plotG

19c57427-41aa-4279-8636-2ea1c54c5bc5 274 3 12 decimal

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

plotG

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

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

http://smath.info/wiki/GetFile.aspx?File=Tutorials/IntroductionSMathStudio088May2010.pdf

4 appVersion 0.98.6179.21440

r c M r c matrix :

Poject collector: fill-in blanks
of project coponents [numerical] Project hello! π 0000000000033 mat 000033 mat :

33 M 00000000033 mat

# # # if # # if

]]>

M 33 M :

M 00000000033 mat

Project 11 el hello!

N 22 el M :

N 00000000000033 mat 22 mat

Project 12 el 3.1416

N 35 el M :

N 00000000000000033 mat 000000000000000033 mat 35 mat

# # # lim

Mapping an expression

<= Undocumented

M a 1 e x y * 22 mat :

ln M map maple a ln 01 x y * ln 22 mat

m a 1 e x y * 41 mat :

ln m map maple a ln 01 x y * ln 41 mat

m a 1 e x y * 41 mat :

f 2^m map maple a f 2^1 f 2^1 exp f 2^x y * f 2^41 mat

The matrix function

<= Undocumented

<= The times table you can expand at will x y φ x y * :

Ω 55 φ matrix maple :

Ω 1234524681036912154812162051015202555 mat

Ω 3 row 369121515 mat

Ω 3 col 369121551 mat

V i 1 Ω rows range u i el i : v Ω 3 col : 21 line for u v augment 21 line :

Pts V 1 col V 2 col . 10 black plotG :

0 V Pts 3 1 sys

η

Two gorgeous utility companions

If you have two matrices [one design, one reference] ... square or rectangular, unwrap each one and plot each one to view as "absolute" . Also, substract one to the other and plot their deviation. Augment each "unwraped", view them element wise ... Much more matching can be done [not offered].

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

V r c Pack i 1 r range v i el V i el : for j 1 c range i 1 r range i r j * + V rows ≤ m i j el V i r j * + el : m i j el 0 : if for for v m augment 31 line :

data 024681 .3 .45 .6 .6 2 .4 .5 - .62 - .65 3 .4 .48 - .6 - .61 4 .38 .45 .55 .59 55 mat :

V data Unwrap :

______________________ V below this line __________________

V 012342 0.3 0.4 0.4 0.38 4 0.45 0.5 - 0.48 - 0.45 6 0.6 0.62 - 0.6 - 0.55 8 0.6 0.65 231 mat

Q i 1 V rows range u i el i : v V : 21 line for u v augment 21 line :

mcol 10 :

M data Unwrap 54 Pack (:

V 012342 0.3 0.4 0.4 0.38 4 0.45 0.5 - 0.48 - 0.45 6 0.6 0.62 - 0.6 - 0.55 8 0.6 0.65 231 mat

sep mcol 5 - mcol 1022 mat :

M 024681 0.3 0.45 0.6 0.6 2 0.4 0.5 - 0.62 - 0.65 3 0.4 0.48 - 0.6 - 0.61 4 0.38 0.45 0.55 0.59 55 mat

xyQ Q 1 col Q 2 col . 10 black plotG :

The "mcol" separator goes in multiple of of the row(data)... mcol => 5,10,15,20,25

M tr 0.21 -

View the column wise matrix c/w col separator

0 Q xyQ 2 sep 5 1 sys

Analyse matrix via truth table

W 1.22 7.36 7.96 7.94 1.26 2.36 4.74 3.07 5.83 4.11 3.78 8.14 3.64 9.93 8.95 9.73 5.13 3.71 5.78 3.16 54 mat :

Truth(M,a,b) ... truth table within [a, b] M a b Truth count 0 : i 1 M rows range j 1 M cols range M i j el a ≥ (M i j el b ≤ (* Z i j el M i j el : 11 line count count 1 + : if for for Z 41 line :

x c x 2 ≥ (x 4 ≤ (* :

