Data Fitting Usage Examples

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

Data Fitting Usage Examples

You can get Fortran source code in the .examplesdatafittingf subdirectory of the Intel® oneAPI Math Kernel Library (oneMKL) installation directory.

C Example of Linear Spline Construction

#include "mkl.h"
#define N 500                     /* Size of partition, number of breakpoints */
#define SPLINE_ORDER DF_PP_LINEAR /* Linear spline to construct */

int main()
{
    int status;          /* Status of a Data Fitting operation */
    DFTaskPtr task;      /* Data Fitting operations are task based */

    /* Parameters describing the partition */
    MKL_INT nx;          /* The size of partition x */
    double x[N];         /* Partition x */
    MKL_INT xhint;       /* Additional information about the structure of breakpoints */

    /* Parameters describing the function */
    MKL_INT ny;          /* Function dimension */
    double y[N];         /* Function values at the breakpoints */
    MKL_INT yhint;       /* Additional information about the function */

    /* Parameters describing the spline */
    MKL_INT  s_order;    /* Spline order */
    MKL_INT  s_type;     /* Spline type */
    MKL_INT  ic_type;    /* Type of internal conditions */
    double* ic;         /* Array of internal conditions */
    MKL_INT  bc_type;    /* Type of boundary conditions */
    double* bc;         /* Array of boundary conditions */

    double scoeff[(N-1)* SPLINE_ORDER];   /* Array of spline coefficients */
    MKL_INT scoeffhint;            /* Additional information about the coefficients */

    /* Initialize the partition */
    nx = N;
    /* Set values of partition x */
    ...
    xhint = DF_NO_HINT;    /* No additional information about the function is provided.
                              By default, the partition is non-uniform. */
    /* Initialize the function */
     ny = 1;               /* The function is scalar. */

    /* Set function values */
    ...
    yhint = DF_NO_HINT;    /* No additional information about the function is provided. */

    /* Create a Data Fitting task */
    status = dfdNewTask1D( &task, nx, x, xhint, ny, y, yhint );

    /* Check the Data Fitting operation status */
    ...

    /* Initialize spline parameters */
    s_order = DF_PP_LINEAR;    /* Spline is of the second order. */
    s_type = DF_PP_DEFAULT;    /* Spline is of the default type. */

    /* Define internal conditions for linear spline construction (none in this example) */
    ic_type = DF_NO_IC;
    ic = NULL;

    /* Define boundary conditions for linear spline construction (none in this example) */
    bc_type = DF_NO_BC;
    bc = NULL;
    scoeffhint = DF_NO_HINT;    /* No additional information about the spline. */

    /* Set spline parameters  in the Data Fitting task */
    status = dfdEditPPSpline1D( task, s_order, s_type, bc_type, bc, ic_type,
                                ic, scoeff, scoeffhint );

    /* Check the Data Fitting operation status */
    ...

    /* Use a standard computation method to construct a linear spline: */
    /* P_{i}(x) = c_{i,0}+c_{i,1}(x-x_{i}), i=0,..., N-2 */
    /* The library packs spline coefficients to array scoeff. */
    /* scoeff[2*i+0]=c_{i,0} and scoeff[2*i+1]=c_{i,1}, i=0,..., N-2 */
    status = dfdConstruct1D( task, DF_PP_SPLINE, DF_METHOD_STD );

    /* Check the Data Fitting operation status */
    ...

    /* Process spline coefficients */
    ...

