quadeos06.f

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

Python version: quadeos06.py, 39 lines, on the right (switch to Python above the code).

Purpose

Quadratic interpolation through three points for the 2006 OPAL equation of state; a copy of QUAD and QUADEOS01 (both removed since rp_1) under its own name, with its own cache.

How it fits

Who calls it: ESAC06 and T6RINTEOS06.

The method

As in QUAD: $y(x) = c_1 + c_2 x + c_3 x^2$ through the three points; with IC = 0 the abscissa factors are computed and cached in slot I (up to 30), otherwise reused. It differs from QUADEOS01 only in its name and in redundant parentheses.

Definitions

functionQUADEOS06

lines 7–42 · GitHub

Called by ESAC06 ×2, T6RINTEOS06 ×6

Change log

The changes since rp_1

Changed since rp_1. Declarations only: IMPLICIT NONE.

1C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 2C 3C QUADEOSS06 4C 5C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 6 7 function quadeos06(ic,i,x,y1,y2,y3,x1,x2,x3) 8C 10/20/26 MHP via Claude 9C code changed to replace implicit typing with IMPLICIT NONE and 10C explicit declarations. 11 IMPLICIT NONE 12 REAL*8 C1,C2,C3,QUADEOS06,X,X1,X2,X3,XX,XX12,XX13,XX1PXX2,XX1SQ, 13 * * XX23,Y1,Y2,Y3,YY 14 INTEGER I,IC 15 16c..... this function performs a quadratic interpolation. 17 18 dimension xx(3),yy(3),xx12(30),xx13(30),xx23(30),xx1sq(30) 19 . . ,xx1pxx2(30) 20 21 save 22 xx(1)=x1 23 xx(2)=x2 24 xx(3)=x3 25 yy(1)=y1 26 yy(2)=y2 27 yy(3)=y3 28 if(ic .eq. 0) then 29 xx12(i)=1D0/(xx(1)-xx(2)) 30 xx13(i)=1D0/(xx(1)-xx(3)) 31 xx23(i)=1D0/(xx(2)-xx(3)) 32 xx1sq(i)=xx(1)*xx(1) 33 xx1pxx2(i)=xx(1)+xx(2) 34 endif 35 c3=(yy(1)-yy(2))*xx12(i) 36 c3=c3-(yy(2)-yy(3))*xx23(i) 37 c3=c3*xx13(i) 38 c2=(yy(1)-yy(2))*xx12(i)-(xx1pxx2(i))*c3 39 c1=yy(1)-xx(1)*c2-xx1sq(i)*c3 40 quadeos06=c1+x*(c2+x*c3) 41 return 42 end

1"""Python version of quadeos06.f (YREC 7be4133): quadratic interpolation 2through three points, for the 2006 OPAL equation of state.""" 3 4import numpy as np 5 6# The cache of abscissa factors, slots 1..30 (SAVE). 7xx12 = np.zeros(31) 8xx13 = np.zeros(31) 9xx23 = np.zeros(31) 10xx1sq = np.zeros(31) 11xx1pxx2 = np.zeros(31) 12 13 14def quadeos06(ic: int, i: int, x: float, y1: float, y2: float, y3: float, x1: float, x2: float, x3: float) -> float: 15 """The value at x of the quadratic through (x1, y1), (x2, y2), 16 (x3, y3). With ic = 0 the abscissa factors are computed and cached in 17 slot i; otherwise slot i is reused. 18 19 Translates: quadeos06.f#QUADEOS06 (7be4133) 20 21 Returns the interpolated value. 22 23 """ 24 25 # The abscissa factors, computed or reused (Fortran lines 22–34). 26 if ic == 0: 27 xx12[i] = 1.0 / (x1 - x2) 28 xx13[i] = 1.0 / (x1 - x3) 29 xx23[i] = 1.0 / (x2 - x3) 30 xx1sq[i] = x1 * x1 31 xx1pxx2[i] = x1 + x2 32 33 # The coefficients and the value (Fortran lines 35–40). 34 c3 = (y1 - y2) * xx12[i] 35 c3 = c3 - (y2 - y3) * xx23[i] 36 c3 = c3 * xx13[i] 37 c2 = (y1 - y2) * xx12[i] - xx1pxx2[i] * c3 38 c1 = y1 - x1 * c2 - xx1sq[i] * c3 39 return c1 + x * (c2 + x * c3)