Hello.
In Numbers (iWork '08), is there any way to calculate the elements resulting from multiplying a Matrix (square table) to a Vector (single-column table) in another Vector (single-column table)?
I'm currently multiplying term by term, but it's a pain for lots of data. There must be a smarter way to do that.
Numbers '08-OTHER, Mac OS X (10.7.3)
Numbers doesn't support Matrix math, not in either Numbers 08 or Numbers 09.
Jerry
Numbers doesn't support Matrix math, not in either Numbers 08 or Numbers 09.
Jerry
So, is there any better way to accomplish the same operation using functions rather than multiplying term-by-term, cell-by-cell?
there is a function called sumproduct() you can use to assist in this task:
I've already tried, but I can find no practical use of SUMPRODUCT() in my specific problem; only if I copied the contents of the vector between every line of the matrix, and then used SUMPRODUCT() onto the pairs. It's better than nothing, but still hackishy.
So if you have the following two matrices:
V[10] and W[10, 10] then you want to perform operations to make a new matrix X which is 10 x 10 and is:
V[0]*W[0, 0], V[1]*W[0, 1], ... V[9]*W[0, 9]
V[0]*W[1, 0], V[1]*W[1, 1], ... V[9]*W[1, 9]
.
.
.
V[0]*W[9, 0], V[1]*W[9, 1],... V[9]*W[9, 9]
right?
If the answer to my previous question is "Yes", then you can use a method like this:
I am multiplying a 1 dimensional array times a two dimensional array resulting in a two dimensional array.
To make this easier I transpose the 2D array, then multiply each row in table "Vector 1" by the corresponding row in each column of the table "Vector 2". This is stored in the table "Result Transposed". Then I un-transpose and store in the table "Result".
To do this we can start with transposing the table "Vector 2" into the table "Vector 2 Transposed" (the table with the highlighted cell in the image above):
A1=OFFSET(Vector 2 :: $A$1, COLUMN()-1, ROW()-1, 1, 1)
select A1 and fill to the right
select A1 thru J1 and fill down
Now let's put together the table "Result Transposed":
A1=Vector 1 :: $A1*Vector 2 Transposed :: A1
select A1 and fill DOWN
now select A1 through A10 and fill to the right
Now let's un trasnpose the data in table "Result Transposed" and store in the table "Result":
in table "Result":
A1=OFFSET(Result Transposed :: $A$1, COLUMN()-1, ROW()-1, 1, 1)
select A1 and fill to the right
now select A1 thru J1 and fill down
That sure is a better way, but we're not done yet.
You got close; my intention was to multiply what you called "Vector 1" with "Vector 2" (a Matrix, although mathematically speaking you would need to invert the terms order) resulting in another "Vector 3" (which would be a single-column table; each line the sum of all numbers in a line of "Result").
Your method involves creating buffer/auxiliary tables... would there be a way to merge all these operations within a single formula, on the destination cell?
With regards to:
You got close; my intention was to multiply what you called "Vector 1" with "Vector 2" (a Matrix, although mathematically speaking you would need to invert the terms order) resulting in another "Vector 3" (which would be a single-column table; each line the sum of all numbers in a line of "Result").
Please be specific with what you would like similar to the v[0]*W[0, 1]...
The aux tables can be combined but I do not like doing that because:
1) it makes reading what you did more difficult
2) it make debugging more difficult
As I indicated you can hide the aux tables so you won't see them.
MV,
The free LibreOffice will probably do what you need with no sleight of hand and you can copy the results into a Numbers document if Numbers has other features you wish to retain.
Jerry
Ok. Let A[10] be a Vector, and B[10,10] a Matrix. B*A=C, wich is a Vector of type C[10]. So (in [Column, Line] notation) :
C[0]=A[0]*B[0,0]+A[1]*B[1,0]+A[2]*B[2,0] (...) A[9]*B[9,0]
C[1]=A[0]*B[0,1]+A[1]*B[1,1]+A[2]*B[2,1] (...) A[9]*B[9,1]
(...)
C[9]=A[0]*B[0,9]+A[1]*B[1,9]+A[2]*B[2,9] (...) A[9]*B[9,9]
That's exactly the operation I'm trying to accomplish; a classical, mathematically defined, Vector * Matrix operation, wich results into a Vector of size equal to the Matrix's height and can only be made if the Vector's size and the Matrix's width are equal.
Gotta try LibreOffice Spreadsheets later. I didn't knew I could copy data without having to save a .csv file for exchanging values between them. That sure is handy.
As for now, I've (mostly) solved my problem by making a separate "scratch" table on which I can copy all the lines of the matrix, interleaved with the Vector's values, and obtain the results on a separate column nearby. The problem is that I cannot copy the data without Numbers trying to copy the formula too; I just want the values!
Currently I'm retyping the results onto the definite result table.
Everyone, thanks for the help.
you can paste values only by using the menu item "Edit > Paste Values"
So based on your input I think you want something like this:
the only difference is that the last table "Result" is now a single column with the formulas:
A1=SUM(Result Transposed :: A1:J1)
select A1 and fill down
you can make the final solution look like this by:
1) disabling the table name
2) sliding the aux tables under the table "Vector 2"
Exactly what I described some messages ago. The only downside is having to use the transposed table (or transposed Vector (1), if that would eliminate the need for the Matrix transposing). If no matrix operations are supplied with Numbers, then I guess your method is the one who comes the closest.
I should correct an error just found in trying to simplify the result:
The formula for the previous table "Result" should be:
A1=SUM(INDIRECT("Result Transposed :: "&CHAR(CODE("A")+ROW()-1)&"1:"&CHAR(CODE("A")+ROW()-1)&"10"))
select A1 and fill down.
Now there is a way without an aux table:
the table "Result" is now:
A1=SUMPRODUCT(Vector 1 :: $A$1:$A$10, TRANSPOSE(Vector 2 :: A1:J1))
select A1 and fill down (no aux tables)
Advanced Math (Matrix * Vector)
