Include Files

Description

The editor modifies parameters that describe the order, type, boundary conditions, internal conditions, and coefficients of a spline. The spline order definition is provided in the

"Mathematical Conventions"

section. You can set the spline order to any value supported by Data Fitting functions. The table below lists the available values:

To perform computations with a spline not supported by Data Fitting routines, set the parameter defining the spline order and pass the spline coefficients to the library in the supported format. For format description, see figure

"Row-major Coefficient Storage Format"

.

The table below lists the supported spline types:

If you perform computations with look-up or step-wise constant interpolants, set the spline order to the

DF_PP_STD

value.

Construction of specific splines may require boundary or internal conditions. To compute coefficients of such splines, you should pass boundary or internal conditions to the library by specifying the type of the conditions and providing the necessary values. For splines that do not require additional conditions, such as linear splines, set condition types to

DF_NO_BC

and

DF_NO_IC

, and pass

NULL

pointers to the conditions. The table below defines the supported boundary conditions:

You can combine the values of boundary conditions with a bitwise

OR

operation. This permits you to pass combinations of first and second derivatives at the endpoints of the interpolation interval into the library. To pass a first derivative at the left endpoint and a second derivative at the right endpoint, set the boundary conditions to

DF_BC_1ST_LEFT_DER

OR

DF_BC_2ND_RIGHT_DER

.

You should pass the combined boundary conditions as an array of two elements. The first entry of the array contains the value of the boundary condition for the left endpoint of the interpolation interval, and the second entry - for the right endpoint. Pass other boundary conditions as arrays of one element.

For the conditions defined as a combination of valid values, the library applies the following rules to identify the boundary condition type:

If not required for spline construction, the value of boundary conditions is ignored.
Not-a-knot condition has the highest priority. If set, other boundary conditions are ignored.
Free-end condition has the second priority after the not-a-knot condition. If set, other boundary conditions are ignored.
Periodic boundary condition has the next priority after the free-end condition.
The first derivative has higher priority than the second derivative at the right and left endpoints.

If you set the periodic boundary condition, make sure that function values at the endpoints of the interpolation interval are identical. Otherwise, the library returns an error code. The table below specifies the values to be provided for each type of spline if the periodic boundary condition is set.

Internal conditions supported in the Data Fitting domain that you can use for the

ic_type

parameter are the following:

To construct a Subbotin quadratic spline, you have three options to get the array of knots in the library:

If you do not provide the knots, the library uses the default values of knots
t
= {
t
i
},
i
= 0, ...,
n
according to the rule:
t
0
=
x
0
,
t
n
=
x
n
-1
,
t
i
= (
x
i
+
x
i
-1
)/2,
i
= 1, ...,
n
- 1
.
If you provide the knots in an array of size
n
+ 1, the knots form a non-uniform partition. Make sure that the knot values you provide meet the following conditions:
t
0
=
x
0
,
t
n
=
x
n
-1
,
t
i
∈ (
x
i
-1
,
x
i
),
i
= 1,...,
n
- 1.
If you provide the knots in an array of size 4, the knots form a uniform partition
t
0
=
x
0
,
t
1
=
l
,
t
2
=
r
,
t
3
=
x
n
- 1
, where
l
∈ (
x
0
,
x
1
) and
r
∈ (
x
n
- 2
,
x
n
- 1
).
In this case, you need to set the value of the
ic_type
parameter holding the type of internal conditions to
DF_IC_Q_KNOT
OR
DF_UNIFORM_PARTITION
.
Since the partition is uniform, perform an
OR
operation with the
DF_UNIFORM_PARTITION
partition hint value described in Table Hint Values for Partition x.

For computations based on look-up and step-wise constant interpolants, you can avoid calling the

df?EditPPSpline1D

editor and directly call one of the routines for spline-based computation of spline values, derivatives, or integrals. For example, you can call the

df?Construct1D

routine to construct the required spline with the given attributes, such as order or type.

The memory location of the spline coefficients is defined by the

scoeff

parameter. Make sure that the size of the array is sufficient to hold

ny

*

s_order

* (

nx

-1) values.

The

df?EditPPSpline1D

routine supports the following hint values for spline coefficients: