hatch, scale

f04b4019-99b8-429e-ba55-edf7bcd938fe 60 3 5 decimal

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

hatch, scale

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

XY 7 326.8 15 268.3 20 246.4 25 215.9 30 202.2 45 166.3 90 107.8 120 95.9 150 70.7 18063102 mat :

D 2500 : (Dose injection [mg] ≡ τ 1 : (Duration injection [min] ≡ 21 line

4 appVersion 0.98.6179.21440 ≡ Timing 23 sec ≡ 21 mat

t f D τ / 0 t ≤ (t τ ≤ (& 0 cases : x g 0 : 21 sys

f g 0 τ 5 hatch

Given Aminohippuric DE system t X t diff 1 V1 / t f k01 k21 + (X 1 el * - k12 X 2 el * + (* ≡ t Y t diff 1 V1 / k12 k21 / * (k21 X 1 el * k12 X 2 el * - (* ≡ 21 mat

t X D 1 V1 / t f k01 k21 + (X 1 el * - k12 X 2 el * + (* 1 V2 / k12 k21 / * (k21 X 1 el * k12 X 2 el * - (* 21 mat :

k01 0.08 : k12 0.12735 : k21 0.12664 : 31 sys

V1 6.654 : V2 4.7 : 21 sys

init 22.85 27.97 21 mat :

'N 206' optimum points sol init 1200206 t X D rkfixed :

sol 1 22.85 27.97 1.966 380.268 32.494 2.932 369.703 41.335 3.898 359.607 49.68 4.864 349.957 57.553 53 mat

rewamp this point approximately sol 12 el 400 :

sol_1 sol 1 col sol 2 col augment : sol_2 sol 1 col sol 3 col augment : ax sol 1 col : ay sol 2 col : 12 mat bx sol 1 col : by sol 3 col : 12 mat data XY o 5 black plot : 51 line

x Φ1 ax ay x cinterp : x Φ2 bx by x cinterp : 21 line

sol_1 sol_2 data 3 1 sys

Source/end project ... Mathcad 11

1. source: research lab from Austria [Wschrabi]

2. collaboration: Viktor, jmG

3. date: 27 February 2009

Mathcad 11 optimized parameters meet 1/1 the

research Lab software INUsoft

]]>

Xsol x Φ1 x Φ2 - 0 ≡ x 4050 solve : 45.5

Xsol Φ1 162.9

Custom bar Size/Fill

j v fillBar data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - (range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - (range V V stem j el stack : for V V data data rows row stack : 71 line : ----------------------------------------------- Lo Hi Number xd vU 0 : dx Hi Lo - Number / : i 1 Number range vU i el Lo dx - (dx i * + : for vU 41 line : --------------------------- Number vx j el : vU Number size - Number size + fill xd : 21 line p i 1 vU rows range Y i el v : for vU Y augment 21 line : Bar p Stem : 71 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

X XY 1 col : Y XY 2 col : n XY rows : 13 mat

Δ i 1 XY rows range δ i el X i el Φ1 Y i el - eval : for X δ augment 21 line :

Δ 7 3.298 15 2.46 20 3.369 - 25 4.688 30 0.054 45 2.494 - 90 2.092 120 6.152 - 150 3.337 180 1.767 - 102 mat

Δ 2 col sum 2.145

Analysing Rkadapt stability

Δ 1 BarSize 1 1 sys

Export populated solutions

L H N xd U 0 : dx H L - N / : 12 mat i 1 N 1 + (range U i el L dx - (dx i * + eval : for U 31 line :

L 0 : H 200 : N 400 : 13 mat u L H N xd : 21 sys

t0 1 time :

x U_1 ax ay x cinterp : x U_2 bx by x cinterp : 21 sys

U1 n 1 u rows range u1 n el u n el U_1 eval : for u u1 augment 21 line :

U2 n 1 u rows range u2 n el u n el U_2 eval : for u u2 augment 21 line :

U1 U2 data 3 1 sys

OBSERVE . . . U_1(x), U_2(x)

interpolate on the canvas and on command.

They must be passed to program module to

produce the desired discrete export.

This transit is fast [cinterp is native fast].

]]>

1 time t0 - 8 s *

β 205.9592 192.0681 19.23 158.7927 41 mat :

x c 10 x ≤ (x 200 ≤ (& cases :

x β f β 1 el x - β 3 el / exp * β 2 el x - β 4 el / exp * + :

x β f x c * data 2 1 sys

U2 1 26.805 10 92.403 20 134.518 30 154.697 40 162.131 50 162.267 60 158.326 70 152.206 80 145.022 90 137.422 100 129.777 110 122.297 120 115.094 130 108.224 140 101.71 150 95.555 160 89.754 170 84.294 180 79.16 190 74.334 200 69.8 212 mat :

U2 U2 o 5 black plot :

β 205.9592 192.0681 19.23 158.7927 41 mat :

x c 10 x ≤ (x 200 ≤ (& cases :

x β f β 1 el x - β 3 el / exp * β 2 el x - β 4 el / exp * + :

α 7.987 3.9774 25.225 80.6037 41 mat :

x α Φ α 1 el x - α 3 el / exp * α 2 el x - α 4 el / exp * + :

plot x β f x c * x α Φ x * x c * U2 data 41 sys :

plot

Lab data injection ODE

reaction 2nd ODE sol'n

]]>

About Aminohippuric . . .

