Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
qmr
quasi minimal resiqual method with preconditioning
Calling Sequence
[x,flag,err,iter,res] = qmr(A,Ap,b,x0,M1,M1p,M2,M2p,maxi,tol) [x,flag,err,iter,res] = qmr(A,b,x0,M1,M2,maxi,tol)
Arguments
- A
matrix of size n-by-n or function.
matrix.If A is a matrix, it can be dense or sparsefunction.If A is a function which returnsA*x, it must have the following header :function y=A(x)
If A is a function which returns
A*xorA'*xdepending t. Ift = "notransp", the function returnsA*x. Ift = "transp", the function returnsA'*x. It must have the following header :function y=A(x, t)
- Ap
function returning
A'*x. It must have the followinf header :function y=Ap(x)
- b
right hand side vector
- x0
initial guess vector (default: zeros(n,1))
- M1
left preconditioner : matrix or function (In the first case, default: eye(n,n)). If
M1is a function, she returns either,only
M1*xM1*xorM1'*xdependingt.
or
- M1p
must only be provided when
M1is a function returningM1*x. In this caseM1pis the function which returnsM1'*x.- M2
right preconditioner : matrix or function (In the first case, default: eye(n,n)). If
M2is a function, she returns eitheronly
M2*xM2*xorM2'*xdependingt.
or
- M2p
must only be provided when
M2is a function returningM2*x. In this caseM2pis the function which returnsM2'*x- maxi
maximum number of iterations (default: n)
- tol
error tolerance (default: 1000*%eps)
- x
solution vector
- flag
- 0 =
gmresconverged to the desired tolerance withinmaxiiterations- 1 =
no convergence given
maxi
- res
residual vector
- err
final residual norm
- iter
number of iterations performed
Description
Solves the linear system Ax=b using the Quasi Minimal Residual Method with preconditioning.
Examples
// If A is a matrix A=[ 94 0 0 0 0 28 0 0 32 0 0 59 13 5 0 0 0 10 0 0 0 13 72 34 2 0 0 0 0 65 0 5 34 114 0 0 0 0 0 55 0 0 2 0 70 0 28 32 12 0 28 0 0 0 0 87 20 0 33 0 0 0 0 0 28 20 71 39 0 0 0 10 0 0 32 0 39 46 8 0 32 0 0 0 12 33 0 8 82 11 0 0 65 55 0 0 0 0 11 100]; b=ones(10,1); [x,flag,err,iter,res] = qmr(A, b) [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) // If A is a function function y=Atimesx(x, t) A=[ 94 0 0 0 0 28 0 0 32 0 0 59 13 5 0 0 0 10 0 0 0 13 72 34 2 0 0 0 0 65 0 5 34 114 0 0 0 0 0 55 0 0 2 0 70 0 28 32 12 0 28 0 0 0 0 87 20 0 33 0 0 0 0 0 28 20 71 39 0 0 0 10 0 0 32 0 39 46 8 0 32 0 0 0 12 33 0 8 82 11 0 0 65 55 0 0 0 0 11 100]; if (t == 'notransp') then y = A*x; elseif (t == 'transp') then y = A'*x; end endfunction [x,flag,err,iter,res] = qmr(Atimesx, b) [x,flag,err,iter,res] = qmr(Atimesx, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) // OR function y=funA(x) A = [ 94 0 0 0 0 28 0 0 32 0 0 59 13 5 0 0 0 10 0 0 0 13 72 34 2 0 0 0 0 65 0 5 34 114 0 0 0 0 0 55 0 0 2 0 70 0 28 32 12 0 28 0 0 0 0 87 20 0 33 0 0 0 0 0 28 20 71 39 0 0 0 10 0 0 32 0 39 46 8 0 32 0 0 0 12 33 0 8 82 11 0 0 65 55 0 0 0 0 11 100]; y = A*x endfunction function y=funAp(x) A = [ 94 0 0 0 0 28 0 0 32 0 0 59 13 5 0 0 0 10 0 0 0 13 72 34 2 0 0 0 0 65 0 5 34 114 0 0 0 0 0 55 0 0 2 0 70 0 28 32 12 0 28 0 0 0 0 87 20 0 33 0 0 0 0 0 28 20 71 39 0 0 0 10 0 0 32 0 39 46 8 0 32 0 0 0 12 33 0 8 82 11 0 0 65 55 0 0 0 0 11 100]; y = A'*x endfunction [x,flag,err,iter,res] = qmr(funA, funAp, b) [x,flag,err,iter,res] = qmr(funA, funAp, b, zeros(10,1), eye(10,10), eye(10,10), 10, 1d-12) // If A is a matrix, M1 and M2 are functions function y=M1timesx(x, t) M1 = eye(10,10); if(t=="notransp") then y = M1*x; elseif (t=="transp") then y = M1'*x; end endfunction function y=M2timesx(x, t) M2 = eye(10,10); if(t=="notransp") then y = M2*x; elseif (t=="transp") then y = M2'*x; end endfunction [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), M1timesx, M2timesx, 10, 1d-12) // OR function y=funM1(x) M1 = eye(10,10); y = M1*x; endfunction function y=funM1p(x) M1 = eye(10,10); y = M1'*x; endfunction function y=funM2(x) M2 = eye(10,10); y = M2*x; endfunction function y=funM2p(x) M2 = eye(10,10); y = M2'*x; endfunction [x,flag,err,iter,res] = qmr(A, b, zeros(10,1), funM1, funM1p, funM2, funM2p, 10, 1d-12) // If A, M1, M2 are functions [x,flag,err,iter,res] = qmr(funA, funAp, b, zeros(10,1), funM1, funM1p, funM2, funM2p, 10, 1d-12) [x,flag,err,iter,res] = qmr(Atimesx, b, zeros(10,1), M1timesx, M2timesx, 10, 1d-12)
History
| Version | Description |
| 5.4.0 | Calling qmr(A, Ap) is deprecated. qmr(A) should be used instead. The following function is an example :
function y=A(x, t) Amat = eye(2,2); if ( t== "notransp") then y = Amat*x; elseif (t == "transp") then y = Amat'*x; end endfunction |
| Report an issue | ||
| << pcg | Linear Equations (Iterative Solvers) | chfact >> |