Matlab Introduction 2

1
Matlab Introduction 2
http//www.math.iastate.edu/wu/math597x.html
http//www.math.iastate.edu/wu/Math597xHW0000

• Math/BCB/ComS597x
• Zhijun Wu
• Department of Mathematics

2
Conditional Statements
if . . . . . .
elseif . . . . . .
elseif . . . . . . .
. . else . . .
end
switch . . . case . . .,
. . . case . . .,
. . . . . . otherwise,
. . . end
3
Control Statements
for i 1 n for j 1 n
. . . end end
while . . . . . .
. . . . . .
end
4
Examples
gtgt gtgt for i 1 8 for j 1 8
if i j
A (i,j) 2.0 elseif abs
(i-j) 1 A (i,j) -1.0
else A (i,j)
0.0 end end
end gtgt gtgt A
5
User Defined Functions
tridiag.m function A tridiag (n,
d, t) for i 1 n for j 1
n if i j A
(i,j) d elseif abs (i-j)
1 A (i,j) t
else A (i,j) 0.0
end end end
gtgt gtgt tridiag (8, 2.0, -1.0) gtgt gtgt tridiag (5,
2.5, -0.5)
6
Matlab Programs
GenerateTridiagonalMatrix.m n input
(matrix dimension? n ) d input (diagonal
element? d ) t input (off-diagonal
element? t ) A tridiag (n, d, t)
gtgt gtgt GenerateTridiagonalMatrix
7
x11, x12, x13 x21, x22, x23 . . . xm1, xm2, xm3
y11, y12, y13 y21, y22, y23 . . . ym1, ym2, ym3
Y
X
dx11, dx12, , dx1m
dx21, dx22, , dx2m DX .
. .
dxm1, dxm2, , dxmm
dy11, dy12, , dy1m
dy21, dy22, , dy2m DY .
. .
dym1, dym2, , dymm
DME
8
x11, x12, x13 x21, x22, x23 . . . xm1, xm2, xm3
y11, y12, y13 y21, y22, y23 . . . ym1, ym2, ym3
X
Y
RMSD
9
Translation
x11, x12, x13 x21, x22, x23 . . . xm1, xm2, xm3
x11, x12, x13 x21, x22, x23 . . . xm1, xm2, xm3
xc1, xc2, xc3 xc1, xc2, xc3 . . . xc1, xc2, xc3
X
X
-
y11, y12, y13 y21, y22, y23 . . . ym1, ym2, ym3
y11, y12, y13 y21, y22, y23 . . . ym1, ym2, ym3
yc1, yc2, yc3 yc1, yc2, yc3 . . . yc1, yc2, yc3
Y
Y
-
10
Rotation
q11, q12, q13 q21, q22, q23 q31, q32, q33
Q
C YT X, C U S VT, Q U VT
11
? Tryptophan Sidechain 1 (SC1)
Tryptophan Sidechain 2 ? (SC2)
12
ATOM 176 CB TRP A 24 21.993 62.291
198.878 1.00167.56 1HMV 539 ATOM 177 CG
TRP A 24 20.895 63.281 198.700
1.00175.32 1HMV 540 ATOM 178 CD1 TRP A
24 20.992 64.646 198.784 1.00172.94
1HMV 541 ATOM 179 CD2 TRP A 24 19.502
62.990 198.504 1.00182.28 1HMV 542 ATOM
180 NE1 TRP A 24 19.747 65.217 198.667
1.00177.11 1HMV 543 ATOM 181 CE2 TRP A
24 18.812 64.227 198.493 1.00183.04
1HMV 544 ATOM 182 CE3 TRP A 24 18.768
61.798 198.344 1.00184.13 1HMV 545 ATOM
183 CZ2 TRP A 24 17.417 64.312 198.324
1.00185.26 1HMV 546 ATOM 184 CZ3 TRP A
24 17.379 61.882 198.175 1.00184.14
1HMV 547 ATOM 185 CH2 TRP A 24 16.721
63.133 198.169 1.00185.96 1HMV 548
ATOM 611 CB TRP A 88 15.541 91.776
216.531 1.00 55.41 1HMV 974 ATOM 612 CG
TRP A 88 15.585 93.269 216.262 1.00
59.04 1HMV 975 ATOM 613 CD1 TRP A 88
16.415 94.169 216.856 1.00 62.82 1HMV
976 ATOM 614 CD2 TRP A 88 14.735
94.039 215.381 1.00 64.72 1HMV 977 ATOM
615 NE1 TRP A 88 16.139 95.441 216.425
1.00 67.62 1HMV 978 ATOM 616 CE2 TRP A
88 15.112 95.394 215.513 1.00 67.35
1HMV 979 ATOM 617 CE3 TRP A 88 13.693
93.714 214.495 1.00 66.16 1HMV 980 ATOM
618 CZ2 TRP A 88 14.482 96.441 214.787
1.00 60.38 1HMV 981 ATOM 619 CZ3 TRP A
88 13.062 94.764 213.767 1.00 56.70
1HMV 982 ATOM 620 CH2 TRP A 88 13.465
96.105 213.923 1.00 54.35 1HMV 983
13
21.993 62.291 198.878 20.895 63.281
198.700 20.992 64.646 198.784 19.502 62.990
198.504 19.747 65.217 198.667 18.812 64.227
198.493 18.768 61.798 198.344 17.417 64.312
198.324 17.379 61.882 198.175 16.721 63.133
198.169
X
10 3
15.541 91.776 216.531 15.585 93.269
216.262 16.415 94.169 216.856 14.735 94.039
215.381 16.139 95.441 216.425 15.112 95.394
215.513 13.693 93.714 214.495 14.482 96.441
214.787 13.062 94.764 213.767 13.465 96.105
213.923
Y
10 3
14
Calculation of DME for SC1 and SC2
gtgt gtgt for i 1 10 for j 1 10
DX (i,j) sum ((X (i,) X (j,))
. 2) DX (i,j) sqrt (DX
(i,j)) end end gtgt gtgt for i 1
10 for j 1 10 DY
(i,j) sum ((Y (i,) Y (j,)) . 2)
DY (i,j) sqrt (DY (i,j)) end
end gtgt gtgt dme sqrt (sum (sum ((DX DY)
. 2))) / 10 gtgt
15
Calculation of RMSD for SC1 and SC2
gtgt gtgt xc sum (X) / 10 yc sum (Y) /
10 gtgt gtgt XX (,1) X (,1) - xc (1) gtgt XX
(,2) X (,2) - xc (2) gtgt XX (,3) X (,3)
- xc (3) gtgt gtgt YY (,1) Y (,1) - yc (1) gtgt
YY (,2) Y (,2) - yc (2) gtgt YY (,3) Y
(,3) - yc (3) gtgt gtgt C YY XX gtgt U, S,
V svd ( C ) gtgt Q U V gtgt gtgt rmsd
sqrt (sum (sum ((XX YY Q) . 2)) / 10) gtgt