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dynamic_data.hpp
-
1 namespace atomic {
2 namespace dynamic_data {
3  /* Represent SEXP as double so it can be put on the tape. Same for
4  char pointers.
5 
6  FIXME: Portability.
7  Currently assuming sizeof(double) >= sizeof(pointer) which should
8  be OK for most common 32/64 bit operating systems.
9  */
10 
11 #ifdef WITH_LIBTMB
12  double sexp_to_double(SEXP x);
13  SEXP double_to_sexp(double x);
14  double charptr_to_double(const char *x);
15  const char* double_to_charptr(double x);
16 #else
17  double sexp_to_double(SEXP x) {
18  SEXP* px = &x;
19  double* py = (double*) px;
20  return py[0];
21  }
22  SEXP double_to_sexp(double x) {
23  double* px = &x;
24  SEXP* py = (SEXP*) px;
25  return py[0];
26  }
27  double charptr_to_double(const char *x) {
28  const char** px = &x;
29  double* py = (double*) px;
30  return py[0];
31  }
32  const char* double_to_charptr(double x) {
33  double* px = &x;
34  const char** py = (const char**) px;
35  return py[0];
36  }
37 #endif // #ifdef WITH_LIBTMB
38 
39  TMB_ATOMIC_VECTOR_FUNCTION(
40  // atomic name
41  list_lookup_by_index
42  ,
43  // output dim
44  1
45  ,
46  // forward double
47  SEXP data = double_to_sexp( tx[0] );
48  int index = (int) tx[1];
49  ty[0] = sexp_to_double( VECTOR_ELT(data, index) );
50  ,
51  // reverse
52  px[0] = 0; px[1] = 0;
53  )
54 
55  TMB_ATOMIC_VECTOR_FUNCTION(
56  // atomic name
57  list_lookup_by_name
58  ,
59  // output dim
60  1
61  ,
62  // forward double
63  SEXP list = double_to_sexp( tx[0] );
64  const char* str = double_to_charptr( tx[1] );
65  SEXP elmt = R_NilValue;
66  SEXP names = Rf_getAttrib(list, R_NamesSymbol);
67  int i;
68  for (i = 0; i < Rf_length(list); i++) {
69  if(strcmp(CHAR(STRING_ELT(names, i)), str) == 0) {
70  elmt = VECTOR_ELT(list, i);
71  break;
72  }
73  }
74  ty[0] = sexp_to_double( elmt );
75  ,
76  // reverse
77  px[0] = 0; px[1] = 0;
78  )
79 
80  TMB_ATOMIC_VECTOR_FUNCTION(
81  // atomic name
82  envir_lookup_by_name
83  ,
84  // output dim
85  1
86  ,
87  // forward double
88  SEXP envir = double_to_sexp( tx[0] );
89  const char* nam = double_to_charptr( tx[1] );
90  SEXP res = Rf_findVar(Rf_install(nam), envir);
91  ty[0] = sexp_to_double( res );
92  ,
93  // reverse
94  px[0] = 0; px[1] = 0;
95  )
96 
97  // Convert SEXP to vector
98  TMB_ATOMIC_VECTOR_FUNCTION(
99  // atomic name
100  sexp_to_vector
101  ,
102  // output dim
103  LENGTH( double_to_sexp( asDouble(tx[0]) ))
104  ,
105  // forward double
106  SEXP data = double_to_sexp( tx[0] );
107  int n = LENGTH( data );
108  if (n != (int) ty.size())
109  Rf_error("Data update: "
110  "number of items to replace (%i) "
111  "does not match replacement length (%i)",
112  ty.size(), n);
113  double* pdata = REAL(data);
114  for (int i = 0; i<n; i++) ty[i] = pdata[i];
115  ,
116  // reverse
117  px[0] = 0;
118  )
119 
120 
121  // Input: double x, Type y
122  // Output double x (now with fake dependence on y)
123  TMB_ATOMIC_VECTOR_FUNCTION(
124  // atomic name
125  set_dependent
126  ,
127  // output dim
128  1
129  ,
130  // forward double
131  ty[0] = tx[0];
132  ,
133  // reverse
134  px[0] = 0; px[1] = 0;
135  )
136 
137 
138  /* Interfaces */
139  template<class Type>
140  Type set_dependent(double x, Type fake_parameter) {
141  CppAD::vector<Type> tx(2);
142  tx[0] = x;
143  tx[1] = fake_parameter;
144  return set_dependent(tx)[0];
145  }
146 
147  template<class Type>
148  vector<Type> sexp_to_vector(Type sexp) {
149  CppAD::vector<Type> tx(1);
150  tx[0] = sexp;
151  CppAD::vector<Type> ty(sexp_to_vector(tx));
152  return ty;
153  }
154 
155  // Output: SEXP represented by Type
156  template<class Type>
157  Type envir_lookup_by_name(Type envir, const char* name) {
158  CppAD::vector<Type> tx(2);
159  tx[0] = envir;
160  tx[1] = charptr_to_double( name );
161  return envir_lookup_by_name(tx)[0];
162  }
163 
164  // Output: SEXP represented by Type
165  template<class Type>
166  Type list_lookup_by_name(Type list, const char* name) {
167  CppAD::vector<Type> tx(2);
168  tx[0] = list;
169  tx[1] = charptr_to_double( name );
170  return list_lookup_by_name(tx)[0];
171  }
172 
173  // Output: SEXP represented by Type
174  template<class Type>
175  Type list_lookup_by_index(Type list, Type index) {
176  CppAD::vector<Type> tx(2);
177  tx[0] = list;
178  tx[1] = index;
179  return list_lookup_by_index(tx)[0];
180  }
181 
182  // Fill elements from y into x
183  template<class T1, class T2>
184  void cpy(T1 &x, T2 y) {
185  for (int i=0; i<y.size(); i++) {
186  x.coeffRef(i) = y.coeffRef(i);
187  }
188  }
189 
190  // Scalar case
191  template<class Type>
192  void cpy(Type &x, vector<Type> y) {
193  x = y[0];
194  }
195 
196 }
197 }
198 
221 #define DATA_UPDATE(name) \
222 atomic::dynamic_data::cpy(name, \
223  atomic::dynamic_data::sexp_to_vector( \
224  atomic::dynamic_data::list_lookup_by_name( \
225  atomic::dynamic_data::envir_lookup_by_name( \
226  atomic::dynamic_data::set_dependent( \
227  atomic::dynamic_data::sexp_to_double( \
228  ENCLOS(TMB_OBJECTIVE_PTR -> report) \
229  ), \
230  TMB_OBJECTIVE_PTR -> theta[0] \
231  ), \
232  "data" \
233  ), \
234  #name \
235  ) \
236  ) \
237 );
vector
Vector class used by TMB.