W 24 Truth 00000 2.36 0 3.07 00 3.78 0 3.64 0000 3.71 0 3.16 54 mat

A robust construct of the Scale function Mat Low High Scale Mat 0 : min Mat Min : max Mat Max : maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 Mat rows range j 1 Mat cols range N i j el Mat i j el min - maxmin / : for for HighLow N * Low + 71 line :

Vectorise operator 6179 W c W * vectorize 00000 2.36 0 3.07 00 3.78 0 3.64 0000 3.71 0 3.16 54 mat

Round OFF a matrix M n Mround i 1 M rows range j 1 M cols range m i j el M i j el n round : for for m 21 line :

Strip repeated in vector v Strip v v sort : k 0 : i 1 v rows 1 - (range v i 1 + el v i el - 0 ≠ R k k 1 + : el v i el : 11 line if 11 line for R v v rows el stack 41 line :

M n round vectorize

Strip 0's in vector

Strip paired 0's

v Strip0 k 0 : i 1 v rows range v i el 0 ≠ R k k 1 + : el v i el : 11 line End of strip if 11 line for R 31 line :

data Strip2 u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line END of strip if 11 line for R 31 line 31 line :

data 000012340000567800910102 mat :

v 10305616 mat transpose :

v Strip0 transpose 135614 mat

N data Strip2 :

N 3 el 5612 mat

<= Extract a particular row

N 1212 mat 3412 mat 5612 mat 7812 mat 91012 mat 51 mat

Strip2 (data) will strip 0's from dual vectors that have paired values and paired 0's. Very useful to clean "Contour Extract Advisor". Paired values need not be integer.

data UnestV v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

data UnestH v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

U 0520458012561 mat 520458012518061 mat 458012518024532061 mat 8012518024532040561 mat 12518024532040550061 mat 15 mat :

U UnestH 05458012552080125180204512518024545801802453208012524532040512518032040550065 mat

N UnestV 1234567891052 mat

data Strip2 nest striped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line End of strip if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

data Strip_X nest striped in 'R' u data 1 col : v data 2 col : k 0 : i 2 data rows range u i el u i 1 - el - 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line END of strip if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

data Strip2 1234567891052 mat

XW 0.175 317.303 0.3325 217.0355 0.525 130.1479 0.7 61.3415 0.875 32.4856 1.05 47.5163 1.225 90.6788 1.4 143.2053 1.575 173.5314 1.75 155.6779 1.925 105.1301 2.1 56.8338 2.275 34.1471 2.45 51.1141 2.625 114.8755 2.8 214.0454 2.975 306.0658 3.15 341.7215 3.325 304.952 3.5 214.1093 3.675 111.3089 3.85 42.8756 4.025 15.8375 4.2 7.5659 242 mat :

data ListCollect collects index list select 12357916 mat : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

XW ListCollect 0.175 317.303 0.3325 217.0355 0.525 130.1479 0.875 32.4856 1.225 90.6788 1.575 173.5314 62 mat

data select ListCollect ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 31 line :

select 12357923171511110 mat :

XW select ListCollect 0.175 317.303 0.3325 217.0355 0.525 130.1479 0.875 32.4856 1.225 90.6788 1.575 173.5314 4.025 15.8375 2.975 306.0658 2.625 114.8755 1.925 105.1301 102 mat

data lo hi CollectRange collects range select lo hi range : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

XW 37 CollectRange 0.525 130.1479 0.7 61.3415 0.875 32.4856 1.05 47.5163 1.225 90.6788 52 mat

Here, submatrix is a better candidate

sub XW 37 range 12 range el :

sub 0.525 130.148 0.7 61.342 0.875 32.486 1.05 47.516 1.225 90.679 52 mat

M 0.19 0.59 0.35 0.82 0.71 0.61 0.27 0.59 0.12 0.03 2.66 4.21 0.45 0.23 5.48 5.20 44 mat :

Vectorise Diagonal Mat Dia Diagonal elements i 1 Mat rows range Dia i el Mat i i el : for Dia 31 line :

