naginterfaces.library.fit.dim2_​spline_​evalm

naginterfaces.library.fit.dim2_spline_evalm(x, y, lamda, mu, c)

dim2_spline_evalm calculates values of a bicubic spline from its B-spline representation. The spline is evaluated at all points on a rectangular grid.

For full information please refer to the NAG Library document for e02df

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/e02/e02dff.html

Parameters

xfloat, array-like, shape $\left(\text{mx}\right)$

$x$ and $y$ must contain $x_{\text{q}}$, for $\text{q}=1,2,\dots ,m_x$, and $y_{\text{r}}$, for $\text{r}=1,2,\dots ,m_y$, respectively. These are the $x$ and $y$ coordinates that define the rectangular grid of points at which values of the spline are required.

yfloat, array-like, shape $\left(\text{my}\right)$

$x$ and $y$ must contain $x_{\text{q}}$, for $\text{q}=1,2,\dots ,m_x$, and $y_{\text{r}}$, for $\text{r}=1,2,\dots ,m_y$, respectively. These are the $x$ and $y$ coordinates that define the rectangular grid of points at which values of the spline are required.

lamdafloat, array-like, shape $\left(\text{px}\right)$

$lamda$ and $mu$ must contain the complete sets of knots $\left\{\lambda \right\}$ and $\left\{\mu \right\}$ associated with the $x$ and $y$ variables respectively.

mufloat, array-like, shape $\left(\text{py}\right)$

$lamda$ and $mu$ must contain the complete sets of knots $\left\{\lambda \right\}$ and $\left\{\mu \right\}$ associated with the $x$ and $y$ variables respectively.

cfloat, array-like, shape $((\text{px}-4)\times (\text{py}-4))$

$c[(\text{py}-4)\times (\text{i}-1)+\text{j}-1]$ must contain the coefficient $c_{\text{i}\text{j}}$ described in Notes, for $\text{j}=1,2,\dots ,\text{py}-4$, for $\text{i}=1,2,\dots ,\text{px}-4$.

Returns

fffloat, ndarray, shape $(\text{mx}\times \text{my})$

$ff[\text{my}\times (\text{q}-1)+\text{r}-1]$ contains the value of the spline at the point $(x_{\text{q}},y_{\text{r}})$, for $\text{r}=1,2,\dots ,m_y$, for $\text{q}=1,2,\dots ,m_x$.

Raises

NagValueError

(errno $1$)

On entry, $\text{my}=⟨value⟩$.

Constraint: $\text{my}\ge 1$.

(errno $1$)

On entry, $\text{mx}=⟨value⟩$.

Constraint: $\text{mx}\ge 1$.

(errno $1$)

On entry, $\text{py}=⟨value⟩$.

Constraint: $\text{py}\ge 8$.

(errno $1$)

On entry, $\text{px}=⟨value⟩$.

Constraint: $\text{px}\ge 8$.

(errno $3$)

On entry, the knots in $mu$ are not in nondecreasing order.

(errno $3$)

On entry, the knots in $lamda$ are not in nondecreasing order.

(errno $4$)

On entry, $mu\left[3\right]\le y\left[0\right]<\cdots <y[\text{my}-1]\le mu[\text{py}-4]$ is violated.

(errno $4$)

On entry, $lamda\left[3\right]\le x\left[0\right]<\cdots <x[\text{mx}-1]\le lamda[\text{px}-4]$ is violated.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

dim2_spline_evalm calculates values of the bicubic spline $s(x,y)$ on a rectangular grid of points in the $x$-$y$ plane, from its augmented knot sets $\left\{\lambda \right\}$ and $\left\{\mu \right\}$ and from the coefficients $c_{ij}$, for $\text{j}=1,2,\dots ,\text{py}-4$, for $\text{i}=1,2,\dots ,\text{px}-4$, in its B-spline representation

$$s(x,y)=\sum _{ij}{c}_{ij}{M}_i\left(x\right)N_j\left(y\right)\text{.}$$

Here $M_i\left(x\right)$ and $N_j\left(y\right)$ denote normalized cubic B-splines, the former defined on the knots ${\lambda }_i$ to ${\lambda }_{i+4}$ and the latter on the knots ${\mu }_j$ to ${\mu }_{j+4}$.

The points in the grid are defined by coordinates $x_q$, for $\text{q}=1,2,\dots ,m_x$, along the $x$ axis, and coordinates $y_r$, for $\text{r}=1,2,\dots ,m_y$, along the $y$ axis.

This function may be used to calculate values of a bicubic spline given in the form produced by interp.dim2_spline_grid, dim2_spline_panel(), dim2_spline_grid() and dim2_spline_sctr(). It is derived from the function B2VRE in Anthony et al. (1982).

References

Anthony, G T, Cox, M G and Hayes, J G, 1982, DASL – Data Approximation Subroutine Library, National Physical Laboratory

Cox, M G, 1978, The numerical evaluation of a spline from its B-spline representation, J. Inst. Math. Appl. (21), 135–143