How to find the determinant of 15 X 15 symbolic matrix?
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I am trying to solve the problem which involves manipulations of symbolic equations to get a 15 X 15 matrix ( Sylvester matrix). each term of matrix is a polynomial in one variable, say x. The determinant of this matrix suppose to give 40 degree polynomial equation in x.
As I tried to find determinant using ' det() ' function, computation exceeds the size of memory (8 GB)and computer hung in between.
Is there any other way to compute a determinant of such a big matrix in symbolic form?or else is there any way to get the polynomial (numerical methods)?
Thanks.
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Risposte (3)
Sergey Kasyanov
il 24 Apr 2018
Hi,
I encountered the similar problem recently and I wrote a simple script for this task. It's designed for parallel computing of Gauss elimination but it will be usefull for you too.
You should use function GaussElminitaion:
ADet=det(GaussElimination(AMatrix));
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Murthy MVVS
il 17 Apr 2021
Modificato: Walter Roberson
il 25 Gen 2022
I have a 13 x 13 matrix given as M. I am using Matlab 2021a
If I use your code as detM = prod(diag(GaussElimination(M,'NULL')))
I am getting error as,
Error: File: GaussElimination.m Line: 55 Column: 13
Unable to classify the variable 'A1' in the body of the parfor-loop. For more information, see Parallel for
Loops in MATLAB, "Solve Variable Classification Issues in parfor-Loops".
And
If I use the matlab 'det' as detM = det(M)
I am getting error as,
detM =
Warning: Unable to display symbolic object because 'symengine' was reset. Repeat commands to regenerate
result.
> In sym/disp (line 44)
In sym/display>displayVariable (line 89)
In sym/display (line 51)
In det_m (line 37)
The matlab script file is,
%%%%%%%%% det_m.m %%%%%%%%%
clear all;
clc;
syms a1 a3 a7 a9 a10 a11;
syms b2 b3 b8 b12 b13;
syms c1 c3 c4 c7 c9 c10 c11;
syms d4 d6 d7 d9 d10 d11;
syms e5 e6 e8 e12 e13;
syms f4 f6 f7 f9 f10 f11;
syms g1 g3 g4 g6 g7 g9 g10 g11 g12;
syms h2 h5 h8 h9 h11 h12 h13;
syms i1 i3 i4 i6 i7 i8 i9 i10 i11 i13;
syms j1 j3 j4 j6 j7 j8 j9 j10 j11 j13;
syms k1 k3 k4 k6 k7 k8 k9 k10 k11 k13;
syms l2 l5 l7 l8 l10 l12 l13;
syms m2 m5 m8 m9 m11 m12 m13;
M = [
[ a1, 0, a3, 0, 0, 0, a7, 0, a9, a10, a11, 0, 0]
[ 0, b2, b3, 0, 0, 0, 0, b8, 0, 0, 0, b12, b13]
[ c1, 0, c3, 0, 0, 0, c7, 0, c9, c10, c11, 0, 0]
[ 0, 0, 0, d4, 0, d6, d7, 0, d9, d10, d11, 0, 0]
[ 0, 0, 0, 0, e5, e6, 0, e8, 0, 0, 0, e12, e13]
[ 0, 0, 0, f4, 0, f6, f7, 0, f9, f10, f11, 0, 0]
[ g1, 0, g3, g4, 0, g6, g7, 0, g9, g10, g11, g12, 0]
[ 0, h2, 0, 0, h5, 0, 0, h8, h9, 0, h11, h12, h13]
[ i1, 0, i3, i4, 0, i6, i7, i8, i9, i10, i11, 0, i13]
[ j1, 0, j3, j4, 0, j6, j7, j8, j9, j10, j11, 0, j13]
[ k1, 0, k3, k4, 0, k6, k7, k8, k9, k10, k11, 0, k13]
[ 0, l2, 0, 0, l5, 0, l7, l8, 0, l10, 0, l12, l13]
[ 0, m2, 0, 0, m5, 0, 0, m8, m9, 0, m11, m12, m13]
]
detM = prod(diag(GaussElimination(M,'NULL')))
% detM = det(M)
%%%%%%%%% End det_m.m %%%%%%%%%
Walter Roberson
il 17 Apr 2021
You need about 8 terabytes of memory (or more) to store the determinant of that matrix.
