- bicg(A, b, x0 = None, tol = 1.0000000000000001e-05, maxiter = None, xtype = None, callback = None)
Use BIConjugate Gradient iteration to solve A x = b
Inputs:
A -- An array or an object with matvec(x) and rmatvec(x) methods
to represent A * x and A^H * x respectively. May also have
psolve(b) and rpsolve(b) methods for representing solutions
to the preconditioning equations M * x = b and
M^H * x = b respectively.
b -- An n-length vector
Outputs:
x -- The converged solution
info -- output result
0 : successful exit
>0 : convergence to tolerance not achieved, number of iterations
<0 : illegal input or breakdown
Optional Inputs:
x0 -- (0) default starting guess.
tol -- (1e-5) relative tolerance to achieve
maxiter -- (10*n) maximum number of iterations
xtype -- The type of the result. If None, then it will be
determined from A.dtype.char and b. If A does not have a
typecode method then it will compute A.matvec(x0) to get a
typecode. To save the extra computation when A does not
have a typecode attribute use xtype=0 for the same type as
b or use xtype='f','d','F',or 'D'
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
- bicgstab(A, b, x0 = None, tol = 1.0000000000000001e-05, maxiter = None, xtype = None, callback = None)
Use BIConjugate Gradient STABilized iteration to solve A x = b
Inputs:
A -- An array or an object with a matvec(x) method
to represent A * x. May also have a psolve(b) methods for
representing solution to the preconditioning equation
M * x = b.
b -- An n-length vector
Outputs:
x -- The converged solution
info -- output result
0 : successful exit
>0 : convergence to tolerance not achieved, number of iterations
<0 : illegal input or breakdown
Optional Inputs:
x0 -- (0) default starting guess.
tol -- (1e-5) relative tolerance to achieve
maxiter -- (10*n) maximum number of iterations
xtype -- The type of the result. If None, then it will be
determined from A.dtype.char and b. If A does not have a
typecode method then it will compute A.matvec(x0) to get a
typecode. To save the extra computation when A does not
have a typecode attribute use xtype=0 for the same type as
b or use xtype='f','d','F',or 'D'
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
- cg(A, b, x0 = None, tol = 1.0000000000000001e-05, maxiter = None, xtype = None, callback = None)
Use Conjugate Gradient iteration to solve A x = b (A^H = A)
Inputs:
A -- An array or an object with a matvec(x) method
to represent A * x. May also have a psolve(b) methods for
representing solution to the preconditioning equation
M * x = b.
b -- An n-length vector
Outputs:
x -- The converged solution
info -- output result
0 : successful exit
>0 : convergence to tolerance not achieved, number of iterations
<0 : illegal input or breakdown
Optional Inputs:
x0 -- (0) default starting guess.
tol -- (1e-5) relative tolerance to achieve
maxiter -- (10*n) maximum number of iterations
xtype -- The type of the result. If None, then it will be
determined from A.dtype.char and b. If A does not have a
typecode method then it will compute A.matvec(x0) to get a
typecode. To save the extra computation when A does not
have a typecode attribute use xtype=0 for the same type as
b or use xtype='f','d','F',or 'D'
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
- cgs(A, b, x0 = None, tol = 1.0000000000000001e-05, maxiter = None, xtype = None, callback = None)
Use Conjugate Gradient Squared iteration to solve A x = b
Inputs:
A -- An array or an object with a matvec(x) method
to represent A * x. May also have a psolve(b) methods for
representing solution to the preconditioning equation
M * x = b.
b -- An n-length vector
Outputs:
x -- The converged solution
info -- output result
0 : successful exit
>0 : convergence to tolerance not achieved, number of iterations
<0 : illegal input or breakdown
Optional Inputs:
x0 -- (0) default starting guess.
tol -- (1e-5) relative tolerance to achieve
maxiter -- (10*n) maximum number of iterations
xtype -- The type of the result. If None, then it will be
determined from A.dtype.char and b. If A does not have a
typecode method then it will compute A.matvec(x0) to get a
typecode. To save the extra computation when A does not
have a typecode attribute use xtype=0 for the same type as
b or use xtype='f','d','F',or 'D'
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
- gmres(A, b, x0 = None, tol = 1.0000000000000001e-05, restrt = None, maxiter = None, xtype = None, callback = None)
Use Generalized Minimal RESidual iteration to solve A x = b
Inputs:
A -- An array or an object with a matvec(x) method
to represent A * x. May also have a psolve(b) methods for
representing solution to the preconditioning equation
M * x = b.
b -- An n-length vector
Outputs:
x -- The converged solution
info -- output result
0 : successful exit
>0 : convergence to tolerance not achieved, number of iterations
<0 : illegal input or breakdown
Optional Inputs:
x0 -- (0) default starting guess.
tol -- (1e-5) relative tolerance to achieve
restrt -- (n) When to restart (change this to get faster performance -- but
may not converge).
maxiter -- (10*n) maximum number of iterations
xtype -- The type of the result. If None, then it will be
determined from A.dtype.char and b. If A does not have a
typecode method then it will compute A.matvec(x0) to get a
typecode. To save the extra computation when A does not
have a typecode attribute use xtype=0 for the same type as
b or use xtype='f','d','F',or 'D'
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
- qmr(A, b, x0 = None, tol = 1.0000000000000001e-05, maxiter = None, xtype = None, callback = None)
Use Quasi-Minimal Residual iteration to solve A x = b
Inputs:
A -- An array or an object with matvec(x) and rmatvec(x) methods
to represent A * x and A^H * x respectively. May also have
psolve(b,<which>) and rpsolve(b,<which>) methods for
representing solutions to the preconditioning equations
M * x = b and M^H * x = b respectively. The <which> argument
may be given to specify 'left' or 'right' preconditioning.
b -- An n-length vector
Outputs:
x -- The converged solution
info -- output result
0 : successful exit
>0 : convergence to tolerance not achieved, number of iterations
<0 : illegal input or breakdown
Optional Inputs:
x0 -- (0) default starting guess.
tol -- (1e-5) relative tolerance to achieve
maxiter -- (10*n) maximum number of iterations
xtype -- The type of the result. If None, then it will be
determined from A.dtype.char and b. If A does not have a
typecode method then it will compute A.matvec(x0) to get a
typecode. To save the extra computation when A does not
have a typecode attribute use xtype=0 for the same type as
b or use xtype='f','d','F',or 'D'
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17