6f93bd22-0437-47f2-a8ac-462c950ff098 35 3 5 auto

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

Times Table n M i 1 n range j 1 n range M i j el i j * : for for M 21 line :

Explode mirror Matrix M mirror v M M cols col : ct 1 : j M cols ct range N 1 ct el M j col : ct ct 1 + : 21 line for N Unest N v N 1 el : j 2 N cols range v v N j el augment : for v 81 line :

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

5 M 1234524681036912154812162051015202555 mat

5 M Dia 149162551 mat

5 M mirror 5432110864215129632016128425201510555 mat

camping tonight ! size 5 : X 1 size range : Y size M mirror Dia : xy X Y size - augment : 41 line

Y 5898551 mat

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Smath built-in   f(x) menu 123424683691248121644 mat norme 30

4 M tr 30

Smath built-in   f(x) menu 4 M Diag 1000040000900001644 mat

Smath user Diagonal: trace = Euclidean norm

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 :

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, i.e: Euclidean norm

4 M Dia 1491641 mat

4 M tr 30

4 M Dia sum 30

The other Diagonal:from the mirror matrix

Explode mirror Matrix M mirror v M M cols col : ct 1 : j M cols ct range N 1 ct el M j col : ct ct 1 + : 21 line for N Unest N v N 1 el : j 2 N cols range v v N j el augment : for v 81 line :

5 M mirror 5432110864215129632016128425201510555 mat

5 M mirror Dia 5898551 mat

3 M mirror tr 13.27

3 M 123 0.82 246 0.59 369 4.21 0.45 0.23 5.48 5.2 44 mat

5 M mirror Dia sum 35

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 32 :

U L H N xd :

V U :

x y f 1 x 2^y 2^+ (- 0.25 / exp * :

M Min Max Scale Max Min - (M M min - M max M min - 106 -^+ / (* Min + :

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 :

Is this Gaussian spot symmetric ? Answer: YES

N tr 10.026158

N mirror tr 10.026158

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M diag2vec v M rows M cols 12 mat min : out v 1 matrix : n 1 v range out n el M n n el : for out 41 line :

a h k l b m n p c 33 mat diag2vec a b c 31 mat

a h k l b m n p c q r s 43 mat diag2vec a b c 31 mat

a h k q l b m r n p c s 34 mat diag2vec a b c 31 mat

M diag2vec M rows M cols ≠ Matrix must be square error v M rows M cols 12 mat min : out v 1 matrix : n 1 v range out n el M n n el : for out 41 line if 11 line :

a h k l b m n p c 33 mat diag2vec a b c 31 mat

a h k l b m n p c q r s 43 mat diag2vec #

a h k q l b m r n p c s 34 mat diag2vec #

Vectorise Diagonal Mat Dia i 1 Mat rows range Dia i el Mat i i el : for Dia 21 line :

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

2d matrix f(x)

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 21 line 31 line :

Collapse all programs in utilities top WS

M lo hi Scale hi lo - (M M min - M max M min - 106 -^+ / (* lo + :

L 1 - : H 1 : N 32 : 13 mat U L H N xd : V U : 12 mat 21 line

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 :

x y f 1 x 2^y 2^+ (- 0.25 / exp * : N x y f U V Sym : 21 line

N N 0255 Scale :

Symmetry N tr N mirror tr 21 mat 10.026 10.026 21 mat