Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

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
const
dfsIntegrCallBack
 for
dfsIntegrateEx1D
const
dfdIntegrCallBack
 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
const
dfsInterpCallBack
 for
dfsIntegrateEx1D
const
dfdInterpCallBack
 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
const
dfsIntegrCallBack
 for
dfsIntegrateEx1D
const
dfdIntegrCallBack
 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
const
dfsSearchCellsCallBack
 for
dfsIntegrateEx1D
const
dfdSearchCellsCallBack
 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
.
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-u