Smath  built-in M Diag 0.19 0000 0.61 0000 2.66 0000 5.2 44 mat

M Dia 0.19 0.61 2.66 5.2 41 mat

M tr 8.66

M Dia sum 8.66

The trace of a square matrix tr(M) is the Σ of the diagonal elements.

index [indices] of integer search matrix/vector. No match = "idx_not defined"

M 12345648933 mat :

h 611526672316357553377120 mat transpose :

value table col lookup k 1 : j k table rows range table j col el value ≡ index k el j : k k 1 + : 21 line continue if for k 1 ≡ index NO match : index if 31 line :

4 M 1 lookup 2321 mat

6 h 1 lookup 1561141 mat

13 h 1 lookup NO match

Locating the first occurrence of a specific element in a vector

w v 1500 range : i 1 v rows range vy i el 1000 v i el cos * Ceil : for vy 31 line :

check if occurrence is unique

400 w 1 lookup 39711 mat

v x search j 0 : i 1 v length range j j 1 + : v i el x ≡ vv v i el : break 21 line vv NO match : if 21 line for j vv 21 mat 31 line :

w 400 search 39740021 mat

w 700 search 15070021 mat

w 145 - search 8145 - 21 mat

w 400 - search 500 NO match 21 mat

Create a 2D matrix of function values

We make it symmetric by equating both directions. You may range V otherwise for an asymmetric option

Mesh U, V  within the bounds L, H L H N xd N intervals U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 51 line :

L 1 - :

H 1 :

N 24 :

U L H N xd :

V U :

x y f 255 x 2^y 2^+ (- 0.25 / exp * :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

N x y f U V Sym :

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 N

N 0.1 0.2 0.3 0.5 0.8 1.2 1.7 0.2 0.3 0.6 0.9 1.5 2.3 3.3 0.3 0.6 1 1.7 2.7 4.1 5.8 0.5 0.9 1.7 2.8 4.5 6.9 9.9 0.8 1.5 2.7 4.5 7.3 11 15.9 57 mat

Matrix stuff

A 1221 - 22 mat :

B 1 - 12122 mat :

C 1 - 21422 mat :

I 2 identity :

s f C s I * A - (1 -^(* B * :

s f maple 1 - 21422 mat

Numeric/Auto 5 f eval 0.7 0.2 1.1 1.6 22 mat

Mathcad 11 0.7 0.2 1.1 1.6 22 mat ≡

Accumulate col, given Vector/Matrix

Accumulate  a range in selected "col" M s e col Σ Ranged accumulator vy M s e col col submatrix : Σ 1 el vy 1 el : i 2 vy rows range Σ i el vy i el Σ i 1 - el + : for Σ 51 line :

V 109875 π 61 mat :

M 0.19 0.59 0.35 0.82 0.71 0.61 0.27 0.59 0.12 0.03 2.66 4.21 0.45 0.23 5.48 5.20 44 mat :

Optimise: numeric V 161 Σ 1019273439 42.1416 61 mat

M 143 Σ 0.35 0.62 3.28 8.76 41 mat

vx 46542844125225260416 mat transpose :

vx 161 Σ transpose 465893133415861838244216 mat

12 + 34 + 21 sys 3721 sys

"sys"

M 12345678933 mat :

M 22 vminor 137922 mat

"vminor"

M 22 minor 12 -

"minor"

collect x sqrt x ln x exp 31 sys :

If A is a square matrix, then the minor of the entry in the i-th row and j-th column (also called the (i,j) minor, or a first minor) is the determinant of the submatrix formed by deleting the i-th row and j-th column. This number is often denoted Mi,j.

collect 2 el x ln

# # # # # 51 sys

System 12 + 34 + 21 sys sys2mat :

# # 21 sys sys ≡

System 3721 mat

MySystem 12 + 34 + 21 sys π e 21 sys e ln e sqrt π sqrt 31 sys 31 mat :

Nest MySystem sys2mat :