Definition: vector.hpp:17
+
1 namespace atomic {
2 namespace dynamic_data {
3  /* Represent SEXP as double so it can be put on the tape. Same for
4  char pointers.
5 
6  FIXME: Portability.
7  Currently assuming sizeof(double) >= sizeof(pointer) which should
8  be OK for most common 32/64 bit operating systems.
9  */
10 
11 #ifdef WITH_LIBTMB
12  double sexp_to_double(SEXP x);
13  SEXP double_to_sexp(double x);
14  double charptr_to_double(const char *x);
15  const char* double_to_charptr(double x);
16 #else
17  double sexp_to_double(SEXP x) {
18  SEXP* px = &x;
19  double* py = (double*) px;
20  return py[0];
21  }
22  SEXP double_to_sexp(double x) {
23  double* px = &x;
24  SEXP* py = (SEXP*) px;
25  return py[0];
26  }
27  double charptr_to_double(const char *x) {
28  const char** px = &x;
29  double* py = (double*) px;
30  return py[0];
31  }
32  const char* double_to_charptr(double x) {
33  double* px = &x;
34  const char** py = (const char**) px;
35  return py[0];
36  }
37 #endif // #ifdef WITH_LIBTMB
38 
39  TMB_ATOMIC_VECTOR_FUNCTION(
40  // atomic name
41  list_lookup_by_index
42  ,
43  // output dim
44  1
45  ,
46  // forward double
47  SEXP data = double_to_sexp( tx[0] );
48  int index = (int) tx[1];
49  ty[0] = sexp_to_double( VECTOR_ELT(data, index) );
50  ,
51  // reverse
52  px[0] = 0; px[1] = 0;
53  )
54 
55  TMB_ATOMIC_VECTOR_FUNCTION(
56  // atomic name
57  list_lookup_by_name
58  ,
59  // output dim
60  1
61  ,
62  // forward double
63  SEXP list = double_to_sexp( tx[0] );
64  const char* str = double_to_charptr( tx[1] );
65  SEXP elmt = R_NilValue;
66  SEXP names = Rf_getAttrib(list, R_NamesSymbol);
67  int i;
68  for (i = 0; i < Rf_length(list); i++) {
69  if(strcmp(CHAR(STRING_ELT(names, i)), str) == 0) {
70  elmt = VECTOR_ELT(list, i);
71  break;
72  }
73  }
74  ty[0] = sexp_to_double( elmt );
75  ,
76  // reverse
77  px[0] = 0; px[1] = 0;
78  )
79 
80  TMB_ATOMIC_VECTOR_FUNCTION(
81  // atomic name
82  envir_lookup_by_name
83  ,
84  // output dim
85  1
86  ,
87  // forward double
88  SEXP envir = double_to_sexp( tx[0] );
89  const char* nam = double_to_charptr( tx[1] );
90  SEXP res = Rf_findVar(Rf_install(nam), envir);
91  ty[0] = sexp_to_double( res );
92  ,
93  // reverse
94  px[0] = 0; px[1] = 0;
95  )
96 
97  // Convert SEXP to vector
98  TMB_ATOMIC_VECTOR_FUNCTION(
99  // atomic name
100  sexp_to_vector
101  ,
102  // output dim
103  LENGTH( double_to_sexp( asDouble(tx[0]) ))
104  ,
105  // forward double
106  SEXP data = double_to_sexp( tx[0] );
107  int n = LENGTH( data );
108  if (n != (int) ty.size())
109  Rf_error("Data update: "
110  "number of items to replace (%i) "
111  "does not match replacement length (%i)",
112  (int) ty.size(), n);
113  double* pdata = REAL(data);
114  for (int i = 0; i<n; i++) ty[i] = pdata[i];
115  ,
116  // reverse
117  px[0] = 0;
118  )
119 
120 
121  // Input: double x, Type y
122  // Output double x (now with fake dependence on y)
123  TMB_ATOMIC_VECTOR_FUNCTION(
124  // atomic name
125  set_dependent
126  ,
127  // output dim
128  1
129  ,
130  // forward double
131  ty[0] = tx[0];
132  ,
133  // reverse
134  px[0] = 0; px[1] = 0;
135  )
136 
137 
138  /* Interfaces */
139  template<class Type>
140  Type set_dependent(double x, Type fake_parameter) {
141  CppAD::vector<Type> tx(2);
142  tx[0] = x;
143  tx[1] = fake_parameter;
144  return set_dependent(tx)[0];
145  }
146 
147  template<class Type>
148  vector<Type> sexp_to_vector(Type sexp) {
149  CppAD::vector<Type> tx(1);
150  tx[0] = sexp;
151  CppAD::vector<Type> ty(sexp_to_vector(tx));
152  return ty;
153  }
154 
155  // Output: SEXP represented by Type
156  template<class Type>
157  Type envir_lookup_by_name(Type envir, const char* name) {
158  CppAD::vector<Type> tx(2);
159  tx[0] = envir;
160  tx[1] = charptr_to_double( name );
161  return envir_lookup_by_name(tx)[0];
162  }
163 
164  // Output: SEXP represented by Type
165  template<class Type>
166  Type list_lookup_by_name(Type list, const char* name) {
167  CppAD::vector<Type> tx(2);
168  tx[0] = list;
169  tx[1] = charptr_to_double( name );
170  return list_lookup_by_name(tx)[0];
171  }
172 
173  // Output: SEXP represented by Type
174  template<class Type>
175  Type list_lookup_by_index(Type list, Type index) {
176  CppAD::vector<Type> tx(2);
177  tx[0] = list;
178  tx[1] = index;
179  return list_lookup_by_index(tx)[0];
180  }
181 
182  // Fill elements from y into x
183  template<class T1, class T2>
184  void cpy(T1 &x, T2 y) {
185  for (int i=0; i<y.size(); i++) {
186  x.coeffRef(i) = y.coeffRef(i);
187  }
188  }
189 
190  // Scalar case
191  template<class Type>
192  void cpy(Type &x, vector<Type> y) {
193  x = y[0];
194  }
195 
196 }
197 }
198 
221 #define DATA_UPDATE(name) \
222 atomic::dynamic_data::cpy(name, \
223  atomic::dynamic_data::sexp_to_vector( \
224  atomic::dynamic_data::list_lookup_by_name( \
225  atomic::dynamic_data::envir_lookup_by_name( \
226  atomic::dynamic_data::set_dependent( \
227  atomic::dynamic_data::sexp_to_double( \
228  ENCLOS(TMB_OBJECTIVE_PTR -> report) \
229  ), \
230  TMB_OBJECTIVE_PTR -> theta[0] \
231  ), \
232  "data" \
233  ), \
234  #name \
235  ) \
236  ) \
237 );
vector
Vector class used by TMB.
