df?Integrate1D/df?IntegrateEx1D

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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df?Integrate1D/df?IntegrateEx1D

Computes a spline-based integral.

Syntax

status = dfsIntegrate1D(task, method, nlim, llim, llimhint, rlim, rlimhint, ldatahint, rdatahint, r, rhint)

status = dfdIntegrate1D(task, method, nlim, llim, llimhint, rlim, rlimhint, ldatahint, rdatahint, r, rhint)

status = dfsIntegrateEx1D(task, method, nlim, llim, llimhint, rlim, rlimhint, ldatahint, rdatahint, r, rhint, le_cb, le_params, re_cb, re_params, i_cb, i_params, search_cb, search_params)

status = dfdIntegrateEx1D(task, method, nlim, llim, llimhint, rlim, rlimhint, ldatahint, rdatahint, r, rhint, le_cb, le_params, re_cb, re_params, i_cb, i_params, search_cb, search_params)

Include Files

mkl.h

Input Parameters

Name	Type	Description
task	DFTaskPtr	Descriptor of the task.
method	const MKL_INT	Integration method. The supported value is DF_METHOD_PP.
nlim	const MKL_INT	Number of pairs of integration limits.
llim	const float* for dfsIntegrate1D/dfsIntegrateEx1D const double* for dfdIntegrate1D/dfdIntegrateEx1D	Array of size nlim that defines the left-side integration limits.
llimhint	const MKL_INT	A flag describing the structure of the left-side integration limits llim. For the list of possible values of llimhint, see table "Hint Values for Integration Limits". If you set the flag to the DF_NO_HINT value, the library assumes that the left-side integration limits define a non-uniform partition.
rlim	const float* for dfsIntegrate1D/dfsIntegrateEx1D const double* for dfdIntegrate1D/dfdIntegrateEx1D	Array of size nlim that defines the right-side integration limits.
rlimhint	const MKL_INT	A flag describing the structure of the right-side integration limits rlim. For the list of possible values of rlimhint, see table "Hint Values for Integration Limits". If you set the flag to the DF_NO_HINT value, the library assumes that the right-side integration limits define a non-uniform partition.
ldatahint	const float* for dfsIntegrate1D/dfsIntegrateEx1D const double* for dfdIntegrate1D/dfdIntegrateEx1D	Array that contains additional information about the structure of partition x and left-side integration limits. For details on the ldatahint array, see table "Structure of the datahint Array" in the description of the df?Interpolate1D function.
rdatahint	const float* for dfsIntegrate1D/dfsIntegrateEx1D const double* for dfdIntegrate1D/dfdIntegrateEx1D	Array that contains additional information about the structure of partition x and right-side integration limits. For details on the rdatahint array, see table "Structure of the datahint Array" in the description of the df?Interpolate1D function.
rhint	const MKL_INT	A flag describing the structure of the results. For the list of possible values of rhint, see table "Hint Values for Integration Results". If you set the flag to the DF_NO_HINT value, the library stores the results in row-major format.
le_cb	constdfsIntegrCallBack for dfsIntegrateEx1D constdfdIntegrCallBack for dfdIntegrateEx1D	User-defined callback function for integration on interval [ llim`[i]`, min(rlim`[i]`, `a`)) for llim`[i]` < `a` . Set to NULL if you are not supplying a callback function.
le_params	const void*	Pointer to additional user-defined parameters passed by the library to the le_cb function. Set to NULL if there are no additional parameters or if you are not supplying a callback function.
re_cb	constdfsInterpCallBack for dfsIntegrateEx1D constdfdInterpCallBack for dfdIntegrateEx1D	User-defined callback function for integration on interval [max(llim`[i]`, `b`), rlim`[i]`) for rlim`[i]`≥`b`. Set to NULL if you are not supplying a callback function.
re_params	const void*	Pointer to additional user-defined parameters passed by the library to the re_cb function. Set to NULL if there are no additional parameters or if you are not supplying a callback function.
i_cb	constdfsIntegrCallBack for dfsIntegrateEx1D constdfdIntegrCallBack for dfdIntegrateEx1D	User-defined callback function for integration on interval [max(`a`, llim`[i]`, ), min(rlim`[i]`, `b`)). Set to NULL if you are not supplying a callback function.
i_params	const void*	Pointer to additional user-defined parameters passed by the library to the i_cb function. Set to NULL if there are no additional parameters or if you are not supplying a callback function.
search_cb	constdfsSearchCellsCallBack for dfsIntegrateEx1D constdfdSearchCellsCallBack for dfdIntegrateEx1D	User-defined callback function for computing indices of cells that can contain interpolation sites. Set to NULL if you are not supplying a callback function.
search_params	const void*	Pointer to additional user-defined parameters passed by the library to the search_cb function. Set to NULL if there are no additional parameters or if you are not supplying a callback function.

