プリコンディショナ付きのQuasi Minimal Residual法
[x, flag, err, iter, res] = qmr(A, b, x0, M1, M2, maxi, tol) [x, flag, err, iter, res] = qmr(A,Ap,b,x0,M1,M1p,M2,M2p,maxi,tol) // deprecated
A*x
, it must
have the following header :
function y = A ( x )
A*x
or
A'*x
depending on a option t, it must
have the following header :
function y = A(x, t)
t = "notransp"
: the function returns
A*x
.t = "transp"
: the function returns
A'*x
.A'*x
. It must have the following header :
function y = Ap(x)
M1*x
を返す関数
(前者のデフォルト値: eye(n,n)).
If M1
is a function, it returns either,
M1*x
, orM1*x
or M1'*x
, depending on
t
.M1
が関数の場合のみ指定する
必要があります. この場合, M1p
は
M1'*x
を返す関数です.
M2*x
を
返す関数 (前者のデフォルト値: eye(n,n))
If M2
is a function, it returns either
M2*x
, orM2*x
or M2'*x
depending on
an option t
.M2
が関数の場合のみ指定する
必要があります. この場合,
M2p
はM2'*x
を返す関数です.
flag
=0:
gmr
は
maxi
回の反復の間に
許容誤差内に収束しましたflag
=1:
指定したmaxi
回の反復の間に
収束しませんでした-7 < flag < 0
: A breakdown occurred because
one of the scalar quantities calculated was equal to zero.プリコンディショナ付きのQuasi Minimal Residual法により,
線形システムAx=b
を解きます.
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 b = ones(10,1); [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 b = ones(10,1); [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:
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); 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
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); 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:
Version | Description |
5.4.0 | qmr(A, Ap) のコールは廃止されました. qmr(A) を代わりに使用してください. |