Definition: vector.hpp:17
atomic
Namespace with special functions and derivatives.
Definition: atomic_convolve.hpp:4
TMB_ATOMIC_VECTOR_FUNCTION
#define TMB_ATOMIC_VECTOR_FUNCTION( ATOMIC_NAME, OUTPUT_DIM, ATOMIC_DOUBLE, ATOMIC_REVERSE)
Construct atomic vector function based on known derivatives.
Definition: tmbad_atomic_macro.hpp:217
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diff --git a/sparse__matrix__exponential_8hpp.html b/sparse__matrix__exponential_8hpp.html index 5be356273..70c9dc5bd 100644 --- a/sparse__matrix__exponential_8hpp.html +++ b/sparse__matrix__exponential_8hpp.html @@ -28,7 +28,7 @@
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diff --git a/spatial_8cpp-example.html b/spatial_8cpp-example.html index bb604969f..9699a3e83 100644 --- a/spatial_8cpp-example.html +++ b/spatial_8cpp-example.html @@ -28,7 +28,7 @@
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diff --git a/spde_aniso_8cpp-example.html b/spde_aniso_8cpp-example.html index 1195da9af..6120c8d83 100644 --- a/spde_aniso_8cpp-example.html +++ b/spde_aniso_8cpp-example.html @@ -28,7 +28,7 @@
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diff --git a/spde_aniso_speedup_8cpp-example.html b/spde_aniso_speedup_8cpp-example.html index 9789f6d7c..f2db76b92 100644 --- a/spde_aniso_speedup_8cpp-example.html +++ b/spde_aniso_speedup_8cpp-example.html @@ -28,7 +28,7 @@
TMB Documentation -  v1.9.8 +  v1.9.9
diff --git a/splines_8hpp.html b/splines_8hpp.html index 8851a40af..6290154b6 100644 --- a/splines_8hpp.html +++ b/splines_8hpp.html @@ -28,7 +28,7 @@
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diff --git a/splines_8hpp_source.html b/splines_8hpp_source.html index a0a6f59e3..374615f90 100644 --- a/splines_8hpp_source.html +++ b/splines_8hpp_source.html @@ -28,7 +28,7 @@
TMB Documentation -  v1.9.8 +  v1.9.9
@@ -73,7 +73,7 @@
splines.hpp
-Go to the documentation of this file.
1 
5 namespace tmbutils {
6 
7 // Copyright (C) 2013-2015 Kasper Kristensen
8 // License: GPL-2
9 
10 /*
11  * R : A Computer Language for Statistical Data Analysis
12  * Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka
13  * Copyright (C) 1998--2001 Robert Gentleman, Ross Ihaka and the
14  * R Development Core Team
15  *
16  * This program is free software; you can redistribute it and/or modify
17  * it under the terms of the GNU General Public License as published by
18  * the Free Software Foundation; either version 2 of the License, or
19  * (at your option) any later version.
20  *
21  * This program is distributed in the hope that it will be useful,
22  * but WITHOUT ANY WARRANTY; without even the implied warranty of
23  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
24  * GNU General Public License for more details.
25  *
26  * You should have received a copy of the GNU General Public License
27  * along with this program; if not, a copy is available at
28  * http://www.r-project.org/Licenses/
29  */
30 
31 /* Spline Interpolation
32  * --------------------
33  * C code to perform spline fitting and interpolation.
34  * There is code here for:
35  *
36  * 1. Natural splines.
37  *
38  * 2. Periodic splines
39  *
40  * 3. Splines with end-conditions determined by fitting
41  * cubics in the start and end intervals (Forsythe et al).
42  *
43  *
44  * Computational Techniques
45  * ------------------------
46  * A special LU decomposition for symmetric tridiagonal matrices
47  * is used for all computations, except for periodic splines where
48  * Choleski is more efficient.
49  */
50 
58 template <class Type>
59 class splinefun
60 {
61 private:
62  /* Input to R's "spline_coef" */
63  int method[1];
64  int n[1];
65  Type *x;
66  Type *y;
67  Type *b;
68  Type *c;
69  Type *d;
70  Type *e;
71 
72  /* Not used */
73  //int errno, EDOM;
74 
75  /* Memory management helpers */
76  void clear() {
77  if (*n != 0) {
78  delete [] x;
79  delete [] y;
80  delete [] b;
81  delete [] c;
82  delete [] d;
83  delete [] e;
84  }
85  }
86  void alloc(int n_) {
87  *n = n_;
88  x = new Type[*n];
89  y = new Type[*n];
90  b = new Type[*n];
91  c = new Type[*n];
92  d = new Type[*n];
93  e = new Type[*n];
94  }
95  void copy_from(const splinefun &fun) {
96  *method = fun.method[0];
97  *n = fun.n[0];
98  alloc(*n);
99  for(int i = 0; i < *n; i++) {
100  x[i] = fun.x[i];
101  y[i] = fun.y[i];
102  b[i] = fun.b[i];
103  c[i] = fun.c[i];
104  d[i] = fun.d[i];
105  e[i] = fun.e[i];
106  }
107  }
108 
109 public:
110  /* Construct spline */
111  splinefun() {
112  x = y = b = c = d = e = NULL;
113  *method = *n = 0;
114  };
115  splinefun(const splinefun &fun){
116  copy_from(fun);
117  }
118  splinefun& operator=(const splinefun &x) {
119  if (this != &x) {
120  (*this).clear();
121  (*this).copy_from(x);
122  }
123  return *this;
124  }
125  ~splinefun() {
126  clear();
127  };
137  splinefun(const vector<Type> &x_,
138  const vector<Type> &y_,
139  int method_ = 3) {
140  method[0] = method_;
141  n[0] = x_.size();
142  alloc( x_.size() );
143  for(int i=0; i < *n; i++) {
144  x[i] = x_[i];
145  y[i] = y_[i];
146  }
147  spline_coef(method, n, x, y, b, c, d, e);
148  }
149 
151  Type operator()(const Type &x_) {
152  Type u[1];
153  Type v[1];
154  int nu[1];
155  u[0] = x_;
156  nu[0] = 1;
157  spline_eval(method, nu, u, v,
158  n, x, y, b, c, d);
159  return v[0];
160  }
162  vector<Type> operator() (const vector<Type> &x) {
163  vector<Type> y(x.size());
164  for (int i=0; i<x.size(); i++) y[i] = (*this)(x[i]);
165  return y;
166  }
167 
168  /* ------------------------------------------------------------------
169  * The following is copy-pasted from R-package "stats" where "double"
170  * has been replaced by "Type".
