Computing Methods in Crystallography by J. S. Rollett

By J. S. Rollett

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For a binary computer it is convenient, and may be fastest, to use ex = 2(l°9ie)x = 21-4427* Q]\ The integral part of y = 1·4427Λ: can then be used to shift the result up or down the appropriate number of binary places, while the fractional part z of y is used in a series valid for O ^ z ^ l . The Chebyshev series is again useful and Clenshaw (1954) gives n A„ 0-64503 5270 0 -0-31284 1606 1 0-03870 4116 2 -0-00320 8683 3 0-00019 9919 4 -0-00000 9975 5 0-00000 0415 6 -0-00000 0015 7 e~x = Σ AnT'n(x), Ogxgl (12) n = C> 42 J.

S. parameter number for current atomic parameter; 20. s. parameter 0; 21. Set shift = appropriate δξ; 22. Go to 24 if not vibration parameter; 23. Add δΒ" or appropriate element of δΒ', if vibration parameter; 24. Go to 26 if shifts not output; 25. Output applied shift; 26. Advance parameter type, go to 19 until no more parameters this atom ; 27. Advance r, go to 18 until r = ra +1 ; 56 J. S. ROLLETT [6, §14-15 28. Add all shifts to corresponding atomic parameters; 29. Output all new parameters in form suitable for re-input (this should be suppressed only when the cycle time is very short); 30.

The algorithm for this is 1. Get y 2 = X i - x 2 Y3 = y4 = 2. Get y2 = 3. Get y 2 = 4. -x4; Ly2, y^, y4 similarly (convert to orthogonal axes in  units). y^/Cy^yD* Y& Y* similarly (normalise to unit length). equations Γ vT " 7 2 7 3 L 74 . Ys = +1Ί +1 +i ! T 5. Get y5 = y'5. d/(y'5 ys). ) r 6. Getx 5 = Xi+£/ y 5 . Step 4 fails if the matrix is singular, because any two of the vectors y 2 , y3, y 4 are parallel, or because all three of them are coplanar. CHAPTER 4 ALGEBRA OF LEAST SQUARES LINEAR OBSERVATIONAL EQUATIONS 1.

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