    /* Deallocate Data Fitting task resources */
    status = dfDeleteTask( &task ) ;

    /* Check the Data Fitting operation status */
    ...
    return 0 ;
}

C Example of Cubic Spline-Based Interpolation

#include "mkl.h"

#define NX 100                     /* Size of partition, number of breakpoints */
#define NSITE 1000                 /* Number of interpolation sites */
#define SPLINE_ORDER DF_PP_CUBIC   /* A cubic spline to construct */

int main()
{
    int status;          /* Status of a Data Fitting operation */
    DFTaskPtr task;      /* Data Fitting operations are task based */

    /* Parameters describing the partition */
    MKL_INT nx;          /* The size of partition x */
    double x[NX];         /* Partition x */
    MKL_INT xhint;       /* Additional information about the structure of breakpoints */

    /* Parameters describing the function */
    MKL_INT ny;          /* Function dimension */
    double y[NX];         /* Function values at the breakpoints */
    MKL_INT yhint;       /* Additional information about the function */

    /* Parameters describing the spline */
    MKL_INT  s_order;    /* Spline order */
    MKL_INT  s_type;     /* Spline type */
    MKL_INT  ic_type;    /* Type of internal conditions */
    double* ic;         /* Array of internal conditions */
    MKL_INT  bc_type;    /* Type of boundary conditions */
    double* bc;         /* Array of boundary conditions */

    double scoeff[(NX-1)* SPLINE_ORDER];   /* Array of spline coefficients */
    MKL_INT scoeffhint;            /* Additional information about the coefficients */

    /* Parameters describing interpolation computations */
    MKL_INT nsite;        /* Number of interpolation sites */
    double site[NSITE];   /* Array of interpolation sites */
    MKL_INT sitehint;     /* Additional information about the structure of
                             interpolation sites */

    MKL_INT ndorder, dorder;    /* Parameters defining the type of interpolation */

    double* datahint;   /* Additional information on partition and interpolation sites */

    double r[NSITE];    /* Array of interpolation results */
    MKL_INT rhint;     /* Additional information on the structure of the results */
    MKL_INT* cell;      /* Array of cell indices */

    /* Initialize the partition */
    nx = NX;

    /* Set values of partition x */
    ...
    xhint = DF_NON_UNIFORM_PARTITION;  /* The partition is non-uniform. */

    /* Initialize the function */
     ny = 1;               /* The function is scalar. */

    /* Set function values */
    ...
    yhint = DF_NO_HINT;    /* No additional information about the function is provided. */

    /* Create a Data Fitting task */
    status = dfdNewTask1D( &task, nx, x, xhint, ny, y, yhint );

    /* Check the Data Fitting operation status */
    ...

    /* Initialize spline parameters */
    s_order = DF_PP_CUBIC;     /* Spline is of the fourth order (cubic spline). */
    s_type = DF_PP_BESSEL;     /* Spline is of the Bessel cubic type. */

    /* Define internal conditions for cubic spline construction (none in this example) */
    ic_type = DF_NO_IC;
    ic = NULL;

    /* Use not-a-knot boundary conditions. In this case, the is first and the last
     interior breakpoints are inactive, no additional values are provided. */
    bc_type = DF_BC_NOT_A_KNOT;
    bc = NULL;
    scoeffhint = DF_NO_HINT;    /* No additional information about the spline. */

    /* Set spline parameters  in the Data Fitting task */
    status = dfdEditPPSpline1D( task, s_order, s_type, bc_type, bc, ic_type,
                                ic, scoeff, scoeffhint );

    /* Check the Data Fitting operation status */
    ...

    /* Use a standard method to construct a cubic Bessel spline: */
    /* P_{i}(x) = c_{i,0} + c_{i,1}(x - x_{}_{i}) + c_{i,2}(x - x_{}_{i})^{2} + c_{i,3}(x - x_{i})^{3}, */
    /* The library packs spline coefficients to array scoeff: */
    /* scoeff[4*i+0] = c_{i,0}, scoef[4*i+1] = c_{i,1},         */
    /* scoeff[4*i+2] = c_{i,2}, scoef[4*i+1] = c_{i,3},         */
    /* i=0,...,N-2  */
    status = dfdConstruct1D( task, DF_PP_SPLINE, DF_METHOD_STD );

    /* Check the Data Fitting operation status */
    ...

