inter3.f

37 lines · 1 definitions · on GitHub (7be4133)

Python version: inter3.py, 39 lines, on the right (switch to Python above the code).

Purpose

INTER3 returns the weights of 3-point Lagrange interpolation, and of its first derivative, at a point $x$.

How it fits

Called by SETSCV (interpolation in the SCV equation-of-state tables), SURFP and KCSURFP (interpolation in gravity in the surface-pressure tables). No modules, no calls. The 4-point version is INTERP.

The header's "Livermore opacity tables" is from an older use. The comment says INTER3 is "the interpolation routine for density in the Livermore opacity tables" (lines 18–19 ↗), but its only callers are the SCV EOS set-up (setscv.f, line 114 ↗; setscv.f, line 193 ↗; setscv.f, line 208 ↗; setscv.f, line 242 ↗) and the surface-pressure routines (surfp.f, line 81 ↗; kcsurfp.f, line 90 ↗), none an opacity routine.

The method

For nodes $a_1, a_2, a_3$ (A), the weights B and derivative weights C are

$$B_i(x) = \prod_{j\ne i}\frac{x-a_j}{a_i-a_j},\qquad C_i(x) = \frac{dB_i}{dx} = \frac{\sum_{j\ne i}\prod_{k\ne i,j}(x-a_k)}{\prod_{j\ne i}(a_i-a_j)},$$

so that $f(x) \approx \sum_i B_i f(a_i)$ and $f'(x) \approx \sum_i C_i f(a_i)$.

Definitions

subroutineINTER3

lines 8–37 · GitHub

3-point Lagrange weights and derivative weights (above).

Called by KCSURFP, SETSCV ×4, SURFP

Change log

The changes since rp_1

Changed since rp_1. Declarations only: IMPLICIT NONE.

1 2C 3C 4CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 5C INTER3 6CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 7C INTER3 8 SUBROUTINE INTER3(A,B,C,X) 9C 10/20/26 MHP via Claude 10C code changed to replace implicit typing with IMPLICIT NONE and 11C explicit declarations. 12 IMPLICIT NONE 13 REAL*8 A,A21,A31,A32,B,C,D1,D2,D3,X,XA1,XA2,XA3 14 15 DIMENSION A(3),B(3),C(3) 16 SAVE 17 18C INTER3 IS THE INTERPOLATION ROUTINE FOR DENSITY IN THE LIVERMORE 19C OPACITY TABLES, AND IT USES A 3-POINT LAGRANGIAN INTERPOLATION SCHEME. 20 A32 = A(3) - A(2) 21 A31 = A(3) - A(1) 22 A21 = A(2) - A(1) 23 D1 = A21*A31 24 D2 = -A21*A32 25 D3 = A31*A32 26 XA1 = X - A(1) 27 XA2 = X - A(2) 28 XA3 = X - A(3) 29 B(1) = (XA2*XA3)/D1 30 B(2) = (XA1*XA3)/D2 31 B(3) = (XA1*XA2)/D3 32 C(1) = (XA2 + XA3)/D1 33 C(2) = (XA1 + XA3)/D2 34 C(3) = (XA1 + XA2)/D3 35 36 RETURN 37 END

1"""Python version of inter3.f (YREC 7be4133): 3-point Lagrange weights 2and derivative weights.""" 3 4import numpy as np 5 6 7def inter3(a: np.ndarray, b: np.ndarray, c: np.ndarray, x: float) -> None: 8 """Set b to the 3-point Lagrange interpolation weights at x for the 9 nodes a[1:4], and c to the weights of the first derivative. 10 11 Translates: inter3.f#INTER3 (7be4133) 12 13 Arguments: a (the nodes), x. 14 Arrays changed in place: b, c (index 0 unused). 15 16 Returns nothing. 17 18 """ 19 20 # The node differences and the denominators (Fortran lines 20–25). 21 a32 = a[3] - a[2] 22 a31 = a[3] - a[1] 23 a21 = a[2] - a[1] 24 d1 = a21 * a31 25 d2 = -a21 * a32 26 d3 = a31 * a32 27 28 # The interpolation weights (Fortran lines 26–31). 29 xa1 = x - a[1] 30 xa2 = x - a[2] 31 xa3 = x - a[3] 32 b[1] = (xa2 * xa3) / d1 33 b[2] = (xa1 * xa3) / d2 34 b[3] = (xa1 * xa2) / d3 35 36 # The derivative weights (Fortran lines 32–34). 37 c[1] = (xa2 + xa3) / d1 38 c[2] = (xa1 + xa3) / d2 39 c[3] = (xa1 + xa2) / d3