n × n` matrix representations of the operators that we diagonalize
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n = 3000
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λ = eigvals(SEg, n);
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src/Plot/Plot.jl

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seriestype --> :surface
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if norm(imag(vals),Inf)>10e-9
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@warn "Imaginary part is non-neglible. Only plotting real part."
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@warn "Imaginary part is non-negligible. Only plotting real part."
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end
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# sort the points
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seriestype --> :surface
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if norm(imag(vals),Inf)>10e-9
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@warn "Imaginary part is non-neglible. Only plotting real part."
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@warn "Imaginary part is non-negligible. Only plotting real part."
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end
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