# how to use eig with the nobalance option as in matlab?

• Last Update :
• Techknowledgy :

[___] = eig(A,balanceOption), where balanceOption is 'nobalance', disables the preliminary balancing step in the algorithm. The default for balanceOption is 'balance', which enables balancing. The eig function can return any of the output arguments in previous syntaxes.,Balance option, specified as: 'balance', which enables a preliminary balancing step, or 'nobalance' which disables it. In most cases, the balancing step improves the conditioning of A to produce more accurate results. However, there are cases in which balancing produces incorrect results. Specify 'nobalance' when A contains values whose scale differs dramatically. For example, if A contains nonzero integers, as well as very small (near zero) values, then the balancing step might scale the small values to make them as significant as the integers and produce inaccurate results.,The 'balance' and 'nobalance' options for the standard eigenvalue problem.,If you specify the LAPACK library callback class, then the code generator supports these options: The 'balance' and 'nobalance' options for the standard eigenvalue problem.The computation of left eigenvectors.

`A = gallery('lehmer', 4)`
```A = 4× 4

1.0000 0.5000 0.3333 0.2500
0.5000 1.0000 0.6667 0.5000
0.3333 0.6667 1.0000 0.7500
0.2500 0.5000 0.7500 1.0000```
`e = eig(A)`
```e = 4× 1

0.2078
0.4078
0.8482
2.5362```
`D = eig(A, 'matrix')`
```D = 4× 4

0.2078 0 0 0
0 0.4078 0 0
0 0 0.8482 0
0 0 0 2.5362```

Suggestion : 2

In order to compute the eigenvalues without the balance option., Use [W,D] = eig (A.'); W = conj (W) to compute the left eigenvectors. [V,D] = eig (A,'nobalance') finds eigenvalues and eigenvectors without a preliminary balancing step. , 3 days ago Use the nobalance option in this event. See the balance function for more details. [V,D] = eig(A,B) ... In MATLAB, the function eig solves for the eigenvalues , and optionally the eigenvectors . The generalized eigenvalue problem is to determine the nontrivial solutions of … ,In MATLAB I can issue the command:

`[X, L] = eig(A, 'nobalance');`
`[X, L] = eig(A, 'nobalance');`
```from oct2py
import octave...[X, L] = octave.eig(A)```
```from oct2py
import octave...A = octave.balance(A)[X, L] = octave.eig(A)```

Suggestion : 3

qz          QZ factorization for generalized eigenvalues ,condeig     Condition number with respect to eigenvalues , Eigenvalues and eigenvectors

```d = eig(A)[V, D] = eig(A)[V, D] = eig(A, 'nobalance')
d = eig(A, B)[V, D] = eig(A, B)```
```[VB, DB] = eig(B)
B * VB - VB * DB[VN, DN] = eig(B, 'nobalance')
B * VN - VN * DN```
`Solution will not converge.`

Suggestion : 4

lambda = eig(A,balanceOption) specifies a balancing option as one of two strings: 'balance', which enables a preliminary balancing step, or 'nobalance' which disables it. ,lambda = eig(A,B) returns a vector containing the generalized eigenvalues of the pair, (A,B), that satisfy the equation, ,lambda = eig(A) returns a vector containing the eigenvalues, with multiplicity, that satisfy the equation,,[V,D] = eig(___) returns two optional outputs for any of the previous syntaxes. V is a matrix whose columns are eigenvectors. D is a diagonal matrix containing the eigenvalues along the main diagonal. The form and scaling of V depends on the combination of input arguments:

Use the gallery function to create symmetric positive definite matrix.

`A = gallery('lehmer', 4)`
`A = gallery('lehmer',4)`
```A =

1.0000 0.5000 0.3333 0.2500
0.5000 1.0000 0.6667 0.5000
0.3333 0.6667 1.0000 0.7500
0.2500 0.5000 0.7500 1.0000```

Calculate the eigenvalues of A.

`lambda = eig(A)`

Use the gallery function to create a circulant matrix.