    /* Initialize interpolation parameters */
    nsite = NSITE;

    /* Set site values */
    ...

    sitehint = DF_NON_UNIFORM_PARTITION; /* Partition of sites is non-uniform */

    /* Request to compute spline values */
    ndorder = 1;
    dorder = 1;
    datahint = DF_NO_APRIORI_INFO;  /* No additional information about breakpoints or
                                       sites is provided. */
    rhint = DF_MATRIX_STORAGE_ROWS; /* The library packs interpolation results
                                       in row-major format. */
    cell = NULL;                    /* Cell indices are not required. */

    /* Solve interpolation problem using the default method: compute the spline values
       at the points site(i), i=0,..., nsite-1 and place the results to array r */
    status = dfdInterpolate1D( task, DF_INTERP, DF_METHOD_PP, nsite, site,
    sitehint, ndorder, &dorder, datahint, r, rhint, cell );

    /* Check Data Fitting operation status */
     ...

    /* De-allocate Data Fitting task resources */
     status = dfDeleteTask( &task );
    /* Check Data Fitting operation status */
     ...
    return 0;
}

C Example of Cell Search

#include "mkl.h"

#define NX 100                     /* Size of partition, number of breakpoints */
#define NSITE 1000                 /* Number of interpolation sites */

int main()
{
    int status;          /* Status of a Data Fitting operation */
    DFTaskPtr task;      /* Data Fitting operations are task based */

    /* Parameters describing the partition */
    MKL_INT nx;          /* The size of partition x */
    float x[2];         /* Partition x is uniform and holds endpoints
                            of interpolation interval [a, b] */
    MKL_INT xhint;       /* Additional information about the structure of breakpoints */

    /* Parameters describing the function */
    MKL_INT ny;          /* Function dimension */
    float   *y;          /* Function values at the breakpoints */
    MKL_INT yhint;       /* Additional information about the function */

    /* Parameters describing cell search */
    MKL_INT nsite;       /* Number of interpolation sites */
    float  site[NSITE]; /* Array of interpolation sites  */
    MKL_INT sitehint;    /* Additional information about the structure of sites */

    float* datahint;     /* Additional information on partition and interpolation sites */

    MKL_INT cell[NSITE]; /* Array for cell indices */

    /* Initialize a uniform partition */
    nx = NX;
    /* Set values of partition x: for uniform partition,           */
    /* provide end-points of the interpolation interval [-1.0,1.0] */
    x[0] = -1.0f; x[1] = 1.0f;
    xhint = DF_UNIFORM_PARTITION; /* Partition is uniform */

    /* Initialize function parameters */
    /* In cell search, function values are not necessary and are set to zero/NULL values */
    ny    = 0;
    y     = NULL;
    yhint = DF_NO_HINT;

    /* Create a Data Fitting task */
    status = dfsNewTask1D( &task, nx, x, xhint, ny, y, yhint );

    /* Check Data Fitting operation status */
    ...

    /* Initialize interpolation (cell search) parameters */
    nsite = NSITE;

   /* Set sites in the ascending order */
    ...
    sitehint = DF_SORTED_DATA;      /* Sites are provided in the ascending order. */
    datahint = DF_NO_APRIORI_INFO;  /* No additional information
                                       about breakpoints/sites is provided.*/

    /* Use a standard method to compute indices of the cells that contain
       interpolation sites. The library places the index of the cell containing
       site(i) to the cell(i), i=0,...,nsite-1 */
    status = dfsSearchCells1D( task, DF_METHOD_STD, nsite, site, sitehint,
                            datahint, cell );
    /* Check Data Fitting operation status */
     ...

    /* Process cell indices */
     ...

    /* Deallocate Data Fitting task resources */
    status = dfDeleteTask( &task );

    /* Check Data Fitting operation status */
     ...
    return 0;
}

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Data Fitting Usage Examples

C Example of Linear Spline Construction

C Example of Cubic Spline-Based Interpolation

C Example of Cell Search