Computes a spline-based integral.
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)
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. |
Name |
Type |
Description |
---|---|---|
status |
INTEGER |
Status of the routine:
|
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. |
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:
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(1, 1) |
... |
I(1, nlim) |
... |
... |
... |
I (ny, 1) |
... |
I(ny , nlim) |
Column-major format
I(1, 1) |
... |
I (ny, 1) |
... |
... |
... |
I(1, nlim) |
... |
I(ny , nlim) |
Using the llimhint and rlimhint parameters, you can provide the following 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.