Intel® oneAPI Math Kernel Library Developer Reference - Fortran

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

Input Parameters

Name

Type

Description

task

TYPE(DF_TASK)

Descriptor of the task.

method

INTEGER

Integration method. The supported value is DF_METHOD_PP.

nlim

INTEGER

Number of pairs of integration limits.

llim

REAL(KIND=4) DIMENSION(*) for dfsintegrate1d/dfsintegrateex1d

REAL(KIND=8) DIMENSION(*) for dfdintegrate1d/dfdintegrateex1d

Array of size nlim that defines the left-side integration limits.

llimhint

INTEGER

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

REAL(KIND=4) DIMENSION(*) for dfsintegrate1d/dfsintegrateex1d

REAL(KIND=8) DIMENSION(*) for dfdintegrate1d/dfdintegrateex1d

Array of size nlim that defines the right-side integration limits.

rlimhint

INTEGER

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

REAL(KIND=4) DIMENSION(*) for dfsintegrate1d/dfsintegrateex1d

REAL(KIND=8) DIMENSION(*) 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?intepolate1d function.

rdatahint

REAL(KIND=4) DIMENSION(*) for dfsintegrate1d/dfsintegrateex1d

REAL(KIND=8) DIMENSION(*) 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?intepolate1d function.

rhint

INTEGER

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

INTEGER

User-defined callback function for integration on interval [ llim(i), min(rlim(i), a)) for llim(i) < a .

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 integration on interval [max(llim(i), b), rlim(i)) for rlim(i)b.

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 integration on interval [max(a, llim(i), ), min(rlim(i), b)).

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

REAL(KIND=4) DIMENSION(*) for dfsintegrate1d/dfsintegrateex1d

REAL(KIND=8) DIMENSION(*) 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.

Description

The df?integrate1d/df?integrateex1d routine computes spline-based integral on user-defined intervals

,

where rli = rlim(i), lli = llim(i), and i = 1, ..., ny.

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:

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:

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

See Also