Nest 3721 mat 3.1416 2.7183 21 mat 1 1.6487 1.7725 31 mat 31 mat

Matrix editor

Link to download the matrix editor: http://smath.info/wiki/GetFile.aspx?File=Tools%2fSMathMatrixEditor%20V1.2.zip 1. Download 2. Click "Run" 3. Copy/Paste in SmathSudio directory

M 05204580125152045801251802204580125180245345801251802453204801251802453204055125180245320405500667 mat :

rows order u 12365416 mat :

cols order v 712365417 mat :

Extract 'a' col that has rows ordered in 'u' data col u Order select order in col ct 1 : i u a ct 1 el data i col el : ct ct 1 + : 21 line for a 41 line :

M 3 u Order 20458024518012561 mat

order cols in matrix data v OrderCol r 1 : i 1 M rows range c 1 : j v M r c el data i j el : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

M v OrderCol 10520125804525204518012580320458024518012544580125320245180580125180405320245612518024550040532067 mat

order rows in matrix data u OrderRow r 1 : i u c 1 : j 1 M cols range M r c el data i j el : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

M u OrderRow 05204580125152045801251802204580125180245312518024532040550068012518024532040554580125180245320467 mat

I 2 identity :

A B r c replace U A : i 1 B rows range j 1 B cols range U r i + c j + el B i j el : for for U 31 line :

M I 22 replace 0520458012515204580125180220451018024534580012453204801251802453204055125180245320405500667 mat

Enter 'r' [row], 'c' [col] where the upper left element of the smaller array anchors.

Ω 0 :

plotG(vx,vy,char,size,color) ... UnestH(data)

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

data UnestH v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

M Low High Scale High Low - (M M Min - M Max M Min - 106 -^+ / (* Low + :

The infinite vector circulation

Range 'n' ∞ - n ≤ (n ∞ ≤ (&

User scale xs 1 : ys 1 : 12 mat

v 012345678910111 mat transpose :

n v rotate N v length : p n N mod : p p p 0 ≥ p N + p 0 < ignored cases : Ω v : p 0 ≡ i 1 p range Ω i N + p - el v i el : for i p 1 + (N range Ω i p - el v i el : for 21 line cases Ω 51 line :

n 17 - :

<= Pilot the rotation

v transpose n v rotate transpose 21 mat 012345678910111 mat 567891001234111 mat 21 mat

Vrot n v rotate :

XY xs v * ys Vrot * augment :

rot xs v * ys Vrot * . 10 black plotG :

C 55 + 200 black 15 mat :

Reversible rotation of vector. You can shrink/expand either direction via [xs, ys]. Illustrative plot wrt 'n'.

x n v rotate x 1 + el rot C 4 1 sys

Typical Matrix Scheduler M v transpose 19 - v rotate transpose 0 v rotate transpose 1 v rotate transpose 7 v rotate transpose 51 mat transpose : 012345678910111 mat 345678910012111 mat 012345678910111 mat 123456789100111 mat 789100123456111 mat 15 mat

The "rotated" XY 051627384951060718293104112 mat

U M UnestH : Schedule day Pet Jos Art Leslie 15 mat : Assign Schedule U stack : 31 line

A possible application:

Assume you are looking at aspecific star, you need several

parameters [Azimut, Horizon, Focus ...]. If the vector 'v' is

wrt parameters, easy to address and automate the system.

]]>

Assign day Pet Jos Art Leslie 030171412825239363410474505856169672710783808949191051021006125 mat

'R' is subscripted to explode  100*Random(1) v transpose R 1001 Random 1 el * Floor : R v rotate transpose 31 mat 012345678910111 mat 78123456789100111 mat 31 mat

U U 0255 Scale :

v 012345678910111 mat

Implicit 'zoom fractional' Up/Down M a b zoom a b ≡ (a b | (1 ≠ (& (=> ≡ => implicit conditions ≡ i 1 M rows a * (range j 1 M cols b * (range N i j el M i a / Ceil j b / Ceil el : a 1 ≥ N i j el M i a / Floor j b / Floor el : cases for for N 41 line :

image U 1010 zoom :