171  *-------------------------------------------------------------------
172  */
173 
174  /*
175  * Natural Splines
176  * ---------------
177  * Here the end-conditions are determined by setting the second
178  * derivative of the spline at the end-points to equal to zero.
179  *
180  * There are n-2 unknowns (y[i]'' at x[2], ..., x[n-1]) and n-2
181  * equations to determine them. Either Choleski or Gaussian
182  * elimination could be used.
183  */
184 
185  void natural_spline(int n, Type *x, Type *y, Type *b, Type *c, Type *d)
186  {
187  int nm1, i;
188  Type t;
189 
190  x--; y--; b--; c--; d--;
191 
192  if(n < 2) {
193  //errno = EDOM;
194  return;
195  }
196 
197  if(n < 3) {
198  t = (y[2] - y[1]);
199  b[1] = t / (x[2]-x[1]);
200  b[2] = b[1];
201  c[1] = c[2] = d[1] = d[2] = 0.0;
202  return;
203  }
204 
205  nm1 = n - 1;
206 
207  /* Set up the tridiagonal system */
208  /* b = diagonal, d = offdiagonal, c = right hand side */
209 
210  d[1] = x[2] - x[1];
211  c[2] = (y[2] - y[1])/d[1];
212  for( i=2 ; i<n ; i++) {
213  d[i] = x[i+1] - x[i];
214  b[i] = 2.0 * (d[i-1] + d[i]);
215  c[i+1] = (y[i+1] - y[i])/d[i];
216  c[i] = c[i+1] - c[i];
217  }
218 
219  /* Gaussian elimination */
220 
221  for(i=3 ; i<n ; i++) {
222  t = d[i-1]/b[i-1];
223  b[i] = b[i] - t*d[i-1];
224  c[i] = c[i] - t*c[i-1];
225  }
226 
227  /* Backward substitution */
228 
229  c[nm1] = c[nm1]/b[nm1];
230  for(i=n-2 ; i>1 ; i--)
231  c[i] = (c[i]-d[i]*c[i+1])/b[i];
232 
233  /* End conditions */
234 
235  c[1] = c[n] = 0.0;
236 
237  /* Get cubic coefficients */
238 
239  b[1] = (y[2] - y[1])/d[1] - d[i] * c[2];
240  c[1] = 0.0;
241  d[1] = c[2]/d[1];
242  b[n] = (y[n] - y[nm1])/d[nm1] + d[nm1] * c[nm1];
243  for(i=2 ; i<n ; i++) {
244  b[i] = (y[i+1]-y[i])/d[i] - d[i]*(c[i+1]+2.0*c[i]);
245  d[i] = (c[i+1]-c[i])/d[i];
246  c[i] = 3.0*c[i];
247  }
248  c[n] = 0.0;
249  d[n] = 0.0;
250 
251  return;
252  }
253 
254  /*
255  * Splines a la Forsythe Malcolm and Moler
256  * ---------------------------------------
257  * In this case the end-conditions are determined by fitting
258  * cubic polynomials to the first and last 4 points and matching
259  * the third derivitives of the spline at the end-points to the
260  * third derivatives of these cubics at the end-points.
261  */
262 
263  void fmm_spline(int n, Type *x, Type *y, Type *b, Type *c, Type *d)
264  {
265  int nm1, i;
266  Type t;
267 
268  /* Adjustment for 1-based arrays */
269 
270  x--; y--; b--; c--; d--;
271 
272  if(n < 2) {
273  //errno = EDOM;
274  return;
275  }
276 
277  if(n < 3) {
278  t = (y[2] - y[1]);
279  b[1] = t / (x[2]-x[1]);
280  b[2] = b[1];
281  c[1] = c[2] = d[1] = d[2] = 0.0;
282  return;
283  }
284 
285  nm1 = n - 1;
286 
287  /* Set up tridiagonal system */
288  /* b = diagonal, d = offdiagonal, c = right hand side */
289 
290  d[1] = x[2] - x[1];
291  c[2] = (y[2] - y[1])/d[1];/* = +/- Inf for x[1]=x[2] -- problem? */
292  for(i=2 ; i<n ; i++) {
293  d[i] = x[i+1] - x[i];
294  b[i] = 2.0 * (d[i-1] + d[i]);
295  c[i+1] = (y[i+1] - y[i])/d[i];
296  c[i] = c[i+1] - c[i];
297  }
298 
299  /* End conditions. */
300  /* Third derivatives at x[0] and x[n-1] obtained */
301  /* from divided differences */
302 
303  b[1] = -d[1];
304  b[n] = -d[nm1];
305  c[1] = c[n] = 0.0;
306  if(n > 3) {
307  c[1] = c[3]/(x[4]-x[2]) - c[2]/(x[3]-x[1]);
308  c[n] = c[nm1]/(x[n] - x[n-2]) - c[n-2]/(x[nm1]-x[n-3]);
309  c[1] = c[1]*d[1]*d[1]/(x[4]-x[1]);
310  c[n] = -c[n]*d[nm1]*d[nm1]/(x[n]-x[n-3]);
311  }
312 
313  /* Gaussian elimination */
314 
315  for(i=2 ; i<=n ; i++) {
316  t = d[i-1]/b[i-1];
317  b[i] = b[i] - t*d[i-1];
318  c[i] = c[i] - t*c[i-1];
319  }
320 
321  /* Backward substitution */
322 
323  c[n] = c[n]/b[n];
324  for(i=nm1 ; i>=1 ; i--)
325  c[i] = (c[i]-d[i]*c[i+1])/b[i];
326 
327  /* c[i] is now the sigma[i-1] of the text */
328  /* Compute polynomial coefficients */
329 
330  b[n] = (y[n] - y[n-1])/d[n-1] + d[n-1]*(c[n-1]+ 2.0*c[n]);
331  for(i=1 ; i<=nm1 ; i++) {
332  b[i] = (y[i+1]-y[i])/d[i] - d[i]*(c[i+1]+2.0*c[i]);
333  d[i] = (c[i+1]-c[i])/d[i];
334  c[i] = 3.0*c[i];
335  }
336  c[n] = 3.0*c[n];
337  d[n] = d[nm1];
338  return;
339  }
340 
341 
342  /*
343  * Periodic Spline
344  * ---------------
345  * The end conditions here match spline (and its derivatives)
346  * at x[1] and x[n].