laith saadi
il 25 Gen 2022
Modificato: Walter Roberson
il 25 Gen 2022
clear all;
clc;
syms a1 a3 a7 a9 a10 a11;
syms b2 b3 b8 b12 b13;
syms c1 c3 c4 c7 c9 c10 c11;
syms d4 d6 d7 d9 d10 d11;
syms e5 e6 e8 e12 e13;
syms f4 f6 f7 f9 f10 f11;
syms g1 g3 g4 g6 g7 g9 g10 g11 g12;
syms h2 h5 h8 h9 h11 h12 h13;
syms i1 i3 i4 i6 i7 i8 i9 i10 i11 i13;
syms j1 j3 j4 j6 j7 j8 j9 j10 j11 j13;
syms k1 k3 k4 k6 k7 k8 k9 k10 k11 k13;
syms l2 l5 l7 l8 l10 l12 l13;
syms m2 m5 m8 m9 m11 m12 m13;
M = [
[ a1, 0, a3, 0, 0, 0, a7, 0, a9, a10, a11, 0, 0]
[ 0, b2, b3, 0, 0, 0, 0, b8, 0, 0, 0, b12, b13]
[ c1, 0, c3, 0, 0, 0, c7, 0, c9, c10, c11, 0, 0]
[ 0, 0, 0, d4, 0, d6, d7, 0, d9, d10, d11, 0, 0]
[ 0, 0, 0, 0, e5, e6, 0, e8, 0, 0, 0, e12, e13]
[ 0, 0, 0, f4, 0, f6, f7, 0, f9, f10, f11, 0, 0]
[ g1, 0, g3, g4, 0, g6, g7, 0, g9, g10, g11, g12, 0]
[ 0, h2, 0, 0, h5, 0, 0, h8, h9, 0, h11, h12, h13]
[ i1, 0, i3, i4, 0, i6, i7, i8, i9, i10, i11, 0, i13]
[ j1, 0, j3, j4, 0, j6, j7, j8, j9, j10, j11, 0, j13]
[ k1, 0, k3, k4, 0, k6, k7, k8, k9, k10, k11, 0, k13]
[ 0, l2, 0, 0, l5, 0, l7, l8, 0, l10, 0, l12, l13]
[ 0, m2, 0, 0, m5, 0, 0, m8, m9, 0, m11, m12, m13]
]
detM = prod(diag(GaussElimination(M,'NULL')))
% detM = det(M)
1 Commento
Murthy MVVS
il 26 Gen 2022
Use that function provided by Sergey Kasyanov, which can be downloaded from the given link below.
https://in.mathworks.com/matlabcentral/fileexchange/90661-gausselimination
laith saadi
il 1 Feb 2022
clear all;
clc;
syms a1 a3 a7 a9 a10 a11;
syms b2 b3 b8 b12 b13;
syms c1 c3 c4 c7 c9 c10 c11;
syms d4 d6 d7 d9 d10 d11;
syms e5 e6 e8 e12 e13;
syms f4 f6 f7 f9 f10 f11;
syms g1 g3 g4 g6 g7 g9 g10 g11 g12;
syms h2 h5 h8 h9 h11 h12 h13;
syms i1 i3 i4 i6 i7 i8 i9 i10 i11 i13;
syms j1 j3 j4 j6 j7 j8 j9 j10 j11 j13;
syms k1 k3 k4 k6 k7 k8 k9 k10 k11 k13;
syms l2 l5 l7 l8 l10 l12 l13;
syms m2 m5 m8 m9 m11 m12 m13;
M = [
[ a1, 0, a3, 0, 0, 0, a7, 0, a9, a10, a11, 0, 0]
[ 0, b2, b3, 0, 0, 0, 0, b8, 0, 0, 0, b12, b13]
[ c1, 0, c3, 0, 0, 0, c7, 0, c9, c10, c11, 0, 0]
[ 0, 0, 0, d4, 0, d6, d7, 0, d9, d10, d11, 0, 0]
[ 0, 0, 0, 0, e5, e6, 0, e8, 0, 0, 0, e12, e13]
[ 0, 0, 0, f4, 0, f6, f7, 0, f9, f10, f11, 0, 0]
[ g1, 0, g3, g4, 0, g6, g7, 0, g9, g10, g11, g12, 0]
[ 0, h2, 0, 0, h5, 0, 0, h8, h9, 0, h11, h12, h13]
[ i1, 0, i3, i4, 0, i6, i7, i8, i9, i10, i11, 0, i13]
[ j1, 0, j3, j4, 0, j6, j7, j8, j9, j10, j11, 0, j13]
[ k1, 0, k3, k4, 0, k6, k7, k8, k9, k10, k11, 0, k13]
[ 0, l2, 0, 0, l5, 0, l7, l8, 0, l10, 0, l12, l13]
[ 0, m2, 0, 0, m5, 0, 0, m8, m9, 0, m11, m12, m13]
]
detM = prod(diag(GaussElimination(M,'NULL')))
% detM = det(M)
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