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DistanceGeometry

# DistanceGeometry - = Î 2 Â½ w i2 z i = Î 3 Â½ w i3 Î 1 = 18...

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Metric Matrix Distance Geometry Metric matrix with elements: g ij = x i x j +y i y j +z i z j centroid: x i = 0 y i = 0 z i = 0. g ij = 1 2 ( d 2 i0 + d 2 j0 - d 2 ij ) d 2 i0 = 1 N j i N d 2 ij - 1 N 2 j=1 N k>j d 2 jk d 2 10 = 1 3 ( d 2 12 + d 2 13 ) - 1 3 2 ( d 2 12 + d 2 13 + d 2 23 ) example: d 12 = d 23 = 5 d 13 = 6 d 2 10 = 1 3 ( 5 2 + 6 2 ) - 1 3 2 ( 5 2 + 6 2 + 5 2 ) = 10.777 or d 10 = 3.283 d 2 20 = 1 3 ( 5 2 + 5 2 ) - 1 3 2 ( 5 2 + 6 2 + 5 2 ) = 7.111 or d 20 = 2.667 g 11 = 1 2 ( d 2 10 + d 2 10 ) = 10.778 g 12 = 1 2 ( d 2 10 + d 2 20 - d 2 12 ) = -3.556 G = 10.778 -3.556 -7.222 -3.556 7.111 -3.556 -7.222 -3.556 10.778 G w q = λ q w q q = x, y, or z x i = λ 1 ½ w i1 y i
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Unformatted text preview: = Î» 2 Â½ w i2 z i = Î» 3 Â½ w i3 Î» 1 = 18 w 1 = ï£­ ï£¬ ï£« ï£¸ ï£· ï£¶ 0.707-0.707 Î» 2 = 10.67 w 2 = ï£­ ï£¬ ï£« ï£¸ ï£· ï£¶ 0.408-0.816 0.408 x 1 = 18 1/2 0.707 = 3 y 1 = 10.67 1/2 0.408 = 1.333 x 2 = 18 1/2 0 = 0 y 2 = 10.67 1/2-0.816 = -2.667 x 3 = 18 1/2-0.707 = -3 y 3 = 10.67 1/2 0.408 = 1.333 1 2 3 d 12 d 23 d 13 1 2 3 d 12 d 23 d 13 x y x 1 , y 1 x 2 , y 2 x 3 , y 3 d 10 d 30 d 20...
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