How to expand a symbolic matrix expression?
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Lee Jong Hyun
am 3 Aug. 2023
Kommentiert: Dyuman Joshi
am 4 Aug. 2023
I want to expand all terms in a complex symbolic matrix expression by the distributive law of the expression.
tempa1 = symmatrix('A1',[2 2]);
tempb1 = symmatrix('B1',[2 2]);
tempc1 = symmatrix('C1',[2 2]);
tempd1 = symmatrix('D1',[2 2]);
for nn = 2:5
tempa2 = symmatrix(sprintf('A%d',nn),[2 2]);
tempb2 = symmatrix(sprintf('B%d',nn),[2 2]);
tempc2 = symmatrix(sprintf('C%d',nn),[2 2]);
tempd2 = symmatrix(sprintf('D%d',nn),[2 2]);
tempa = tempa1*tempb2+tempc1*tempd2+tempb1*tempa2+tempd1;
tempb = tempa2*tempb1+tempc2*tempd1+tempb2*tempa1+tempd2;
tempc = tempa1*tempb1+tempc1*tempd1+tempb1*tempa1+tempd2;
tempd = tempa2*tempb2+tempc2*tempd2+tempb2*tempa2+tempd1;
tempa1 = tempa;
tempb1 = tempb;
tempc1 = tempc;
tempd1 = tempd;
end
vec_1 = symmatrix('vec_1',[2 1]);
result = tempa*vec_1;
When the variable result is executed, it is output as a complex matrix expression.
The variable result is a 2 by 2 symbolic matrix, and each element is also returned as a symbolic expression.
However, the information I need is not an element expression, but a string of expressions output when the variable result is executed.
When the variable result is executed, looking at the output result, the variable vec_1 is expressed by multiplying the result of tempa outside the bracket.
I want all the brackets to be solved and each term to be multiplied by vec_1.
A bulti-in function called 'expand' is identified as the most similar function to what I want.
However, this function is not supported for symmatrix input.
To use this function, if you run symmatrix2sym on the variable result, it returns all element representations.
Please, let me know that.
Thank you.
3 Kommentare
Paul
am 4 Aug. 2023
Hi Lee Jong Hyun,
I could be wrong, but I don't think you'll be able to easily get the result you're looking for.
But suppose you could, i.e., get an expression for tempa in the form (n = 2)
syms A1 A2 B1 B2 C1 D1 D2 [2 2] matrix
syms vec_1 [2 1] matrix
tempa = A1*B2*vec_1 + B1*A2*vec_1 + C1*D2*vec_1 + D1*vec_1
What whould be the next step in the process? Maybe there's a way to achieve the goal without forming tempa as shown?
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Star Strider
am 3 Aug. 2023
I am not certain what you intend by ‘expand’.
One option could be:
sympref('AbbreviateOutput',false);
that I added, and another the expand function (that does not work here). If you want to see the elements of the matrices, you would need to define their elements, as described in Convert Numeric Matrix to Symbolic Matrix Variable.
sympref('AbbreviateOutput',false);
tempa1 = symmatrix('A1',[2 2]);
tempb1 = symmatrix('B1',[2 2]);
tempc1 = symmatrix('C1',[2 2]);
tempd1 = symmatrix('D1',[2 2]);
for nn = 2:5
tempa2 = symmatrix(sprintf('A%d',nn),[2 2]);
tempb2 = symmatrix(sprintf('B%d',nn),[2 2]);
tempc2 = symmatrix(sprintf('C%d',nn),[2 2]);
tempd2 = symmatrix(sprintf('D%d',nn),[2 2]);
tempa = tempa1*tempb2+tempc1*tempd2+tempb1*tempa2+tempd1;
tempb = tempa2*tempb1+tempc2*tempd1+tempb2*tempa1+tempd2;
tempc = tempa1*tempb1+tempc1*tempd1+tempb1*tempa1+tempd2;
tempd = tempa2*tempb2+tempc2*tempd2+tempb2*tempa2+tempd1;
tempa1 = tempa;
tempb1 = tempb;
tempc1 = tempc;
tempd1 = tempd;
end
vec_1 = symmatrix('vec_1',[2 1]);
result = tempa*vec_1
.
4 Kommentare
Star Strider
am 4 Aug. 2023
I am not certain how to get that result, since the functions I would normally use do not work on symmatrix expressions.
Dyuman Joshi
am 4 Aug. 2023
It might not be possible to get the result OP wants to obtain (as mentioned above) because one can not manipulate the result obtained from the code.
These are the all functions that accept symbolic matrix variables as input, the only functions that manipulates an expression are formula and displayFormula, both of which give the same output.
methods symmatrix
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