347  *
348  * Note: There is an explicit check that the user has supplied
349  * data with y[1] equal to y[n].
350  */
351 
352  void periodic_spline(int n, Type *x, Type *y,
353  Type *b, Type *c, Type *d, Type *e)
354  {
355  Type s;
356  int i, nm1;
357 
358  /* Adjustment for 1-based arrays */
359 
360  x--; y--; b--; c--; d--; e--;
361 
362  if(n < 2 || y[1] != y[n]) {
363  errno = EDOM;
364  return;
365  }
366 
367  if(n == 2) {
368  b[1] = b[2] = c[1] = c[2] = d[1] = d[2] = 0.0;
369  return;
370  } else if (n == 3) {
371  b[1] = b[2] = b[3] = -(y[1] - y[2])*(x[1] - 2*x[2] + x[3])/(x[3]-x[2])/(x[2]-x[1]);
372  c[1] = -3*(y[1]-y[2])/(x[3]-x[2])/(x[2]-x[1]);
373  c[2] = -c[1];
374  c[3] = c[1];
375  d[1] = -2*c[1]/3/(x[2]-x[1]);
376  d[2] = -d[1]*(x[2]-x[1])/(x[3]-x[2]);
377  d[3] = d[1];
378  return;
379  }
380 
381  /* else --------- n >= 4 --------- */
382  nm1 = n-1;
383 
384  /* Set up the matrix system */
385  /* A = diagonal B = off-diagonal C = rhs */
386 
387 #define A b
388 #define B d
389 #define C c
390 
391  B[1] = x[2] - x[1];
392  B[nm1]= x[n] - x[nm1];
393  A[1] = 2.0 * (B[1] + B[nm1]);
394  C[1] = (y[2] - y[1])/B[1] - (y[n] - y[nm1])/B[nm1];
395 
396  for(i = 2; i < n; i++) {
397  B[i] = x[i+1] - x[i];
398  A[i] = 2.0 * (B[i] + B[i-1]);
399  C[i] = (y[i+1] - y[i])/B[i] - (y[i] - y[i-1])/B[i-1];
400  }
401 
402  /* Choleski decomposition */
403 
404 #define L b
405 #define M d
406 #define E e
407 
408  L[1] = sqrt(A[1]);
409  E[1] = (x[n] - x[nm1])/L[1];
410  s = 0.0;
411  for(i = 1; i <= nm1 - 2; i++) {
412  M[i] = B[i]/L[i];
413  if(i != 1) E[i] = -E[i-1] * M[i-1] / L[i];
414  L[i+1] = sqrt(A[i+1]-M[i]*M[i]);
415  s = s + E[i] * E[i];
416  }
417  M[nm1-1] = (B[nm1-1] - E[nm1-2] * M[nm1-2])/L[nm1-1];
418  L[nm1] = sqrt(A[nm1] - M[nm1-1]*M[nm1-1] - s);
419 
420  /* Forward Elimination */
421 
422 #define Y c
423 #define D c
424 
425  Y[1] = D[1]/L[1];
426  s = 0.0;
427  for(i=2 ; i<=nm1-1 ; i++) {
428  Y[i] = (D[i] - M[i-1]*Y[i-1])/L[i];
429  s = s + E[i-1] * Y[i-1];
430  }
431  Y[nm1] = (D[nm1] - M[nm1-1] * Y[nm1-1] - s) / L[nm1];
432 
433 #define X c
434 
435  X[nm1] = Y[nm1]/L[nm1];
436  X[nm1-1] = (Y[nm1-1] - M[nm1-1] * X[nm1])/L[nm1-1];
437  for(i=nm1-2 ; i>=1 ; i--)
438  X[i] = (Y[i] - M[i] * X[i+1] - E[i] * X[nm1])/L[i];
439 
440  /* Wrap around */
441 
442  X[n] = X[1];
443 
444  /* Compute polynomial coefficients */
445 
446  for(i=1 ; i<=nm1 ; i++) {
447  s = x[i+1] - x[i];
448  b[i] = (y[i+1]-y[i])/s - s*(c[i+1]+2.0*c[i]);
449  d[i] = (c[i+1]-c[i])/s;
450  c[i] = 3.0*c[i];
451  }
452  b[n] = b[1];
453  c[n] = c[1];
454  d[n] = d[1];
455  return;
456  }
457 #undef A
458 #undef B
459 #undef C
460 #undef L
461 #undef M
462 #undef E
463 #undef Y
464 #undef D
465 #undef X
466 
467  void spline_coef(int *method, int *n, Type *x, Type *y,
468  Type *b, Type *c, Type *d, Type *e)
469  {
470  switch(*method) {
471  case 1:
472  periodic_spline(*n, x, y, b, c, d, e); break;
473 
474  case 2:
475  natural_spline(*n, x, y, b, c, d); break;
476 
477  case 3:
478  fmm_spline(*n, x, y, b, c, d); break;
479  }
480  }
481 
482  void spline_eval(int *method, int *nu, Type *u, Type *v,
483  int *n, Type *x, Type *y, Type *b, Type *c, Type *d)
484  {
485  /* Evaluate v[l] := spline(u[l], ...), l = 1,..,nu, i.e. 0:(nu-1)
486  * Nodes x[i], coef (y[i]; b[i],c[i],d[i]); i = 1,..,n , i.e. 0:(*n-1)
487  */
488  const int n_1 = *n - 1;
489  int i, j, k, l;
490  Type ul, dx, tmp;
491 
492  if(*method == 1 && *n > 1) { /* periodic */
493  dx = x[n_1] - x[0];
494  for(l = 0; l < *nu; l++) {
495 
496  /* WARNING - "fmod(AD<double>,AD<double>)" is not defined */
497  // v[l] = fmod(u[l]-x[0], dx);
498  if(v[l] < 0.0) v[l] += dx;
499  v[l] += x[0];
500  }
501  }
502  else {
503  for(l = 0; l < *nu; l++)
504  v[l] = u[l];
505  }
506 
507  i = 0;
508  for(l = 0; l < *nu; l++) {
509  ul = v[l];
510  if(ul < x[i] || (i < n_1 && x[i+1] < ul)) {
511  /* reset i such that x[i] <= ul <= x[i+1] : */
512  i = 0;
513  j = *n;
514  do {
515  k = (i+j)/2;
516  if(ul < x[k]) j = k;
517  else i = k;
518  }
519  while(j > i+1);
520  }
521  dx = ul - x[i];
522  /* for natural splines extrapolate linearly left */
523  tmp = (*method == 2 && ul < x[0]) ? 0.0 : d[i];
524 
525  v[l] = y[i] + dx*(b[i] + dx*(c[i] + dx*tmp));
526  }
527  }
528 
529 };
530 
531 }
tmbutils::splinefun::splinefun
splinefun(const vector< Type > &x_, const vector< Type > &y_, int method_=3)
Construct spline function object.
