Functions | |
| boolvec * | surface (const char *surface_name="*") |
| boolvec * | surface_add (REAL weight, const char *surface_name="*") |
| boolvec * | surface_leq (const char *surface_name="*", REAL penalty_factor=0) |
| boolvec * | surface_geq (const char *surface_name="*", REAL penalty_factor=0) |
| boolvec * | trend (REAL D1=1, REAL D2=2, const char *surface_name="*") |
| boolvec * | trend_add (REAL weight, REAL D1=1, REAL D2=0, const char *surface_name="*") |
Detailed Description
Function Documentation
| boolvec* surfit::surface | ( | const char * | surface_name = "*" | ) |
- Tcl syntax:
- surface "surface_name"
- Description:
- Using this rule the resulting surface approximates other surface in least squares meaning.
- Parameters
-
surface_name name of surface dataset
- Math:
- This command adds the following functional to the functional sequence:
where (i,j) - indices of the cells,![\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \sum_{i,j} \left( u_{i,j} - z(x_i, y_j) \right)^2, \]](form_109.png)
- surface value for the (i,j) cell.
| boolvec* surfit::surface_add | ( | REAL | weight, |
| const char * | surface_name = "*" |
||
| ) |
- Tcl syntax:
- surface_add weight "surface_name"
- Description:
- This function modifies previous (modifiable) rule by adding the surface() rule with some weight.
- Parameters
-
weight informational weight for this rule surface_name name of surface dataset
- Math:
- This command modifies previous functional
by adding 
:
where![\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \Phi_0(u_{1,1},\ldots,u_{N,M}) + w\Phi_1(u_{1,1},\ldots,u_{N,M}), \]](form_65.png)
- informational weight,
where (i,j) - indices of the cells,![\[ \Phi_1(u_{1,1},\ldots,u_{N,M}) = \sum_{i,j} \left( u_{i,j} - z(x_i, y_j) \right)^2, \]](form_110.png)
- surface value for the (i,j) cell.
| boolvec* surfit::surface_geq | ( | const char * | surface_name = "*", |
| REAL | penalty_factor = 0 |
||
| ) |
- Tcl syntax:
- surface_geq "surface_name" penalty_factor
- Description:
- This rule adds the surface condition - "the surface should be greater than equal to other surface".
- Parameters
-
surface_name name of surface dataset penalty_factor parameter for penalty algorithm
- Math:
- This command adds the condition:
where (i,j) - indices of the cells,![\[ u_{i,j} \geq z(x_i, y_j) \quad i=1,\ldots,N, \quad j=1,\ldots,M \]](form_112.png)
- surface value for the (i,j) cell.
| boolvec* surfit::surface_leq | ( | const char * | surface_name = "*", |
| REAL | penalty_factor = 0 |
||
| ) |
- Tcl syntax:
- surface_leq "surface_name" penalty_factor
- Description:
- This rule adds the surface condition - "the surface should be lower than equal to other surface".
- Parameters
-
surface_name name of surface dataset penalty_factor parameter for penalty algorithm
- Math:
- This command adds the condition:
where (i,j) - indices of the cells,![\[ u_{i,j} \leq z(x_i, y_j) \quad i=1,\ldots,N, \quad j=1,\ldots,M \]](form_111.png)
- surface value for the (i,j) cell.
| boolvec* surfit::trend | ( | REAL | D1 = 1, |
| REAL | D2 = 2, |
||
| const char * | surface_name = "*" |
||
| ) |
- Tcl syntax:
- trend D1 D2 "surface_name"
- Description:
- This rule determines resulting surface behaviour in regions out low information density. This rule tells, that in these regions resulting surface should be similar to other surface (which is called trend).
- Parameters
-
D1 informational weight for rule that sounds "resulting surface should have the same gradients as trend surface" D2 informational weight for rule that sounds "resulting surface should have the same curvature as trend surface" surface_name name of surface dataset. This is a trend surface.