The MinerrODE originates from Mathsoft id Advisor. Further explored/applied by Viktor and Tom.

The best Minerr parameters aren't possible in Smath, otherwise than painfull trial/error.

Pushing our luck towards possible two model fit functions, that: Smath succeeds perfectly as resumed

by the two functions: f(x,β) fit to the lab data ... Φ(x,α)*x red fit to ODE 2nd solution

]]> Genfit Utilities

vx vy char size clr plotG n vx length : plot vx 1 el vy 1 el char size clr augment : i 2 n range plot plot vx i el vy i el char size clr augment stack : for plot 41 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

Applicable parts are: Optimiz "numeric" XY f φ β Minimize X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

U2 1 26.805 10 9.24 20 6.726 30 5.157 40 4.053 50 3.245 60 2.639 70 2.174 80 1.813 90 1.527 100 1.298 110 1.112 120 0.959 130 0.832 140 0.726 150 0.637 160 0.561 170 0.496 180 0.44 190 0.391 200 0.349 212 mat :

<= reduced Exponential decay_2

deprecate the reduced XY U2 320 range 12 range el :

<= model function x β f 0 β 1 el x - β 3 el / exp * + β 2 el x - β 4 el / exp * + :

in φ(x,β,f,n) -> set 'n' to last index β # el ≡

<= Gradient Vector Function x β φ x β f 4 φ :

X XY 1 col : Y XY 2 col : n XY rows : 31 line

Memo initialise the two Genfit functions blue solution ........... red solutions

1003001010041 mat 205.9592 192.0681 19.23 158.7927 41 mat 12 mat

85205041 mat 7.987 3.9774 25.225 80.6037 41 mat 12 mat

β β 1 el 85205041 mat : iter 9 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

Absolute  residuals δ j 1 XY rows range res j el Y j el X j el β f - eval : for X res augment 21 line :

β 7.987 3.9774 25.225 80.6037 41 mat

bar δ Error :

bar

range/populate L 0 : H 200 : N 199 : 13 mat U L H N xd : 21 line

U rows 200

FIT i 1 U rows range vy i el U i el β f 1 * eval : for U vy augment 21 line :

data XY . 12 black plot :

data FIT 2 1 sys

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.001

======================================================================================

U2 1 26.805 10 92.403 20 134.518 30 154.697 40 162.131 50 162.267 60 158.326 70 152.206 80 145.022 90 137.422 100 129.777 110 122.297 120 115.094 130 108.224 140 101.71 150 95.555 160 89.754 170 84.294 180 79.16 190 74.334 200 69.8 212 mat :

X U2 1 col : Y U2 2 col : n U2 rows : reduced X Y X / vectorize augment : 41 line

reduced 1 26.805 10 9.24 20 6.726 30 5.157 40 4.053 50 3.245 60 2.639 70 2.174 80 1.813 90 1.527 100 1.298 110 1.112 120 0.959 130 0.832 140 0.726 150 0.637 160 0.561 170 0.496 180 0.44 190 0.391 200 0.349 212 mat

Plug 'reduced' in U2 above Genfit that's what we fit for red solution. <= U2 from short cspline collection

======================================================================================

XY 7 326.8 15 268.3 20 246.4 25 215.9 30 202.2 45 166.3 90 107.8 120 95.9 150 70.7 18063102 mat :

<= lab data set Exponential decay_2

<= model function x β f 0 β 1 el x - β 3 el / exp * + β 2 el x - β 4 el / exp * + :

<= Gradient Vector Function x β φ x β f 4 φ :

β β 1 el 1003001010041 mat : iter 7 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β 205.9592 192.0681 19.23 158.7927 41 mat

Export otherwise splined ODE solutions

Export  nicely populated ODE solutons X sol 1 col : t 02001 range : j 1 t length range A j el X sol 2 col t j el cinterp : B j el X sol 3 col t j el cinterp : 21 line for 31 line

optimiz Symbolic A t A augment : B t B augment : 21 sys

A 0 428.222 14002 379.773 3 369.036 4 358.546 5 348.641 6 339.148 7 330.098 8 321.451 9 313.192 102 mat

A B 2 1 sys

sol 1400 27.97 1.966 380.268 32.494 2.932 369.703 41.335 3.898 359.607 49.68 43 mat