mirror of
https://github.com/paboyle/Grid.git
synced 2024-11-10 15:55:37 +00:00
0bc004de7c
Tanh/Zolo * (Cayley/PartFrac/ContFrac) * (Mobius/Shamir/Wilson) Approx Representation Kernel. All are done with space-time taking part in checkerboarding, Ls uncheckerboarded Have only so far tested the Domain Wall limit of mobius, and at that only checked that it i) Inverts ii) 5dim DW == Ls copies of 4dim D2 iii) MeeInv Mee == 1 iv) Meo+Mee+Moe+Moo == M unprec. v) MpcDagMpc is hermitan vi) Mdag is the adjoint of M between stochastic vectors. That said, the RB schur solve, RB MpcDagMpc solve, Unprec solve all converge and the true residual becomes small; so pretty good tests.
87 lines
2.6 KiB
C
87 lines
2.6 KiB
C
/* -*- Mode: C; comment-column: 22; fill-column: 79; -*- */
|
|
|
|
#ifdef __cplusplus
|
|
namespace Grid {
|
|
namespace Approx {
|
|
#endif
|
|
|
|
#define HVERSION Header Time-stamp: <14-OCT-2004 09:26:51.00 adk@MISSCONTRARY>
|
|
|
|
|
|
#ifndef ZOLOTAREV_INTERNAL
|
|
#ifndef PRECISION
|
|
#define PRECISION double
|
|
#endif
|
|
#define ZPRECISION PRECISION
|
|
#define ZOLOTAREV_DATA zolotarev_data
|
|
#endif
|
|
|
|
/* This struct contains the coefficients which parameterise an optimal rational
|
|
* approximation to the signum function.
|
|
*
|
|
* The parameterisations used are:
|
|
*
|
|
* Factored form for type 0 (R0(0) = 0)
|
|
*
|
|
* R0(x) = A * x * prod(x^2 - a[j], j = 0 .. dn-1) / prod(x^2 - ap[j], j = 0
|
|
* .. dd-1),
|
|
*
|
|
* where deg_num = 2*dn + 1 and deg_denom = 2*dd.
|
|
*
|
|
* Factored form for type 1 (R1(0) = infinity)
|
|
*
|
|
* R1(x) = (A / x) * prod(x^2 - a[j], j = 0 .. dn-1) / prod(x^2 - ap[j], j = 0
|
|
* .. dd-1),
|
|
*
|
|
* where deg_num = 2*dn and deg_denom = 2*dd + 1.
|
|
*
|
|
* Partial fraction form
|
|
*
|
|
* R(x) = alpha[da] * x + sum(alpha[j] * x / (x^2 - ap[j]), j = 0 .. da-1)
|
|
*
|
|
* where da = dd for type 0 and da = dd + 1 with ap[dd] = 0 for type 1.
|
|
*
|
|
* Continued fraction form
|
|
*
|
|
* R(x) = beta[db-1] * x + 1 / (beta[db-2] * x + 1 / (beta[db-3] * x + ...))
|
|
*
|
|
* with the final coefficient being beta[0], with d' = 2 * dd + 1 for type 0
|
|
* and db = 2 * dd + 2 for type 1.
|
|
*
|
|
* Cayley form (Chiu's domain wall formulation)
|
|
*
|
|
* R(x) = (1 - T(x)) / (1 + T(x))
|
|
*
|
|
* where T(x) = prod((x - gamma[j]) / (x + gamma[j]), j = 0 .. n-1)
|
|
*/
|
|
|
|
typedef struct {
|
|
ZPRECISION *a, /* zeros of numerator, a[0 .. dn-1] */
|
|
*ap, /* poles (zeros of denominator), ap[0 .. dd-1] */
|
|
A, /* overall factor */
|
|
*alpha, /* coefficients of partial fraction, alpha[0 .. da-1] */
|
|
*beta, /* coefficients of continued fraction, beta[0 .. db-1] */
|
|
*gamma, /* zeros of numerator of T in Cayley form */
|
|
Delta, /* maximum error, |R(x) - sgn(x)| <= Delta */
|
|
epsilon; /* minimum x value, epsilon < |x| < 1 */
|
|
int n, /* approximation degree */
|
|
type, /* 0: R(0) = 0, 1: R(0) = infinity */
|
|
dn, dd, da, db, /* number of elements of a, ap, alpha, and beta */
|
|
deg_num, /* degree of numerator = deg_denom +/- 1 */
|
|
deg_denom; /* degree of denominator */
|
|
} ZOLOTAREV_DATA;
|
|
|
|
#ifndef ZOLOTAREV_INTERNAL
|
|
|
|
/* zolotarev(epsilon, n, type) returns a pointer to an initialised
|
|
* zolotarev_data structure. The arguments must satisfy the constraints that
|
|
* epsilon > 0, n > 0, and type = 0 or 1. */
|
|
|
|
ZOLOTAREV_DATA* grid_higham(PRECISION epsilon, int n) ;
|
|
ZOLOTAREV_DATA* grid_zolotarev(PRECISION epsilon, int n, int type);
|
|
#endif
|
|
|
|
#ifdef __cplusplus
|
|
}}
|
|
#endif
|