Output Parameters

Name	Type	Description
status	int	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	float* for dfsIntegrate1D/dfsIntegrateEx1D double* for dfdIntegrate1D/dfdIntegrateEx1D	Array of integration results. The size of the array should be sufficient to hold nlim*ny values, where ny is the dimension of the vector-valued function. The integration results are packed according to the settings in rhint. CAUTION: The df?Integrate1D/df?IntegrateEx1D routines do not support in-place computations. You must provide non-aliasing memory locations for the llim and rlim input parameters and the r output parameter.

Name

Type

Description

status

int

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.

float* for dfsIntegrate1D/dfsIntegrateEx1D

double* for dfdIntegrate1D/dfdIntegrateEx1D

Array of integration results. The size of the array should be sufficient to hold nlim*ny values, where ny is the dimension of the vector-valued function. The integration results are packed according to the settings in rhint.

CAUTION:

The df?Integrate1D/df?IntegrateEx1D routines do not support in-place computations. You must provide non-aliasing memory locations for the llim and rlim input parameters and the r output parameter.

Description

The df?Integrate1D/df?IntegrateEx1D routine computes spline-based integral on user-defined intervals

where rl_i = rlim[i], ll_i = llim[i], and i = 0, ..., ny - 1.

If rlim[i] < llim[i], the routine returns

The routine supports the following hint values for integration results:

Hint Values for Integration Results
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 coordinates of vector-valued function y are provided and stored in row-major format.

A common structure of the storage formats for the integration results is as follows:

Row-major format

`I`(0, 0)	...	`I`(0, nlim - 1)
...	...	...
`I` (ny - 1, 0)	...	`I`(ny - 1, nlim - 1)

Column-major format

`I`(0, 0)	...	`I` (ny - 1, 0)
...	...	...
`I`(0, nlim - 1)	...	`I`(ny - 1, nlim - 1)

Using the llimhint and rlimhint parameters, you can provide the following hint values for integration limits:

Hint Values for Integration Limits
Value	Description
DF_SORTED_DATA	Integration limits are sorted in the ascending order and define a non-uniform partition.
DF_NON_UNIFORM_PARTITION	Partition defined by integration limits is non-uniform.
DF_UNIFORM_PARTITION	Partition defined by integration limits is uniform.
DF_NO_HINT	No hint is provided. By default, partition defined by integration limits is interpreted as non-uniform.

To compute integration with splines unsupported in the Data Fitting component, use the extended version of the routine df?IntegrateEx1D. With this routine, you can provide user-defined callback functions that compute:

integrals within, to the left of, or to the right of the interpolation interval [a, b]
indices of cells that contain the provided integration limits or can serve as an approximation for computing the exact indices of such cells

If you do not pass callback functions, the routine uses the default settings.

Parent topic: Data Fitting Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

df?Integrate1D/df?IntegrateEx1D

Syntax

Include Files

Input Parameters

Output Parameters

Description

See Also