Mathematica Asked by J Yeh on February 1, 2021
Let’s say I have an array
a={{1,2,3},
{4,5,6},
{7,8,9}}
I want to have all elements along the diagonal multiplied by 2.
{{2,2,3},
{4,10,6},
{7,8,18}}
What is the best way to do this? I tried
ReplacePart[a,{i_,i_} -> 2 a[[i,i]]]
and
a[[i_, i_]] = 2 a[[i, i]]
Which both gives the error
Part::pkspec1: The expression i cannot be used as a part specification
I suppose I can do
a*SparseArray[{i_,i_} -> 2,{3,3},1]
but I feel like there should be a simpler way to do this.
Using RuleDelayed
instead of Rule
in ReplacePart
:
ReplacePart[a, {i_, i_} :> 2 a[[i, i]]]
or, using Part
assignment as in:
(a[[#, #]] = 2 a[[#, #]]) & /@ Range[3]
Table[a[[i, i]] == 2 a[[i, i]], {i, 1, 3}]
or, using MapAt
:
MapAt[2 # &, a, Table[{j, j}, {j, 3}]]
or, using MapIndexed
:
MapIndexed[If[SameQ @@ #2, 2 #, #] &, a, {2}]
(* or MapIndexed[If[Equal @@ #2, 2 #, #] &, a, {2}] *)
all give
(* {{2, 2, 3}, {4, 10, 6}, {7, 8, 18}} *)
By the way, my favorite is your a*SparseArray[{i_,i_} -> 2, {3,3}, 1]
.
Answered by kglr on February 1, 2021
a = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}
f = # + #*IdentityMatrix[Dimensions@#] &;
f@a
(* {{2, 2, 3}, {4, 10, 6}, {7, 8, 18}} *)
Answered by ciao on February 1, 2021
Since all the good answers are taken, here is one for fun
m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
In this case, since the multiplier happened to be 2, you can just do
LowerTriangularize[m] + UpperTriangularize[m]
and the diagonal will be doubled automatically. But this is only for this example only. In the general case
n=2; (*or any other value*)
DiagonalMatrix[n*Diagonal[m]] + LowerTriangularize[m, -1] + UpperTriangularize[m, 1]
Answered by Nasser on February 1, 2021
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