Definition: splines.hpp:137
+Go to the documentation of this file.
1 
5 namespace tmbutils {
6 
7 // Copyright (C) 2013-2015 Kasper Kristensen
8 // License: GPL-2
9 
10 /*
11  * R : A Computer Language for Statistical Data Analysis
12  * Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka
13  * Copyright (C) 1998--2001 Robert Gentleman, Ross Ihaka and the
14  * R Development Core Team
15  *
16  * This program is free software; you can redistribute it and/or modify
17  * it under the terms of the GNU General Public License as published by
18  * the Free Software Foundation; either version 2 of the License, or
19  * (at your option) any later version.
20  *
21  * This program is distributed in the hope that it will be useful,
22  * but WITHOUT ANY WARRANTY; without even the implied warranty of
23  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
24  * GNU General Public License for more details.
25  *
26  * You should have received a copy of the GNU General Public License
27  * along with this program; if not, a copy is available at
28  * http://www.r-project.org/Licenses/
29  */
30 
31 /* Spline Interpolation
32  * --------------------
33  * C code to perform spline fitting and interpolation.
34  * There is code here for:
35  *
36  * 1. Natural splines.
37  *
38  * 2. Periodic splines
39  *
40  * 3. Splines with end-conditions determined by fitting
41  * cubics in the start and end intervals (Forsythe et al).
42  *
43  *
44  * Computational Techniques
45  * ------------------------
46  * A special LU decomposition for symmetric tridiagonal matrices
47  * is used for all computations, except for periodic splines where
48  * Choleski is more efficient.
49  */
50 
58 template <class Type>
59 class splinefun
60 {
61 private:
62  /* Input to R's "spline_coef" */
63  int method[1];
64  int n[1];
65  Type *x;
66  Type *y;
67  Type *b;
68  Type *c;
69  Type *d;
70  Type *e;
71 
72  /* Not used */
73  //int errno, EDOM;
74 
75  /* Memory management helpers */
76  void clear() {
77  if (*n != 0) {
78  delete [] x;
79  delete [] y;
80  delete [] b;
81  delete [] c;
82  delete [] d;
83  delete [] e;
84  }
85  }
86  void alloc(int n_) {
87  *n = n_;
88  x = new Type[*n];
89  y = new Type[*n];
90  b = new Type[*n];
91  c = new Type[*n];
92  d = new Type[*n];
93  e = new Type[*n];
94  }
95  void copy_from(const splinefun &fun) {
96  *method = fun.method[0];
97  *n = fun.n[0];
98  alloc(*n);
99  for(int i = 0; i < *n; i++) {
100  x[i] = fun.x[i];
101  y[i] = fun.y[i];
102  b[i] = fun.b[i];
103  c[i] = fun.c[i];
104  d[i] = fun.d[i];
105  e[i] = fun.e[i];
106  }
107  }
108 
109 public:
110  /* Construct spline */
111  splinefun() {
112  x = y = b = c = d = e = NULL;
113  *method = *n = 0;
114  };
115  splinefun(const splinefun &fun){
116  copy_from(fun);
117  }
118  splinefun& operator=(const splinefun &x) {
119  if (this != &x) {
120  (*this).clear();
121  (*this).copy_from(x);
122  }
123  return *this;
124  }
125  ~splinefun() {
126  clear();
127  };
137  splinefun(const vector<Type> &x_,
138  const vector<Type> &y_,
139  int method_ = 3) {
140  method[0] = method_;
141  n[0] = x_.size();
142  alloc( x_.size() );
143  for(int i=0; i < *n; i++) {
144  x[i] = x_[i];
145  y[i] = y_[i];
146  }
147  spline_coef(method, n, x, y, b, c, d, e);
148  }
149 
151  Type operator()(const Type &x_) {
152  Type u[1];
153  Type v[1];
154  int nu[1];
155  u[0] = x_;
156  nu[0] = 1;
157  spline_eval(method, nu, u, v,
158  n, x, y, b, c, d);
159  return v[0];
160  }
162  vector<Type> operator() (const vector<Type> &x) {
163  vector<Type> y(x.size());
164  for (int i=0; i<x.size(); i++) y[i] = (*this)(x[i]);
165  return y;
166  }
167 
168  /* ------------------------------------------------------------------
169  * The following is copy-pasted from R-package "stats" where "double"
170  * has been replaced by "Type".
171  *-------------------------------------------------------------------
172  */
173 
174  /*
175  * Natural Splines
176  * ---------------
177  * Here the end-conditions are determined by setting the second
178  * derivative of the spline at the end-points to equal to zero.
179  *
180  * There are n-2 unknowns (y[i]'' at x[2], ..., x[n-1]) and n-2
181  * equations to determine them. Either Choleski or Gaussian
182  * elimination could be used.