U 0 76.5 0 25.5 178.5 25.5 102 25.5 5120451 127.5 51 76.5 229.5 76.5 153 76.5 102255102 178.5 102 127.5 0 127.5 204 127.5 153 25.5 153 229.5 153 178.5 51 178.5 255 178.5 204 76.5 2040204 229.5 102 229.5 25.5 229.5 255 127.5 255512550153115 mat

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 image

Finding the first element in a vector that exceeds a certain treshold

v u 02 π * 0.1 range : i 1 u rows range vy i el u i el sin : for vy 31 line :

v tresh first j 1 : v j el abs tresh ≤ j j 1 + : while j v j el 21 mat 31 line :

v 0.5 first 7 0.5646 21 mat

v 0.875 first 12 0.8912 21 mat

`

Delete 'ONE specified' col/row Square matrix

M 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat :

M c DelColRow N 0 : ct 1 : n 1 M cols range n c ≠ N 1 ct el M n col : ct ct 1 + : 21 line Unest 'N' if for v N 1 el : j 2 N cols range v v N j el augment : for v 61 line :

M 3 DelColRow 05458012552080125180204512518024545801802453208012524532040512518032040550065 mat

M transpose 2 DelColRow transpose 0520458012520458012518024545801251802453208012518024532040512518024532040550056 mat

Mat Frame i 1 Mat rows 2 + range j 1 Mat cols 2 + range frame i j el : for for frame 21 line :

Frame M Frame :

FRAME Frame M 11 replace :

FRAME 05204580125 5204580125180 204580125180245 4580125180245320 80125180245320405 125180245320405500 88 mat

Insert valued matrix: row/col

M 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat :

v 0000 00000062 mat :

ROW 00 00000 00026 mat :

submatrix Smath 6179 =>

M B c InsertCol a M 1 M rows 1 c submatrix : c M 1 M rows c 1 + M cols submatrix : a B c augment 31 line :

a M 1 M rows range 1 c range el ≡ b M 1 M rows range c 1 + (M cols range el ≡ 21 line

M B r InsertRow a M 1 r 1 M cols submatrix : c M r 1 + M rows 1 M cols submatrix : a B c stack 31 line :

a M 1 r range 1 M cols range el ≡ b M r 1 + (M rows range c M cols range el ≡ 21 line

M v 3 InsertCol 0520004580125520450080125180204580 12518024545801250018024532080125180002453204051251802450032040550068 mat

M v transpose 4 InsertRow 052045801255204580125180204580125180245458012518024532000 00000 0008012518024532040512518024532040550086 mat

something hello :

----------the working project is above this region ------

Insert an addressable system

aa 2 sqrt : bb 2 : cc 3 : dd something : ee 5 : ff 6 : gg 1 exp : hh 8 : ii 9 : jj 10 : kk 11 : ll 2 ln : 121 sys

Elements are collected [from the palette]. What a simplified way, compared to indexed addressing ! We just demonstrate inserting "colelement". As the project progresses, the conclusion follows below.

A M 1613 submatrix :

C M 1646 submatrix :

B aa bb cc dd ee ff gg hh ii jj kk ll 62 mat :

New A B C augment :

New 0520 1.4142 24580125520453 hello 80125180204580561251802454580125 2.7183 81802453208012518091024532040512518024511 0.6931 32040550068 mat

Jean Giraud: 2015/12/19

M 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat

Nest Matrix ... Row/Col

M NestCol v M 1 col : ct 1 : j 1 M cols range a 1 ct el M j col : ct ct 1 + : 21 line for a 41 line :

M NestRow v M 1 row : ct 1 : j 1 M rows range a ct 1 el M j row : ct ct 1 + : 21 line for a 41 line :

M NestCol 0520458012561 mat 520458012518061 mat 20458012518024561 mat 458012518024532061 mat 8012518024532040561 mat 12518024532040550061 mat 16 mat

M NestRow 0520458012516 mat 520458012518016 mat 20458012518024516 mat 458012518024532016 mat 8012518024532040516 mat 12518024532040550016 mat 61 mat

un-Nest Matrix ... Row/col

data UnestCol v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

data UnestRow v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

U M NestCol UnestCol :

