df?interpolate1d/df?interpolateex1d

Syntax

FORTRAN:

status = dfsinterpolate1d(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell)

status = dfdinterpolate1d(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell)

status = dfsinterpolateex1d(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell, le_cb, le_params, re_cb, re_params, i_cb, i_params, search_cb, search_params)

status = dfdinterpolateex1d(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell, le_cb, le_params, re_cb, re_params, i_cb, i_params, search_cb, search_params)

C:

status = dfsInterpolate1D(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell)

status = dfdInterpolate1D(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell)

status = dfsInterpolateEx1D(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell, le_cb, le_params, re_cb, re_params, i_cb, i_params, search_cb, search_params)

status = dfdInterpolateEx1D(task, type, method, nsite, site, sitehint, ndorder, dorder, datahint, r, rhint, cell, le_cb, le_params, re_cb, re_params, i_cb, i_params, search_cb, search_params)

Include Files

• Fortran: mkl_df.f90 and mkl_df.f77
• C: mkl_df.h

Input Parameters

Output Parameters

Description

The df?interpolate1d/df?interpolateex1d routine performs spline-based computations with user-defined settings. The routine supports two types of computations for interpolation sites provided in array site:

If the sites do not belong to interpolation interval [a, b] , the library uses:

• polynomial P₀ of the spline constructed on interval [x₀, x₁] for computations at the sites to the left of a.
• polynomial P_n-2 of the spline constructed on interval [x_n-2, x_n-1] for computations at the sites to the right of b.

Interpolation sites support the following hints:

Note

If you pass a sorted array of interpolation sites to the Intel MKL, set the sitehint parameter to the DF_SORTED_DATA value. The library uses this information when choosing the search algorithm and ignores any other data hints about the structure of the interpolation sites.

Data Fitting computation routines can use the following hints to speed up the computation:

• DF_UNIFORM_PARTITION describes the structure of breakpoints and the interpolation sites.
• DF_QUASI_UNIFORM_PARTITION describes the structure of breakpoints.

Pass the above hints to the library when appropriate.

The r pointer defines the memory location for the sets of interpolation and integration results for all coordinates of function y. The sets are stored one by one, in the successive order of the function coordinates from y₁ to y_ny.

You can define the following settings for packing the results within each set:

• Computation type: interpolation, integration, or both.
• Computation parameters: derivative orders.
• Storage format for the results. You can specify the format using the rhint parameter values described in the table below:

For spline-based interpolation, you should set the derivatives whose values are required for the computation. You can provide the derivatives by setting the dorder array of size ndorder as follows:

See below a common structure of the storage formats of the interpolation results within each set r for computing derivatives of order i₁, i₂,...,i_m at nsite interpolation sites. In this description, j is the coordinate of the vector-valued function:

• Row-major format

  rj(i1, 0)	rj(i2, 0)	...	rj(im, 0)
  rj(i1, 1)	rj(i2, 1)	...	rj(im, 1)
  ...	...	...	...
  rj(i1, nsite - 1)	rj(i2, nsite - 1)	...	rj(im, nsite - 1)

• Column-major format

  rj(i1, 0)	rj(i1, 1)	...	rj(i1, nsite - 1)
  rj(i2, 0)	rj(i2, 1)	...	rj(i2, nsite - 1)
  ...	...	...	...
  rj(im, 0)	rj(im, 1)	...	rj(im, nsite - 1)

To speed up Data Fitting computations, use the datahint parameter that provides additional information about the structure of the partition and interpolation sites. This data represents a floating-point or a double array with the following structure:

Data Fitting computation functions support the following types of additional information for datahint[1]:

To compute indices of the cells that contain interpolation sites, provide the pointer to the array of size nsite for the results. The library supports the following scheme of cell indexing for the given partition{x_i}, i=1,...,nx:

cell[j] = i, if site[j] ∈[x_i, x_i+1), i = 0,..., nx,

where

• x₀ = -∞
• x_nx+1 = +∞
• j = 0,..., nsite-1

To perform interpolation computations with spline types unsupported in the Data Fitting component, use the extended version of the routine df?interpolateex1d. With this routine, you can provide user-defined callback functions for computations within, to the left of, or to the right of interpolaton interval [a, b]. The callback functions compute indices of the cells that contain the specified interpolation sites or can serve as an approximation for computing the exact indices of such cells.

If you do not pass any function for computations at the sites outside the interval [a, b], the routine uses the default settings.