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| subroutine | solvers_oct_m::zsym_conjugate_gradients (np, x, b, op, dotp, iter, residue, threshold) |
| | The two following subroutines, sym_conjugate_gradients, and bi_conjugate_gradients, must be called under a common interface: conjugate_gradients. It provides an approximate solution to the linear system problem Ax = b. Solving a symmetric linear system, which is either real or complex symmetric or Hermitian the best choice is sym_conjugate_gradients (does not need \( A^\dagger \)) Solving a real unsymmetric or a complex non-Hermitian system bi_conjugate_gradients has to be chosen (where one does need \( A^\dagger \)). More...
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| subroutine | solvers_oct_m::zbi_conjugate_gradients (np, x, b, op, opt, dotp, iter, residue, threshold) |
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| subroutine, public | solvers_oct_m::zqmr_sym_gen_dotu (np, x, b, op, dotu, nrm2, prec, iter, residue, threshold, showprogress, converged, use_initial_guess) |
| | for complex symmetric matrices W Chen and B Poirier, J Comput Phys 219, 198-209 (2006) More...
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| subroutine, public | solvers_oct_m::zqmr_gen_dotu (np, x, b, op, opt, dotu, nrm2, prec, prect, iter, residue, threshold, showprogress, converged) |
| | for general complex matrices taken from 'An Implementation of the QMR Method based on Coupled Two-Term Recurrences' by R. W. Freund and N. M. Nachtigal (page 25) http: More...
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| complex(real64) function, dimension(size(b, 1), size(b, 2)), public | solvers_oct_m::zidrs (b, s, preconditioner, matrixvector, ddotprod, zdotprod, tolerance, maximum_iterations, variant, flag, relres, iterations, x0, U0, omega, resvec, H) |
| | This is the "Induced Dimension Reduction", IDR(s) (for s=4). IDR(s) is a robust and efficient short recurrence Krylov subspace method for solving large nonsymmetric systems of linear equations. It is described in [Peter Sonneveld and Martin B. van Gijzen, SIAM J. Sci. Comput. 31, 1035 (2008)]. More...
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| real(real64) function | dtrace_dot (v, w) |
| | Trace inner product of complex matrices. More...
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| complex(real64) function | ztrace_dot (v, w) |
| | Trace inner product of complex matrices. More...
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| complex(real64) function, dimension(s) | zp_dot (P, R0, w, s) |
| | P inner product of complex matrices. More...
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| real(real64) function | dfrob_norm (v) |
| | Frobenius norm of complex matrix. More...
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| real(real64) function | zfrob_norm (v) |
| | Frobenius norm of complex matrix. More...
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| subroutine | solvers_oct_m::dsym_conjugate_gradients (np, x, b, op, dotp, iter, residue, threshold) |
| | The two following subroutines, sym_conjugate_gradients, and bi_conjugate_gradients, must be called under a common interface: conjugate_gradients. It provides an approximate solution to the linear system problem Ax = b. Solving a symmetric linear system, which is either real or complex symmetric or Hermitian the best choice is sym_conjugate_gradients (does not need \( A^\dagger \)) Solving a real unsymmetric or a complex non-Hermitian system bi_conjugate_gradients has to be chosen (where one does need \( A^\dagger \)). More...
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| subroutine | solvers_oct_m::dbi_conjugate_gradients (np, x, b, op, opt, dotp, iter, residue, threshold) |
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| subroutine, public | solvers_oct_m::dqmr_sym_gen_dotu (np, x, b, op, dotu, nrm2, prec, iter, residue, threshold, showprogress, converged, use_initial_guess) |
| | for complex symmetric matrices W Chen and B Poirier, J Comput Phys 219, 198-209 (2006) More...
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| subroutine, public | solvers_oct_m::dqmr_gen_dotu (np, x, b, op, opt, dotu, nrm2, prec, prect, iter, residue, threshold, showprogress, converged) |
| | for general complex matrices taken from 'An Implementation of the QMR Method based on Coupled Two-Term Recurrences' by R. W. Freund and N. M. Nachtigal (page 25) http: More...
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| real(real64) function, dimension(size(b, 1), size(b, 2)), public | solvers_oct_m::didrs (b, s, preconditioner, matrixvector, ddotprod, zdotprod, tolerance, maximum_iterations, variant, flag, relres, iterations, x0, U0, omega, resvec, H) |
| | This is the "Induced Dimension Reduction", IDR(s) (for s=4). IDR(s) is a robust and efficient short recurrence Krylov subspace method for solving large nonsymmetric systems of linear equations. It is described in [Peter Sonneveld and Martin B. van Gijzen, SIAM J. Sci. Comput. 31, 1035 (2008)]. More...
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| real(real64) function, dimension(s) | dp_dot (P, R0, w, s) |
| | P inner product of complex matrices. More...
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1.9.4