Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
df?integrate1d/df?integrateex1d 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_df.f90
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?interpolate1ddf?Interpolate1D 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?interpolate1ddf?Interpolate1D 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 \([\text{llim}[i], \min(\text{rlim}[i], a))\) for \(\text{llim}[i] < a\). |
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 \([\max(\text{llim}[i], b), \text{rlim}[i])\) for \(\text{rlim}[i] \geq b\). |
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 \([\max(a, \text{llim}[i]), \min(\text{rlim}[i], b))\). |
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:
|
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 \(\text{nlim} \times \text{ny}\) 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?integrate1ddf?Integrate1D / df?integrateex1ddf?IntegrateEx1D routine computes spline-based integral on user-defined intervals
\(I(i, j) = \int_{\text{ll}_i}^{\text{rl}_i} f_j(x) \, dx\)
where
\(\text{rl}_i = \text{rlim}(i)\), \(\text{ll}_i = \text{llim}(i)\), and \(i = 1, \ldots, \text{ny}\).
If \(\text{rlim}(i) < \text{llim}(i)\), the routine returns
\(I(i, j) = -\int_{\text{rl}_i}^{\text{ll}_i} f_j(x) \, dx\)
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
\(I(1, 1)\)
\(\cdots\)
\(I(1, \text{nlim})\)
\(\vdots\)
\(\ddots\)
\(\vdots\)
\(I(\text{ny}, 1)\)
\(\cdots\)
\(I(\text{ny}, \text{nlim})\)
Column-major format
\(I(1, 1)\)
\(\cdots\)
\(I(\text{ny}, 1)\)
\(\vdots\)
\(\ddots\)
\(\vdots\)
\(I(1, \text{nlim})\)
\(\cdots\)
\(I(\text{ny}, \text{nlim})\)
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?integrateex1ddf?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.