183  */
184 
185  void natural_spline(int n, Type *x, Type *y, Type *b, Type *c, Type *d)
186  {
187  int nm1, i;
188  Type t;
189 
190  x--; y--; b--; c--; d--;
191 
192  if(n < 2) {
193  //errno = EDOM;
194  return;
195  }
196 
197  if(n < 3) {
198  t = (y[2] - y[1]);
199  b[1] = t / (x[2]-x[1]);
200  b[2] = b[1];
201  c[1] = c[2] = d[1] = d[2] = 0.0;
202  return;
203  }
204 
205  nm1 = n - 1;
206 
207  /* Set up the tridiagonal system */
208  /* b = diagonal, d = offdiagonal, c = right hand side */
209 
210  d[1] = x[2] - x[1];
211  c[2] = (y[2] - y[1])/d[1];
212  for( i=2 ; i<n ; i++) {
213  d[i] = x[i+1] - x[i];
214  b[i] = 2.0 * (d[i-1] + d[i]);
215  c[i+1] = (y[i+1] - y[i])/d[i];
216  c[i] = c[i+1] - c[i];
217  }
218 
219  /* Gaussian elimination */
220 
221  for(i=3 ; i<n ; i++) {
222  t = d[i-1]/b[i-1];
223  b[i] = b[i] - t*d[i-1];
224  c[i] = c[i] - t*c[i-1];
225  }
226 
227  /* Backward substitution */
228 
229  c[nm1] = c[nm1]/b[nm1];
230  for(i=n-2 ; i>1 ; i--)
231  c[i] = (c[i]-d[i]*c[i+1])/b[i];
232 
233  /* End conditions */
234 
235  c[1] = c[n] = 0.0;
236 
237  /* Get cubic coefficients */
238 
239  b[1] = (y[2] - y[1])/d[1] - d[i] * c[2];
240  c[1] = 0.0;
241  d[1] = c[2]/d[1];
242  b[n] = (y[n] - y[nm1])/d[nm1] + d[nm1] * c[nm1];
243  for(i=2 ; i<n ; i++) {
244  b[i] = (y[i+1]-y[i])/d[i] - d[i]*(c[i+1]+2.0*c[i]);
245  d[i] = (c[i+1]-c[i])/d[i];
246  c[i] = 3.0*c[i];
247  }
248  c[n] = 0.0;
249  d[n] = 0.0;
250 
251  return;
252  }
253 
254  /*
255  * Splines a la Forsythe Malcolm and Moler
256  * ---------------------------------------
257  * In this case the end-conditions are determined by fitting
258  * cubic polynomials to the first and last 4 points and matching
259  * the third derivitives of the spline at the end-points to the
260  * third derivatives of these cubics at the end-points.
261  */
262 
263  void fmm_spline(int n, Type *x, Type *y, Type *b, Type *c, Type *d)
264  {
265  int nm1, i;
266  Type t;
267 
268  /* Adjustment for 1-based arrays */
269 
270  x--; y--; b--; c--; d--;
271 
272  if(n < 2) {
273  //errno = EDOM;
274  return;
275  }
276 
277  if(n < 3) {
278  t = (y[2] - y[1]);
279  b[1] = t / (x[2]-x[1]);
280  b[2] = b[1];
281  c[1] = c[2] = d[1] = d[2] = 0.0;
282  return;
283  }
284 
285  nm1 = n - 1;
286 
287  /* Set up tridiagonal system */
288  /* b = diagonal, d = offdiagonal, c = right hand side */
289 
290  d[1] = x[2] - x[1];
291  c[2] = (y[2] - y[1])/d[1];/* = +/- Inf for x[1]=x[2] -- problem? */
292  for(i=2 ; i<n ; i++) {
293  d[i] = x[i+1] - x[i];
294  b[i] = 2.0 * (d[i-1] + d[i]);
295  c[i+1] = (y[i+1] - y[i])/d[i];
296  c[i] = c[i+1] - c[i];
297  }
298 
299  /* End conditions. */
300  /* Third derivatives at x[0] and x[n-1] obtained */
301  /* from divided differences */
302 
303  b[1] = -d[1];
304  b[n] = -d[nm1];
305  c[1] = c[n] = 0.0;
306  if(n > 3) {
307  c[1] = c[3]/(x[4]-x[2]) - c[2]/(x[3]-x[1]);
308  c[n] = c[nm1]/(x[n] - x[n-2]) - c[n-2]/(x[nm1]-x[n-3]);
309  c[1] = c[1]*d[1]*d[1]/(x[4]-x[1]);
310  c[n] = -c[n]*d[nm1]*d[nm1]/(x[n]-x[n-3]);
311  }
312 
313  /* Gaussian elimination */
314 
315  for(i=2 ; i<=n ; i++) {
316  t = d[i-1]/b[i-1];
317  b[i] = b[i] - t*d[i-1];
318  c[i] = c[i] - t*c[i-1];
319  }
320 
321  /* Backward substitution */
322 
323  c[n] = c[n]/b[n];
324  for(i=nm1 ; i>=1 ; i--)
325  c[i] = (c[i]-d[i]*c[i+1])/b[i];
326 
327  /* c[i] is now the sigma[i-1] of the text */
328  /* Compute polynomial coefficients */
329 
330  b[n] = (y[n] - y[n-1])/d[n-1] + d[n-1]*(c[n-1]+ 2.0*c[n]);
331  for(i=1 ; i<=nm1 ; i++) {
332  b[i] = (y[i+1]-y[i])/d[i] - d[i]*(c[i+1]+2.0*c[i]);
333  d[i] = (c[i+1]-c[i])/d[i];
334  c[i] = 3.0*c[i];
335  }
336  c[n] = 3.0*c[n];
337  d[n] = d[nm1];
338  return;
339  }
340 
341 
342  /*
343  * Periodic Spline
344  * ---------------
345  * The end conditions here match spline (and its derivatives)
346  * at x[1] and x[n].
347  *
348  * Note: There is an explicit check that the user has supplied
349  * data with y[1] equal to y[n].