V M NestRow UnestRow :

U 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat

V 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat

data Explode data UnestRow v data 1 el : j 2 data rows range v v data j el stack : for v 31 line : j 1 data cols range myU 1 j el data j col UnestRow : for v myU 1 el : j 2 myU cols range v v myU j el augment : for v 41 line 21 line :

data 32.1014 11 mat 1.9591 11 mat 0.2438 11 mat 25.7124 11 mat 1.9591 11 mat 0.1254 11 mat 0.0155 11 mat 1.5539 11 mat 0.2438 11 mat 0.0155 11 mat 0.0077 11 mat 0.1927 11 mat 25.7124 11 mat 1.5539 11 mat 0.1927 11 mat 22.4646 11 mat 44 mat :

data Explode 32.101 1.959 0.244 25.712 1.959 0.125 0.016 1.554 0.244 0.016 0.008 0.193 25.712 1.554 0.193 22.465 44 mat

data UnestRow v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

data Nest2Cols j 1 data cols range nest 1 j el data j col UnestRow : for nest 21 line :

data Nest2Cols 32.101 1.959 0.244 25.712 41 mat 1.959 0.125 0.016 1.554 41 mat 0.244 0.016 0.008 0.193 41 mat 25.712 1.554 0.193 22.465 41 mat 14 mat

data Cols2Matrix j 1 data cols range Utemp 1 j el data j col UnestRow : for v Utemp 1 el : j 2 Utemp cols range v v Utemp j el augment : for v 41 line :

data Cols2Matrix 32.101 1.959 0.244 25.712 1.959 0.125 0.016 1.554 0.244 0.016 0.008 0.193 25.712 1.554 0.193 22.465 44 mat

M 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat :

Extract selected rows/cols

data v ExtractCol collects index list ct 1 : i v a 1 ct el M i col : ct ct 1 + : 21 line for a a collect is nested next:-> unest a V a 1 el : j 2 a cols range V V a j el augment : for V 91 line :

data v ExtractRow collects index list ct 1 : i v a 1 ct el M i row : ct ct 1 + : 21 line for a a collect is nested next:-> unest a V a 1 el : j 2 a cols range V V a j el stack : for V 91 line :

rows/cols selection to be Extracted v 13513 mat :

M v ExtractCol 020805451252080180451252458018032012524540563 mat

data v ExtractRow 052045801252045801251802458012518024532040536 mat

Mirror matrix

M 0.19 0.59 0.35 0.82 0.71 0.61 0.27 0.59 0.12 0.03 2.66 4.21 0.45 0.23 5.48 5.20 44 mat :

Vectorise Diagonal M Dia Diagonal elements i 1 M rows range Dia i el M i i el : for Dia 31 line :

Smath  built-in M Diag 0.19 0000 0.61 0000 2.66 0000 5.2 44 mat

M Dia 0.19 0.61 2.66 5.2 41 mat

Explode mirror Matrix M mirror ct 1 : j M cols ct range mir 1 ct el M j col : ct ct 1 + : 21 line for mir Unest N v mir 1 el : j 2 mir cols range v v mir j el augment : for v 71 line :

M mirror 0.82 0.35 0.59 0.19 0.59 0.27 0.61 0.71 4.21 2.66 0.03 0.12 5.2 5.48 0.23 0.45 44 mat

M mirror Dia 0.82 0.27 0.03 0.45 41 mat

mirror matrix [6179 =>] M M 1 M rows range M cols 1 range el :

M 0.82 0.35 0.59 0.19 0.59 0.27 0.61 0.71 4.21 2.66 0.03 0.12 5.2 5.48 0.23 0.45 44 mat

Nest a mirror Matrix M Nestmirror ct 1 : j M cols ct range Nmir 1 ct el M j col : ct ct 1 + : 21 line for Nmir 31 line :

