zoom, Scale

984976a0-48bf-4243-ad14-e459e5d13846 31 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

f bol else If f bol else cases :

x f x ln 0.25 x ≤ If :

x f

kmax 60 : imax 15 : jmax 15 : i 1 imax range j 1 jmax range B i j el 1001 : for for 41 line

Example: MCD Relax method

B 55 el 5.1 : B 65 el 5.1 : B 75 el 5.1 : 31 line

B 57 el 5.1 - : B 67 el 5.1 - : B 77 el 5.1 - : 31 line

relax(A,B,C,D,E,F,U,rjac) Returns a matrix of solution values for Poisson's equation over a planar square region. Matrices A,B.C,D and E specify coefficients for linearly approximating the Laplacian operator at each n^2 gridpoints. Matrix F gives source function values. Matrix U prescribes boundary values along the four edges and approximates interior values. "rjac" is the Jacobian spectral radius.

P j 1 jmax range i 1 imax range P i j el B i j el B i j el 1000 < 0 cases : for for k 0 kmax range i 2 imax 1 - (range j 2 jmax 1 - (range Avg i j el P i 1 - j el P i 1 + j el + P i j 1 - el + P i j 1 + el + 4 / : for for i 1 imax 1 - (range j 1 jmax 1 - (range P i j el B i j el B i j el 1000 < Avg i j el cases : for for 21 line for P transpose 31 line :

P 000000000 0.162 0.35 0.57 0.775 0.854 0.783 0.59 0 0.298 0.669 1.156 1.677 1.856 1.689 1.186 0 0.36 0.87 1.707 2.922 3.202 2.931 1.734 0 0.271 0.746 1.88 5.1 5.1 5.1 1.886 0 0.023 - 0.038 - 0.034 - 0.01 - 0.006 - 0.016 - 0.057 - 0 0.328 - 0.841 - 1.971 - 5.1 - 5.1 - 5.1 - 2.026 - 0 0.447 - 1.03 - 1.91 - 3.132 - 3.425 - 3.166 - 1.998 - 0 0.433 - 0.926 - 1.512 - 2.096 - 2.31 - 2.144 - 1.621 - 0 0.359 - 0.736 - 1.119 - 1.445 - 1.578 - 1.496 - 1.23 - 0 0.273 - 0.543 - 0.797 - 0.991 - 1.079 - 1.038 - 0.898 - 0 0.191 - 0.376 - 0.538 - 0.66 - 0.715 - 0.699 - 0.62 - 0 0.12 - 0.233 - 0.332 - 0.402 - 0.437 - 0.429 - 0.389 - 0 0.058 - 0.112 - 0.158 - 0.191 - 0.207 - 0.205 - 0.187 - 00000000158 mat

zoom, Scale

v p replicate k 1 : ii 1 v rows range v ii el 0 ≡ continue if j 1 v ii el range T k j + 1 - el p ii el : for k k v ii el + : 31 line for T 31 line :

M h v Zoom p 0 : i 1 M rows range p i el h : for N 0 : j 1 M cols range N 1 j el p M j col replicate : for i 1 M rows range p i el v : for Z 0 : j 1 N transpose cols range Z 1 j el p N transpose j col replicate : for up above is Double nest of nests subscript the output... Unest data Z transpose 1 el : v data 1 el : j 2 data cols range v v data j el augment : for v 131 line :

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - / (* lo + :

image P 0255 Scale :

user zoom Q image 44 Zoom :

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 Q Create Spline Function

Spline_interpolate & CreateMesh surface plot

t0 1 time :

Spline_interpolate & CreateMesh surface plot In this demo, we must prepare the data set by bordering the right and upper side with ascending numbers. We leave these scales in integer to avoid confusion. The program is a dummy function that carries the 3 variates (x,y,M). Smath offers three interpolation options: 1. linterp [linear quadratic], 2. ainterp [Akima cubic spline], 3. cinterp [the more univsersal cubic spline]. The project is concluded by the surface "CreateMesh"

x y M Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x ainterp 51 line :

data P :

Prepare the data set ------------------------------------------------

data C j 1 data cols range C j el j : for C transpose 21 line :

data R i 1 data rows 1 + range R i el i 1 - : for R 21 line :

data C 123456789101112131415115 mat

data R 0123456789101112131415161 mat

data R data C data stack augment

New data R data C data stack augment :

New 11 el x/y :

<= this position may be any alpha/numeric char.

New x/y 12345671000000020 0.162 0.3503 0.5704 0.7753 0.8537 0.7833 30 0.2976 0.6686 1.1558 1.6772 1.8557 1.6894 40 0.3597 0.8704 1.707 2.9217 3.2023 2.9315 50 0.2706 0.7459 1.8797 5.1 5.1 5.1 60 0.0235 - 0.0381 - 0.0345 - 0.0102 - 0.0064 - 0.0158 - 70 0.3277 - 0.841 - 1.971 - 5.1 - 5.1 - 5.1 - 80 0.4469 - 1.0304 - 1.9096 - 3.1321 - 3.4248 - 3.1659 - 90 0.4326 - 0.9258 - 1.5119 - 2.0965 - 2.3095 - 2.1439 - 100 0.3592 - 0.736 - 1.1192 - 1.4448 - 1.5778 - 1.4958 - 110 0.2729 - 0.5431 - 0.7968 - 0.9911 - 1.0787 - 1.0379 - 120 0.1912 - 0.3758 - 0.5383 - 0.6603 - 0.7146 - 0.6989 - 130 0.1203 - 0.2334 - 0.3321 - 0.4024 - 0.4371 - 0.4292 - 140 0.0576 - 0.1119 - 0.1576 - 0.1911 - 0.2066 - 0.205 - 150000000168 mat

The data set is ready for the 3D surface plot----------------------------

u v f u v u v New Spline 31 mat :

<= Introduce the 3D surface plot

M u v f 0200203030 CreateMesh :

M Euler

angle Ω1 1000 angle cos angle sin - 0 angle sin angle cos 33 mat :

Матрица преобразования для поворота вокруг оси y angle Ω2 angle cos 0 angle sin 010 angle sin - 0 angle cos 33 mat :

Матрица преобразования для поворота вокруг оси z angle Ω3 angle cos angle sin - 0 angle sin angle cos 000133 mat :

α π 4 / :

β π 4 / :

φ π 4 / :

α β φ 13 mat π 4 / π 4 / π 4 / 13 mat ≡

γ α Ω1 β Ω2 * φ Ω3 * eval :

M f B M γ * eval : B 1 col B 2 col augment 21 line :

RenToDo ... some viable composite rotation

M f