The documentation is still in infancy, however we provide a few documents in pdf for quick description. All the provided examples in Radial++ contain lots of explanations in each function, please see the examples.

Quick References

RBFs Evaluations

We are working more in C style, but using templates. In the forthcoming release we are going to incorporate the template functions which can be used in any external C++ program or others librarys to perform the evaluaions of radial basis functions with global support.

Thin-Plate Splines

tps_1d evalution for 1d
tps_2d evaluation for 2d
tps_3d evaluation for 3d
tps_nd evaluation for nd

Power Splines

pot_1d evaluation for 1d
pot_2d evaluation for 2d
pot_3d evaluation for 3d
pot_nd evaluation for nd

Gaussian

gau_1d evaluation for 1d
gau_2d evaluation for 2d
gau_3d evaluation for 3d
gau_nd evaluation for nd

Multiquadric

mq_1d evaluation for 1d
mq_2d evaluation for 2d
mq_2d evaluation for 2d
mq_nd evaluation for nd

Inverse Multiquadric

imq_1d evaluation for 1d
imq_2d evaluation for 2d
imq_3d evaluation for 3d
imq_nd evaluation for nd

RBFs Derivatives

We are working more in C style, but using templates. In the forthcoming release we are going to incorporate the template functions which can be used in any external C++ program or others librarys to perform the derivatives of radial basis functions with global support.

Thin-Plate Splines

tps_1d_x 1st derivative with respect to x for 1D
tps_1d_xx 2nd derivative with respect to x for 1D
tps_2d_x 1st derivative with respect to x for 2D
tps_2d_y 1st derivative with respect to y for 2D
tps_2d_xx 2nd derivative with respect to x for 2D
tps_2d_yy 2nd derivative with respect to y for 2D
tps_2d_xy 2nd derivative with respect to xy for 2D
tps_2d_yx 2nd derivative with respect to yx for 2D
tps_3d_x 1st derivative with respect to x for 3D
tps_3d_y 1st derivative with respect to y for 3D
tps_3d_z 1st derivative with respect to z for 3D
tps_3d_xx 2nd derivative with respect to x for 3D
tps_3d_yy 2nd derivative with respect to y for 3D
tps_3d_zz 2nd derivative with respect to z for 3D

Power Splines

pot_1d_x 1st derivative with respect to x for 1D
pot_1d_xx 2nd derivative with respect to x for 1D
pot_2d_x 1st derivative with respect to x for 2D
pot_2d_y 1st derivative with respect to y for 2D
pot_2d_xx 2nd derivative with respect to x for 2D
pot_2d_yy 2nd derivative with respect to y for 2D
pot_2d_xy 2nd derivative with respect to xy for 2D
pot_2d_yx 2nd derivative with respect to yx for 2D
pot_3d_x 1st derivative with respect to x for 3D
pot_3d_y 1st derivative with respect to y for 3D
pot_3d_z 1st derivative with respect to z for 3D
pot_3d_xx 2nd derivative with respect to x for 3D
pot_3d_yy 2nd derivative with respect to y for 3D
pot_3d_zz 2nd derivative with respect to z for 3D

Gaussian

gau_1d_x 1st derivative with respect to x for 1D
gau_1d_xx 2nd derivative with respect to x for 1D
gau_2d_x 1st derivative with respect to x for 2D
gau_2d_y 1st derivative with respect to y for 2D
gau_2d_xx 2nd derivative with respect to x for 2D
gau_2d_yy 2nd derivative with respect to y for 2D
gau_2d_xy 2nd derivative with respect to xy for 2D
gau_2d_yx 2nd derivative with respect to yx for 2D
gau_3d_x 1st derivative with respect to x for 3D
gau_3d_y 1st derivative with respect to y for 3D
gau_3d_z 1st derivative with respect to z for 3D
gau_3d_xx 2nd derivative with respect to x for 3D
gau_3d_yy 2nd derivative with respect to y for 3D
gau_3d_zz 2nd derivative with respect to z for 3D

Multiquadric

mq_1d_x 1st derivative with respect to x for 1D
mq_1d_xx 2nd derivative with respect to x for 1D
mq_2d_x 1st derivative with respect to x for 2D
mq_2d_y 1st derivative with respect to y for 2D
mq_2d_xx 2nd derivative with respect to x for 2D
mq_2d_yy 2nd derivative with respect to y for 2D
mq_2d_xy 2nd derivative with respect to xy for 2D
mq_2d_yx 2nd derivative with respect to yx for 2D
mq_3d_x 1st derivative with respect to x for 3D
mq_3d_y 1st derivative with respect to y for 3D
mq_3d_z 1st derivative with respect to z for 3D
mq_3d_xx 2nd derivative with respect to x for 3D
mq_3d_yy 2nd derivative with respect to y for 3D
mq_3d_zz 2nd derivative with respect to z for 3D

Inverse Multiquadric

imq_1d_x 1st derivative with respect to x for 1D
imq_1d_xx 2nd derivative with respect to x for 1D
imq_2d_x 1st derivative with respect to x for 2D
imq_2d_y 1st derivative with respect to y for 2D
imq_2d_xx 2nd derivative with respect to x for 2D
imq_2d_yy 2nd derivative with respect to y for 2D
imq_2d_xy 2nd derivative with respect to xy for 2D
imq_2d_yx 2nd derivative with respect to yx for 2D
imq_3d_x 1st derivative with respect to x for 3D
imq_3d_y 1st derivative with respect to y for 3D
imq_3d_z 1st derivative with respect to z for 3D
imq_3d_xx 2nd derivative with respect to x for 3D
imq_3d_yy 2nd derivative with respect to y for 3D
imq_3d_zz 2nd derivative with respect to z for 3D

The name descriptions of the derivatives was taken from TUNA:RBF, not the implementations.