M Nestmirror 0.19 0.71 0.12 0.45 41 mat 0.59 0.61 0.03 0.23 41 mat 0.35 0.27 2.66 5.48 41 mat 0.82 0.59 4.21 5.2 41 mat 14 mat

A robust construct of the Scale function M Low High Scale min M Min : max M Max : maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / : for for HighLow N * Low + 61 line :

The Delta Matrix

n s Δ i 1 n range j 1 n range Δ i j el i j + s 1 + ≤ : for for Δ 21 line :

1012 Δ mirror 11111111111111111111111111111101111111110011111111000111111100001111110000011111000000111100000001111010 mat

Ω 3232 Δ 0255 Scale :

iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAIAAAD8GO2jAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACkSURBVEhLtc3bEoIwDEDB/v9HO1ZdHBQKvST7xDTJoTyS5f6gVD4TvOp5P1CvPISS/vAWR/fLcxDRPZMIin8Ml8kdma/ROmVlgVCLrVkqFyxOkbhmd5z7W9YHOe7hYoTLTo66Oevnro+bIU47OBjl+o7tCQKXrM7RaLM3TabB0gqlMzYWiR0Yr9P7ZRZCcscgiurGayDhN0+xtJPqVW69yq2X8gTUoiP7iO8kbwAAAABJRU5ErkJggg== Ω

M 0.8561 - 0.3921 - 0.0719 0.536 1 0.6241 - 0.7865 - 0.7517 - 0.7169 - 0.7169 - 0.3921 - 0.7633 - 0.9722 - 1 - 0.7053 - 0.1601 - 0.7633 - 0.9675 - 0.9954 - 0.7146 - 0.0719 0.768 - 0.7517 - 0.7285 - 0.7193 - 55 mat :

Round OFF Matrix/Vector M n Round i 1 M rows range j 1 M cols range m i j el M i j el n round : for for m 21 line :

Mround M 2 round vectorize :

M 2 Round 0.86 - 0.39 - 0.07 0.54 1 0.62 - 0.79 - 0.75 - 0.72 - 0.72 - 0.39 - 0.76 - 0.97 - 1 - 0.71 - 0.16 - 0.76 - 0.97 - 1 - 0.71 - 0.07 0.77 - 0.75 - 0.73 - 0.72 - 55 mat

Mround 0.86 - 0.39 - 0.07 0.54 1 0.62 - 0.79 - 0.75 - 0.72 - 0.72 - 0.39 - 0.76 - 0.97 - 1 - 0.71 - 0.16 - 0.76 - 0.97 - 1 - 0.71 - 0.07 0.77 - 0.75 - 0.73 - 0.72 - 55 mat

Diagonal of a square matrix Mat Dia Diagonal elements i 1 Mat rows range Dia i el Mat i i el : for Dia 31 line :

M Dia 0.8561 - 0.7865 - 0.9722 - 0.9954 - 0.7193 - 51 mat

M Dia 3 Round 0.856 - 0.787 - 0.972 - 0.995 - 0.719 - 51 mat

S22 issue, created by Dr Martin Kraska: x n d format rs x 10 n^* 0 round eval num2str : l rs strlen : n 0 ≡ rs n 0 > rs 1 l n - substr d rs l n - 1 + n substr concat 10 n -^(x 10 n^* 0 round * eval num2str if if 31 line :

12.34 2 - . format 0

12.34 1 - . format 10

12.34 0 . format 12

12.34 1 . format 12.3

12.34 2 . format 12.34

12.34 3 . format 12.340

12.35 1 . format 12.4

12.65 1 . format 12.7

12.55 1 . format 12.6

useful for collecting data sets for Genfit data row ListCollect ct 1 : i row a ct el data i 1 el : b ct el data i 3 el : add more augment more ct ct 1 + : 51 line for a b augment 31 line :

<----- ..... select cols <-----

M 142567234512375895678945 mat :

row 23413 mat :

