3030`Cubic`), as well as auxiliary quantities `ixm_d`, `ixp_d` and `ixpp_d`
3131"""
3232function define_indices_d {BC} (:: Type{BSpline{Cubic{BC}}} , d, pad)
33- symix, symixm, symixp = symbol (" ix_" ,d), symbol (" ixm_" ,d), symbol (" ixp_" ,d)
34- symixpp, symx, symfx = symbol (" ixpp_" ,d), symbol (" x_" ,d), symbol (" fx_" ,d)
33+ symix, symixm, symixp = Symbol (" ix_" ,d), Symbol (" ixm_" ,d), Symbol (" ixp_" ,d)
34+ symixpp, symx, symfx = Symbol (" ixpp_" ,d), Symbol (" x_" ,d), Symbol (" fx_" ,d)
3535 quote
3636 # ensure that all of ix_d, ixm_d, ixp_d, and ixpp_d are in-bounds no
3737 # matter the value of pad
@@ -53,8 +53,8 @@ If any `ixX_d` for `x ∈ {m, p, pp}` (note: not `c_d`) should fall outside of
5353the data interval, they wrap around.
5454"""
5555function define_indices_d (:: Type{BSpline{Cubic{Periodic}}} , d, pad)
56- symix, symixm, symixp = symbol (" ix_" ,d), symbol (" ixm_" ,d), symbol (" ixp_" ,d)
57- symixpp, symx, symfx = symbol (" ixpp_" ,d), symbol (" x_" ,d), symbol (" fx_" ,d)
56+ symix, symixm, symixp = Symbol (" ix_" ,d), Symbol (" ixm_" ,d), Symbol (" ixp_" ,d)
57+ symixpp, symx, symfx = Symbol (" ixpp_" ,d), Symbol (" x_" ,d), Symbol (" fx_" ,d)
5858 quote
5959 $ symix = clamp (floor (Int, $ symx), 1 , size (itp,$ d))
6060 $ symfx = $ symx - $ symix
@@ -80,11 +80,11 @@ where `p` and `q` are defined in the docstring entry for `Cubic`, and
8080`fx_d` in the docstring entry for `define_indices_d`.
8181"""
8282function coefficients {C<:Cubic} (:: Type{BSpline{C}} , N, d)
83- symm, sym = symbol (" cm_" ,d), symbol (" c_" ,d)
84- symp, sympp = symbol (" cp_" ,d) ,symbol (" cpp_" ,d)
85- symfx = symbol (" fx_" ,d)
86- symfx_cub = symbol (" fx_cub_" , d)
87- sym_1m_fx_cub = symbol (" one_m_fx_cub_" , d)
83+ symm, sym = Symbol (" cm_" ,d), Symbol (" c_" ,d)
84+ symp, sympp = Symbol (" cp_" ,d) ,Symbol (" cpp_" ,d)
85+ symfx = Symbol (" fx_" ,d)
86+ symfx_cub = Symbol (" fx_cub_" , d)
87+ sym_1m_fx_cub = Symbol (" one_m_fx_cub_" , d)
8888 quote
8989 $ symfx_cub = cub ($ symfx)
9090 $ sym_1m_fx_cub = cub (1 - $ symfx)
@@ -108,10 +108,10 @@ where `p` and `q` are defined in the docstring entry for `Cubic`, and
108108`fx_d` in the docstring entry for `define_indices_d`.
109109"""
110110function gradient_coefficients {C<:Cubic} (:: Type{BSpline{C}} , d)
111- symm, sym, symp, sympp = symbol (" cm_" ,d), symbol (" c_" ,d), symbol (" cp_" ,d), symbol (" cpp_" ,d)
112- symfx = symbol (" fx_" ,d)
113- symfx_sqr = symbol (" fx_sqr_" , d)
114- sym_1m_fx_sqr = symbol (" one_m_fx_sqr_" , d)
111+ symm, sym, symp, sympp = Symbol (" cm_" ,d), Symbol (" c_" ,d), Symbol (" cp_" ,d), Symbol (" cpp_" ,d)
112+ symfx = Symbol (" fx_" ,d)
113+ symfx_sqr = Symbol (" fx_sqr_" , d)
114+ sym_1m_fx_sqr = Symbol (" one_m_fx_sqr_" , d)
115115 quote
116116 $ symfx_sqr = sqr ($ symfx)
117117 $ sym_1m_fx_sqr = sqr (1 - $ symfx)
@@ -136,8 +136,8 @@ where `p` and `q` are defined in the docstring entry for `Cubic`, and
136136`fx_d` in the docstring entry for `define_indices_d`.
137137"""
138138function hessian_coefficients {C<:Cubic} (:: Type{BSpline{C}} , d)
139- symm, sym, symp, sympp = symbol (" cm_" ,d), symbol (" c_" ,d), symbol (" cp_" ,d), symbol (" cpp_" ,d)
140- symfx = symbol (" fx_" ,d)
139+ symm, sym, symp, sympp = Symbol (" cm_" ,d), Symbol (" c_" ,d), Symbol (" cp_" ,d), Symbol (" cpp_" ,d)
140+ symfx = Symbol (" fx_" ,d)
141141 quote
142142 $ symm = 1 - $ symfx
143143 $ sym = 3 * $ symfx - 2
149149function index_gen {C<:Cubic,IT<:DimSpec{BSpline}} (:: Type{BSpline{C}} , :: Type{IT} , N:: Integer , offsets... )
150150 if length (offsets) < N
151151 d = length (offsets)+ 1
152- symm, sym, symp, sympp = symbol (" cm_" ,d), symbol (" c_" ,d), symbol (" cp_" ,d), symbol (" cpp_" ,d)
152+ symm, sym, symp, sympp = Symbol (" cm_" ,d), Symbol (" c_" ,d), Symbol (" cp_" ,d), Symbol (" cpp_" ,d)
153153 return :($ symm * $ (index_gen (IT, N, offsets... ,- 1 )) + $ sym * $ (index_gen (IT, N, offsets... , 0 )) +
154154 $ symp * $ (index_gen (IT, N, offsets... , 1 )) + $ sympp * $ (index_gen (IT, N, offsets... , 2 )))
155155 else
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