- Math:
- This command adds the following functional to the functional sequence:
![\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \mathbf{D_1} \frac{h_y}{h_x} \left[ \left( \left( u_{i+1,j}-u_{i,j} \right) - \left( t(x_{i+1,},y_j)-t(x_i,y_j) \right) \right)^2 + \left( (u_{i,j} - u_{i-1,j})-(t(x_i,y_j) - t(x_{i-1},y_j)) \right)^2 \right] + \]](form_113.png)
![\[ \mathbf{D_1} \frac{h_x}{h_y} \left[ \left( \left( u_{i,j+1}-u_{i,j} \right) - \left( t(x_i,y_{j+1})-t(x_i,y_j) \right) \right)^2 + \left( \left( u_{i,j-1} - u_{i,j} \right) - \left( t(x_i,y_{j-1}) - t(x_i,y_j) \right) \right)^2 \right] + \]](form_114.png)
![\[ + \mathbf{D_2} \frac{h_y^2}{h_x^2} \left[ \left( (u_{i+2,j} - 2u_{i+1,j} + u_{i,j}) - (t(x_{i+2},y_j) - 2t(x_{i+1},y_j) + t(x_i,y_j)) \right)^2 + \right. \]](form_115.png)
![\[ \left( (u_{i+1,j} - 2u_{i,j} + u_{i-1,j}) - (t(x_{i+1},y_j) - 2t(x_i,y_j) + t(x_{i-1},y_j)) \right)^2 + \]](form_116.png)
![\[ \left. \left( (u_{i,j} - 2u_{i-1,j} + u_{i-2,j}) - (t(x_i,y_j) - 2t(x_{i-1},y_j) + t(x_{i-2},y_j)) \right)^2 \right] + \]](form_117.png)
![\[ + 2 \mathbf{D_2} \left( \left[ \left( (u_{i+1,j+1} - u_{i,j+1} - u_{i+1,j} + u_{i,j}) - (t(x_{i+1},y_{j+1}) - t(x_i,y_{j+1}) - t(x_{i+1},y_j) + t(x_i,y_j) ) \right) \right] + \right. \]](form_118.png)
![\[ \left. \left[ \left( (u_{i,j+1} - u_{i-1,j+1} - u_{i,j} + u_{i-1,j}) - (t(x_i,y_{j+1}) - t(x_{i-1},y_{j+1}) - t(x_i,y_j) + t(x_{i-1},y_j)) \right) \right] \right) + \]](form_119.png)
![\[ + \mathbf{D_2} \frac{h_x^2}{h_y^2} \left[ \left( (u_{i,j+2} - 2u_{i,j+1} + u_{i,j}) - (t(x_i,y_{j+2}) - 2t(x_i,y_{j+1}) + t(x_i,y_j)) \right)^2 + \right. \]](form_120.png)
![\[ \left( (u_{i,j+1} - 2u_{i,j} + u_{i,j-1}) - (t(x_i,y_{j+1}) - 2t(x_i,y_j) + t(x_i,y_{j-1})) \right)^2 + \]](form_121.png)
![\[ \left. \left( (u_{i,j} - 2u_{i,j-1} + u_{i,j-2}) - (t(x_i,y_j) - 2t(x_i,y_{j-1}) + t(x_i,y_{j-2})) \right)^2 \right] + \]](form_122.png)
![\[ + 2 \mathbf{D_2} \left( \left[ \left( (u_{i+1,j+1} - u_{i+1,j} - u_{i,j+1} + u_{i,j}) - (t(x_{i+1},y_{j+1}) - t(x_{i+1},y_j) - t(x_i,y_{j+1}) + t(x_i,y_j)) \right) \right] + \right. \]](form_123.png)
![\[ \left. \left[ \left( (u_{i+1,j} - u_{i+1,j-1} - u_{i,j} + u_{i,j-1}) - (t(x_{i+1},y_j) - t(x_{i+1},y_{j-1}) - t(x_i,y_j) + t(x_i,y_{j-1})) \right) \right] \right) = \min. \]](form_124.png)
| boolvec* surfit::trend_add | ( | REAL | weight, |
| REAL | D1 = 1, |
||
| REAL | D2 = 0, |
||
| const char * | surface_name = "*" |
||
| ) |
bool trend_add(REAL weight, REAL D1 = 1, REAL D2 = 2, const char * surface_name = "*");
- Tcl syntax:
- trend_add weight D1 D2 "surface_name"
- Description:
- This function modifies previous (modifiable) rule by adding the trend rule with some weight.
- Parameters
-
weight informational weight for trend rule D1 informational weight for rule that sounds "resulting surface should have the same gradients as trend surface" D2 informational weight for rule that sounds "resulting surface should have the same curvature as trend surface" surface_name name of surface dataset. This is a trend surface.