M row ListCollect 242795732 mat

The col/row extractors utilities

add/remove/insert/shuffle
in col(,,,) argument ... at will in-situ data v Col ct 1 : i v a 1 ct el data i col : ct ct 1 + : 21 line for a V a 1 el : j 2 a cols range V V a j el augment : for V 61 line :

add/remove/insert/shuffle
in row(,,,) argument ... at will in-situ data v Row ct 1 : i v a 1 ct el data i row : ct ct 1 + : 21 line for a V a 1 el : j 2 a cols range V V a j el stack : for V 61 line :

M 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat :

Select from in-situ

col 13513 mat :

row 23413 mat :

M row Row 5204580125180204580125180245458012518024532036 mat

M col Col 020805451252080180451252458018032012524540563 mat

NEW M col Col row Row :

NEW 54512520801804512524533 mat

data u v BlocUser ct 1 : i v a 1 ct el data i col : ct ct 1 + : 21 line for V a 1 el : j 2 a cols range V V a j el augment : for ct 1 : i u b 1 ct el V i row : ct ct 1 + : 21 line for U b 1 el : j 2 b cols range U U b j el stack : for U transpose 91 line :

M 05204580125520458012518020458012518024545801251802453208012518024532040512518024532040550066 mat :

col 13513 mat :

row 43213 mat :

New M col row BlocUser :

New 45125245208018054512533 mat

Smath index style A B r c replace U A : i 1 B rows range j 1 B cols range U r i + 1 - (c j + 1 - (el B i j el : for for U 31 line :

M 99 matrix :

user 1234 678933 mat :

New M user 22 replace :

New 00000000001230000004 60000007890000000000000000000000000000000000000000000000000099 mat

M 0 :

N 0 :

U 0 :

V 0 :

W 0 :

Matrix function NOT needed

N 1234 678933 mat :

M 99 el 0 :

M 33 el N :

7

i 15 range j 15 range V i j el M i j el : for for

i 15 range j 15 range U i j el M i 1 + j 1 + el : for for

i 15 range j 15 range W i 2 + j 2 + el M i 1 + j 1 + el : for for

V 0000000000001234 678933 mat 00000000000055 mat

U 0000001234 678933 mat 00000000000000000055 mat

W 0000000000000000000000001234 678933 mat 00000000000000000000000077 mat

N 12345678933 mat :

n 3 :

i 1 n range u i el N 2 row : for Unest the stack v u 1 el : j 2 u rows range v v u j el stack : for v 51 line

v 45645645633 mat

M 1010 Random :

M key FindIndex r M rows : c M cols : 12 mat i 1 : j 1 : 12 mat j c ≤ (M i j el key ≠ (* i r < i i 1 + : i 1 : j j 1 + : 21 line if while j c ≤ i j 21 mat 0 if 41 line :

row
col M M Max FindIndex 6921 mat

user i 0100 range : V 0.1 i * sin vectorize : 21 sys

Find the 1rst element in vector that exceeds
 a prescribed threshold. V treshold FindIdx j 1 : V j el abs treshold ≤ j j 1 + : while j 1 - V j el 21 mat 31 line :

idx V 0.875 FindIdx : 11 0.891 21 mat

i V augment 001 0.1 2 0.199 3 0.296 4 0.389 5 0.479 6 0.565 7 0.644 8 0.717 9 0.783 10 0.841 112 mat

i V augment idx 1 el idx 2 el + 15 red 1 5 mat 2 1 sys

user i 1500 range : V 101 i * cos * vectorize Ceil : 21 sys

Locate the 1rst occurence of a
specific element in a vector V x FindIdx j 1 : V j el x ≠ j j 1 + : while j V j el 21 mat 31 line :

E V 5 FindIdx : 20521 mat

M 05204580125152045801251802204580125180245345801251802453204801251802453204055125180245320405500667 mat :

i M rows 0 + : j M cols 1 + : N i j el 0 : 31 line

A B r c replace U A : i 1 B rows 0 + (range j 1 B cols range U r i + c j + el B i j el : for for U 31 line :

N M 01 replace 10520458012514520458012518027204580125180245304580125180245320408012518024532040550125180245320405500668 mat