`A = gallery('circul', 3)`
`A = gallery('circul',3)`
```A =

1 2 3
3 1 2
2 3 1```

Calculate the eigenvalues and eigenvectors of A.

`[V, D] = eig(A)`

Verify that matrix V diagonalizes A, since the eigenvalues are distinct and the eigenvectors are independent.

`V\ A * V`
`V\A*V`
```ans =

6.0000 + 0.0000 i 0.0000 - 0.0000 i - 0.0000 + 0.0000 i -
0.0000 - 0.0000 i - 1.5000 + 0.8660 i - 0.0000 - 0.0000 i -
0.0000 + 0.0000 i - 0.0000 + 0.0000 i - 1.5000 - 0.8660 i```
1._
```A = [3.0 - 2.0 - 0.9 2 * eps; -
2.0 4.0 1.0 - eps; -
eps / 4 eps / 2 - 1.0 0; -
0.5 - 0.5 0.1 1.0
];```

Calculate the eigenvalues and eigenvectors using the default (balancing) behavior.

`[VB, DB] = eig(A)`
`[VB,DB] = eig(A)`
```VB =

0.6153 - 0.4176 - 0.0000 - 0.1437 -
0.7881 - 0.3261 - 0.0000 0.1264 -
0.0000 - 0.0000 - 0.0000 - 0.9196
0.0189 0.8481 1.0000 0.3432

DB =

5.5616 0 0 0
0 1.4384 0 0
0 0 1.0000 0
0 0 0 - 1.0000```
`A*VB - VB*DB`
```ans =

0.0000 0.0000 - 0.0000 0.0000
0 - 0.0000 0.0000 - 0.0000
0.0000 - 0.0000 0.0000 0.0000
0 0.0000 0.0000 0.6031```

Now, try calculating the eigenvalues and eigenvectors without the balancing step.

`[VN, DN] = eig(A, 'nobalance')`
1._
` A = [1 7 3;2 9 12;5 22 7];`

Pass the transpose of A to the eig function.

`[VL, D] = eig(A ')`
`[VL,D] = eig(A')`
```VL =

-0.1791 - 0.9587 - 0.1881 -
0.8127 0.0649 - 0.7477 -
0.5545 0.2768 0.6368

D =

25.5548 0 0
0 - 0.5789 0
0 0 - 7.9759```

Verify the results satisfy VL*A = D*VL.

`VL * A - D * VL`
`VL*A - D*VL`
```ans =

1.0e-13 *

0.1243 0.2132 0.0178 -
0.0167 - 0.0644 - 0.0339 -
0.0289 - 0.0444 0.0089```
1._
`A = [3 1 0;0 3 1;0 0 3];`

Calculate the eigenvalues and eigenvectors of A.

`[V, D] = eig(A)`
`[V,D] = eig(A)`
```V =

1.0000 - 1.0000 1.0000
0 0.0000 - 0.0000
0 0 0.0000

D =

3 0 0
0 3 0
0 0 3```
`A*V - V*D`
```ans =

1.0e-15 *

0 0.8882 - 0.8882
0 0 0.0000
0 0 0```
1._
```A = [1 / sqrt(2) 0;0 1];
B = [0 1; - 1 / sqrt(2) 0];
[V, D] = eig(A, B)```
```A = [1/sqrt(2) 0; 0 1];
B = [0 1; -1/sqrt(2) 0];
[V,D]=eig(A,B)```
```V =

1.0000 + 0.0000 i 1.0000 + 0.0000 i
0.0000 - 0.7071 i 0.0000 + 0.7071 i

D =

0.0000 + 1.0000 i 0.0000 + 0.0000 i
0.0000 + 0.0000 i 0.0000 - 1.0000 i```

Verify that the results satisfy A*V = B*V*D.

`A * V - B * V * D`

Suggestion : 5
`eig`
```spec;
bdiag```
```d = eig(A, 'balance')[V, D] = eig(A, 'balance')[V, D] = eig(A, 'balance')
d = eig(A, B)
d = eig(A, B)
d = eig(A, B)[V, D] = eig(A, B)```
```d = spec(A)[D, V] = bdiag(A)[V, D] = spec(A)[al, be] = spec(A, B);
d = al. / be;
d = spec(A, B)
d = spec(inv(B) * A)[al, be, V] = spec(A, B);
D = diag(al. / be);```