Solve linear equation in matrix form with least square method

I have linear equation Ax=b, the size of every matrix are : matrix A is 1009*1008, vector b is 1009*1, and vector x is 1008*1.

If I use lsqr command which is lsqr(A,b), this come out

"Error using iterchk (line 38)

Argument must be a floating point matrix or a function handle.

Error in lsqr (line 93)

[atype,afun,afcnstr] = iterchk(A);".

If I try simple matrix, it can calculate easily.

If I use (A.'*A)\(A.'*b), i can get the result, but why this code lsqr(A,b) cannot

I want to know what is wrong and how to solve it.

Actually i have 1009 linear equation and 1008 variable, so i use this method, or is there any method to use to solve this problem?

Answer 1

[Matt J]

If I use (A.'*A)\(A.'*b), i can get the result

An even easier and more accurate way to get it is,

x=A\b

and that is the method you should be using for matrix data of this size. As to why you get the error, perhaps your A matrix is not type double, but some other type? E.g.,

A=randi(3,3,'int8'); 
b=A(:,1);

lsqr(double(A),double(b))

lsqr converged at iteration 3 to a solution with relative residual 2.9e-13.

ans = 3×1

1.0000 -0.0000 -0.0000

lsqr(A,b)

Error using iterchk
Argument must be a floating point matrix or a function handle.

Error in lsqr (line 93)
[atype,afun] = iterchk(A);

[DoinK]

Matrix A item is a very small decimal, so i round them like this before i use any method to find x

A=round(A,10)

I just search how to find the type of A

isa(A,'double')

turns out

logical

0

that means A is not double.

Does round command effect A?

Long before i use round command, i already use vpa to cut off some decimal.

[Matt J]

that means A is not double.

And that means your problem has been identified and solved. Please Accept-click the answer if you agree.

Does round command effect A?

round() can affect the result because it changes the input data. However, it does not cause an error, as you can see yourself from a simple test,

A=rand(3); b=A(:,1);

lsqr(round(A,10),round(b,10))

lsqr converged at iteration 3 to a solution with relative residual 2.8e-12.

ans = 3×1

1.0000 0.0000 0.0000

[Steven Lord]

What do the following commands show before and after you call round on A?

whos A
which -all round

[DoinK]

I dont know what is wrong, but if I use

A\b

the result is

"Warning: Solution does not exist because the system is inconsistent.

> In symengine

In sym/privBinaryOp (line 1050)

In \ (line 399) "

@Steven Lord

it shows

whos A

which -all round

Name Size Bytes Class Attributes

A 1009x1008 8 sym

[Walter Roberson]

lsqr is not defined on symbolic variables.

What shows up for

rank(A)

Is there a particular reason you are using a symbolic matrix? Does your matrix contain symbolic expressions such as 3*x+5*y as terms? Or do you need precision greater than is available in double precision? Or are you expecting double precision values there but you calculated them by symbolic means, such as if you add a calculation with int() and subs() to get what you expected to be numeric values?

[DoinK]

First I have row vector 1*1008, which is all symbol (q1 q2 ...) and matrix F (1008*1008). Then i need to multiply them, i got 1008 linear equation that all equals to zero. After that i have 1 more equation add to them so there are 1009 equation with 1008 variable

there the symbol came from

After that, i use equationtoMatrix to get matrix A and b. And then need to find 1008 value of x with Ax=b. My steps are wrong?

@Walter Roberson

rank(A) is 1008 Sir.

[Matt J]

It doesn't really make sense to be using symbolic math when you have 1000's of variables. However, you can try converting your matrices to doubles,

A=double(A);
b=double(b);

assuming the coefficients of A are all literal numbers.

[Walter Roberson]

I agree, double() the results of equationToMatrix() .

... or simply build it all up numerically in the first place.

[DoinK]

May i know is there any method not to use row vector 1*1008, which is all symbol (q1 q2 ...)?

Like using command that have row vector and can be multiply with matrix.

[Matt J]

The least squares solvers like A\b and lsqrt work with numbers, not symbolic variables. You should follow the advice that has been given to you. Plug numbers into the symbols and convert to double.

[Walter Roberson]

The least squares solvers like A\b and lsqrt work with numbers, not symbolic variables.

syms A [3 3]
syms b [3 1]
A\b

ans = 

However, with a system of rank 1008, unless it is pretty much a diagonal matrix, the time required to solve might be enormous.

[DoinK]

Finally I understood all and was able to solve my matrix.

Thank you so much Sir @Matt J @Steven Lord @Walter Roberson