df?interpolate1d/df?interpolateex1d

Runs data fitting computations.

Syntax

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

  • mkl_df.f90

Input Parameters

Name

Type

Description

task

TYPE(DF_TASK)

Descriptor of the task.

type

INTEGER

Type of spline-based computations. The parameter takes one or more values combined with an OR operation. For the list of possible values, see table "Computation Types Supported by the df?interpolate1d/ df?interpolate1d Routines".

method

INTEGER

Computation method. The supported value is DF_METHOD_PP.

nsite

INTEGER

Number of interpolation sites.

site

REAL(KIND=4) DIMENSION(*) for dfsinterpolate1d/dfsinterpolateex1d

REAL(KIND=8) DIMENSION(*) for dfdinterpolate1d/dfdinterpolateex1d

Array of interpolation sites of size nsite. The structure of the array is defined by the sitehint parameter:

  • If sites form a non-uniform partition, the array should contain nsite values.

  • If sites form a uniform partition, the array should contain two entries that represent the left and the right interpolation sites. The first entry of the array contains the left-most interpolation point. The second entry of the array contains the right-most interpolation point.

sitehint

INTEGER

A flag describing the structure of the interpolation sites. For the list of possible values of sitehint, see table "Hint Values for Interpolation Sites". If you set the flag to DF_NO_HINT, the library interprets the site-defined partition as non-uniform.

ndorder

INTEGER

Maximal derivative order increased by one to be computed at interpolation sites.

dorder

INTEGER DIMENSION(*)

Array of size ndorder that defines the order of the derivatives to be computed at the interpolation sites. If all the elements in dorder are zero, the library computes the spline values only. If you do not need interpolation computations, set ndorder to zero and pass a NULL pointer to dorder.

datahint

REAL(KIND=4) DIMENSION(*) for dfsinterpolate1d/dfsinterpolateex1d

REAL(KIND=8) DIMENSION(*) for dfdinterpolate1d/dfdinterpolateex1d

Array that contains additional information about the structure of partition x and interpolation sites. This data helps to speed up the computation. If you provide a NULL pointer, the routine uses the default settings for computations. For details on the datahint array, see table "Structure of the datahint Array".

r

REAL(KIND=4) DIMENSION(*) for dfsinterpolate1d/dfsinterpolateex1d

REAL(KIND=8) DIMENSION(*) for dfdinterpolate1d/dfdinterpolateex1d

Array for results. If you do not need spline-based interpolation or integration, set this pointer to NULL.

rhint

INTEGER

A flag describing the structure of the results. For the list of possible values of rhint, see table "Hint Values for the rhint Parameter". If you set the flag to DF_NO_HINT, the library stores the result in row-major format.

cell

INTEGER DIMENSION(*)

Array of cell indices in partition x that contain the interpolation sites. Provide this parameter as input if type is DF_INTERP_USER_CELL. If you do not need cell indices, set this parameter to NULL.

le_cb

INTEGER

User-defined callback function for extrapolation at the sites to the left of the interpolation interval.

le_params

INTEGER DIMENSION(*)

Pointer to additional user-defined parameters passed by the library to the le_cb function.

re_cb

INTEGER

User-defined callback function for extrapolation at the sites to the right of the interpolation interval.

re_params

INTEGER DIMENSION(*)

Pointer to additional user-defined parameters passed by the library to the re_cb function.

i_cb

INTEGER

User-defined callback function for interpolation within the interpolation interval.

i_params

INTEGER DIMENSION(*)

Pointer to additional user-defined parameters passed by the library to the i_cb function.

search_cb

INTEGER

User-defined callback function for computing indices of cells that can contain interpolation sites.

search_params

INTEGER DIMENSION(*)

Pointer to additional user-defined parameters passed by the library to the search_cb function.

Output Parameters

Name

Type

Description

status

INTEGER

Status of the routine:

  • DF_STATUS_OK if the routine execution completed successfully.
  • Non-zero error code if the routine execution failed. See "Task Status and Error Reporting" for error code definitions.

r

 

Contains results of computations at the interpolation sites.

cell

 

Array of cell indices in partition x that contain the interpolation sites, which is computed if type is DF_CELL.

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:

Computation Types Supported by the df?interpolate1d/df?interpolateex1d Routines

Type

Description

DF_INTERP

Compute derivatives of predefined order. The derivative of the zero order is the spline value.

DF_INTERP_USER_CELL

Compute derivatives of predefined order given user-provided cell indices. The derivative of the zero order is the spline value.

For this type of the computations you should provide a valid cell array, which holds the indices of cells in the site array containing relevant interpolation sites.

DF_CELL

Compute indices of cells in partition x that contain the sites.

If the indices of cells which contain interpolation types are available before the call to df?interpolate1d/df?interpolateex1d, you can improve performance by using the DF_INTERP_USER_CELL computation type.

Note

If you pass any combination of DF_INTERP, DF_INTERP_USER_CELL, and DF_CELL computation types to the routine, the library uses the DF_INTERP_USER_CELL computation mode.

If you specify DF_INTERP_USER_CELL computation mode and a user-defined callback function for computing cell indices to df?interpolateex1d, the library uses the DF_INTERP_USER_CELL computation mode, and the call-back function is not called.

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 Pn-2 of the spline constructed on interval [xn-2, xn-1] for computations at the sites to the right of b.

Interpolation sites support the following hints:

Hint Values for Interpolation Sites

Value

Description

DF_NON_UNIFORM_PARTITION

Partition is non-uniform.

DF_UNIFORM_PARTITION

Partition is uniform.

DF_SORTED_DATA

Interpolation sites are sorted in the ascending order and define a non-uniform partition.

DF_NO_HINT

No hint is provided. By default, the partition defined by interpolation sites is interpreted as non-uniform.

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 yny.

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:
Hint Values for the rhint Parameter

Value

Description

DF_MATRIX_STORAGE_ROWS

Data is stored in row-major format according to C conventions.

DF_MATRIX_STORAGE_COLS

Data is stored in column-major format according to Fortran conventions.

DF_NO_HINT

No hint is provided. By default, the results are stored in row-major format.

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,...,im at nsite interpolation sites. In this description, j is the coordinate of the vector-valued function:

  • Row-major format

    rj(i1, 1)

    rj(i2, 1)

    ...

    rj(im, 1)

    rj(i1, 2)

    rj(i2, 2)

    ...

    rj(im, 2)

    ...

    ...

    ...

    ...

    rj(i1, nsite)

    rj(i2, nsite )

    ...

    rj(im, nsite )

  • Column-major format

    rj(i1, 1)

    rj(i1, 2)

    ...

    rj(i1, nsite )

    rj(i2, 1)

    rj(i2, 2)

    ...

    rj(i2, nsite )

    ...

    ...

    ...

    ...

    rj(im, 1)

    rj(im, 2)

    ...

    rj(im, nsite )

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:

Structure of the datahint Array

Element Number

Description

1

Task dimension

2

Type of additional information

3

Reserved field

4

The total number q of elements containing additional information.

5

Element (1)

...

...

q+4

Element (q)

Data Fitting computation functions support the following types of additional information for datahint(2):

Types of Additional Information

Type

Element Number

Parameter

DF_NO_APRIORI_INFO

0

No parameters are provided. Information about the data structure is absent.

DF_APRIORI_MOST_LIKELY_CELL

1

Index of the cell that is likely to contain interpolation sites.

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{xi}, i=1,...,nx:

cell(j) = i, if site(j) ∈[xi, xi+1), i = 0,..., nx,

where

  • x0 = -
  • xnx+1 = +
  • j = 1,..., nsite

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.

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