19c57427-41aa-4279-8636-2ea1c54c5bc5 21 4 5 fraction

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

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 :

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

r c M r c matrix :

33 M 00000000033 mat

M 33 M :

M 00000000033 mat

Project 11 el hello!

Project 12 el 3.1416

N 22 el M :

N 00000000000033 mat 22 mat

N 35 el M :

N 00000000000000033 mat 000000000000000033 mat 35 mat

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 :

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

The matrix function

<= Undocumented

x y φ x y * :

<= The times table you can expand at will

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

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 p q Pack j 1 q range i 1 p range i p j * + V rows 1 + < M i j el V i p j * + el : M i j el 0 : if for for u V 1 p 11 submatrix : v M 1 p 1 p 1 - submatrix : u v augment 41 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 __________________

M data Unwrap 55 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 0.61 0.59 251 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

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

0 Q 2 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 :

x c x 2 ≥ (x 4 ≤ (* :

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 31 line :

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

M Min Max Scale Max Min - (M M min - M max M min - / (* Min + :

<= Scale a Matrix

Scaled M 1 - 1 Scale :

Scaled 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 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 :

Scaled 2 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

Strip paired 0's

Strip single 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 undefined 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 Undefined if 11 line for R 31 line 31 line :

v 10305616 mat transpose :

v Strip0 transpose 135614 mat

data 000012340000567800910102 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 Unest v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

N Unest 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 Undefined 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 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 :

Here, submatrix is a better candidate

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

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 :

RemToDo: the other diagonal

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 Dia sum 8.66

M tr 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"

h 611526672316357553377120 mat transpose :

M 12345648933 mat :

value table col lookup k 1 : j k table rows range table j col el value ≡ idx k el j : k k 1 + : 21 line No match if for idx 31 line :

4 M 1 lookup 2321 mat

6 h 1 lookup 1561141 mat

13 h 1 lookup #

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 21 line 41 line :

L 1 - :

H 1 :

N 10 :

U L H N xd :

V U :

x y f 1 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 :

N 0.0003 0.0014 0.0043 0.0097 0.0156 0.0183 0.0156 0.0097 0.0043 0.0014 0.0003 0.0014 0.006 0.0183 0.0408 0.0659 0.0773 0.0659 0.0408 0.0183 0.006 0.0014 0.0043 0.0183 0.0561 0.1249 0.2019 0.2369 0.2019 0.1249 0.0561 0.0183 0.0043 0.0097 0.0408 0.1249 0.278 0.4493 0.5273 0.4493 0.278 0.1249 0.0408 0.0097 0.0156 0.0659 0.2019 0.4493 0.7261 0.8521 0.7261 0.4493 0.2019 0.0659 0.0156 0.0183 0.0773 0.2369 0.5273 0.8521 1 0.8521 0.5273 0.2369 0.0773 0.0183 0.0156 0.0659 0.2019 0.4493 0.7261 0.8521 0.7261 0.4493 0.2019 0.0659 0.0156 0.0097 0.0408 0.1249 0.278 0.4493 0.5273 0.4493 0.278 0.1249 0.0408 0.0097 0.0043 0.0183 0.0561 0.1249 0.2019 0.2369 0.2019 0.1249 0.0561 0.0183 0.0043 0.0014 0.006 0.0183 0.0408 0.0659 0.0773 0.0659 0.0408 0.0183 0.006 0.0014 0.0003 0.0014 0.0043 0.0097 0.0156 0.0183 0.0156 0.0097 0.0043 0.0014 0.0003 1111 mat

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 517522 mat s 100122 mat * 1221 - 22 mat - /

s f maple Stack empty.

s 5 :

s f 1.6 0.7 2.6 1.7 22 mat

Accumulate in Vector/Matrix

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 :

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 :

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

Kind of create fill-in blank

bb 127349251133 mat :

i bb aa i 1 el i : for

It executes the code for every element in the matrix, 6 & 8 & 10 don't exist.

aa transpose 123450709011111 mat

aa i el i 1 aa rows sum 42

bb Unwrap transpose 132245791119 mat

M aa 44 Pack (:

M 1590200037110400044 mat

M M 1 M rows 13 submatrix :

M 159200371140043 mat