350  */
351 
352  void periodic_spline(int n, Type *x, Type *y,
353  Type *b, Type *c, Type *d, Type *e)
354  {
355  Type s;
356  int i, nm1;
357 
358  /* Adjustment for 1-based arrays */
359 
360  x--; y--; b--; c--; d--; e--;
361 
362  if(n < 2 || y[1] != y[n]) {
363  errno = EDOM;
364  return;
365  }
366 
367  if(n == 2) {
368  b[1] = b[2] = c[1] = c[2] = d[1] = d[2] = 0.0;
369  return;
370  } else if (n == 3) {
371  b[1] = b[2] = b[3] = -(y[1] - y[2])*(x[1] - 2*x[2] + x[3])/(x[3]-x[2])/(x[2]-x[1]);
372  c[1] = -3*(y[1]-y[2])/(x[3]-x[2])/(x[2]-x[1]);
373  c[2] = -c[1];
374  c[3] = c[1];
375  d[1] = -2*c[1]/3/(x[2]-x[1]);
376  d[2] = -d[1]*(x[2]-x[1])/(x[3]-x[2]);
377  d[3] = d[1];
378  return;
379  }
380 
381  /* else --------- n >= 4 --------- */
382  nm1 = n-1;
383 
384  /* Set up the matrix system */
385  /* A = diagonal B = off-diagonal C = rhs */
386 
387 #define A b
388 #define B d
389 #define C c
390 
391  B[1] = x[2] - x[1];
392  B[nm1]= x[n] - x[nm1];
393  A[1] = 2.0 * (B[1] + B[nm1]);
394  C[1] = (y[2] - y[1])/B[1] - (y[n] - y[nm1])/B[nm1];
395 
396  for(i = 2; i < n; i++) {
397  B[i] = x[i+1] - x[i];
398  A[i] = 2.0 * (B[i] + B[i-1]);
399  C[i] = (y[i+1] - y[i])/B[i] - (y[i] - y[i-1])/B[i-1];
400  }
401 
402  /* Choleski decomposition */
403 
404 #define L b
405 #define M d
406 #define E e
407 
408  L[1] = sqrt(A[1]);
409  E[1] = (x[n] - x[nm1])/L[1];
410  s = 0.0;
411  for(i = 1; i <= nm1 - 2; i++) {
412  M[i] = B[i]/L[i];
413  if(i != 1) E[i] = -E[i-1] * M[i-1] / L[i];
414  L[i+1] = sqrt(A[i+1]-M[i]*M[i]);
415  s = s + E[i] * E[i];
416  }
417  M[nm1-1] = (B[nm1-1] - E[nm1-2] * M[nm1-2])/L[nm1-1];
418  L[nm1] = sqrt(A[nm1] - M[nm1-1]*M[nm1-1] - s);
419 
420  /* Forward Elimination */
421 
422 #define Y c
423 #define D c
424 
425  Y[1] = D[1]/L[1];
426  s = 0.0;
427  for(i=2 ; i<=nm1-1 ; i++) {
428  Y[i] = (D[i] - M[i-1]*Y[i-1])/L[i];
429  s = s + E[i-1] * Y[i-1];
430  }
431  Y[nm1] = (D[nm1] - M[nm1-1] * Y[nm1-1] - s) / L[nm1];
432 
433 #define X c
434 
435  X[nm1] = Y[nm1]/L[nm1];
436  X[nm1-1] = (Y[nm1-1] - M[nm1-1] * X[nm1])/L[nm1-1];
437  for(i=nm1-2 ; i>=1 ; i--)
438  X[i] = (Y[i] - M[i] * X[i+1] - E[i] * X[nm1])/L[i];
439 
440  /* Wrap around */
441 
442  X[n] = X[1];
443 
444  /* Compute polynomial coefficients */
445 
446  for(i=1 ; i<=nm1 ; i++) {
447  s = x[i+1] - x[i];
448  b[i] = (y[i+1]-y[i])/s - s*(c[i+1]+2.0*c[i]);
449  d[i] = (c[i+1]-c[i])/s;
450  c[i] = 3.0*c[i];
451  }
452  b[n] = b[1];
453  c[n] = c[1];
454  d[n] = d[1];
455  return;
456  }
457 #undef A
458 #undef B
459 #undef C
460 #undef L
461 #undef M
462 #undef E
463 #undef Y
464 #undef D
465 #undef X
466 
467  void spline_coef(int *method, int *n, Type *x, Type *y,
468  Type *b, Type *c, Type *d, Type *e)
469  {
470  switch(*method) {
471  case 1:
472  periodic_spline(*n, x, y, b, c, d, e); break;
473 
474  case 2:
475  natural_spline(*n, x, y, b, c, d); break;
476 
477  case 3:
478  fmm_spline(*n, x, y, b, c, d); break;
479  }
480  }
481 
482  void spline_eval(int *method, int *nu, Type *u, Type *v,
483  int *n, Type *x, Type *y, Type *b, Type *c, Type *d)
484  {
485  /* Evaluate v[l] := spline(u[l], ...), l = 1,..,nu, i.e. 0:(nu-1)
486  * Nodes x[i], coef (y[i]; b[i],c[i],d[i]); i = 1,..,n , i.e. 0:(*n-1)
487  */
488  const int n_1 = *n - 1;
489  int i, j, k, l;
490  Type ul, dx, tmp;
491 
492  if(*method == 1 && *n > 1) { /* periodic */
493  dx = x[n_1] - x[0];
494  for(l = 0; l < *nu; l++) {
495 
496  /* WARNING - "fmod(AD<double>,AD<double>)" is not defined */
497  v[l] = fmod(asDouble(u[l]-x[0]), asDouble(dx));
498  if(v[l] < 0.0) v[l] += dx;
499  v[l] += x[0];
500  }
501  }
502  else {
503  for(l = 0; l < *nu; l++)
504  v[l] = u[l];
505  }
506 
507  i = 0;
508  for(l = 0; l < *nu; l++) {
509  ul = v[l];
510  if(ul < x[i] || (i < n_1 && x[i+1] < ul)) {
511  /* reset i such that x[i] <= ul <= x[i+1] : */
512  i = 0;
513  j = *n;
514  do {
515  k = (i+j)/2;
516  if(ul < x[k]) j = k;
517  else i = k;
518  }
519  while(j > i+1);
520  }
521  dx = ul - x[i];
522  /* for natural splines extrapolate linearly left */
523  tmp = (*method == 2 && ul < x[0]) ? 0.0 : d[i];
524 
525  v[l] = y[i] + dx*(b[i] + dx*(c[i] + dx*tmp));
526  }
527  }
528 
529 };
530 
531 }
tmbutils::splinefun::splinefun
splinefun(const vector< Type > &x_, const vector< Type > &y_, int method_=3)
Construct spline function object.
Definition: splines.hpp:137
tmbutils::splinefun
Spline Interpolation.
Definition: splines.hpp:59
tmbutils::vector
Vector class used by TMB.
Definition: tmbutils.hpp:18
tmbutils::splinefun::operator()
Type operator()(const Type &x_)
Evaluate spline - scalar argument case.
Definition: splines.hpp:151
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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TMB Documentation -  v1.9.8 +  v1.9.9
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