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1 files changed, 281 insertions, 0 deletions

diff --git a/src/basis.c b/src/basis.c
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+/*
+ * Basis sets for pseudospectral methods
+ * Copyright (C) 2016 Anton Khirnov <anton@khirnov.net>
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#include <errno.h>
+#include <math.h>
+
+#include "basis.h"
+#include "common.h"
+
+typedef struct BasisSet {
+    /* evaluate the idx-th basis function at the specified point*/
+    double (*eval)      (const MDBasisSetContext *s, double coord, unsigned int idx);
+    /* evaluate the first derivative of the idx-th basis function at the specified point*/
+    double (*eval_diff1)(const MDBasisSetContext *s, double coord, unsigned int idx);
+    /* evaluate the second derivative of the idx-th basis function at the specified point*/
+    double (*eval_diff2)(const MDBasisSetContext *s, double coord, unsigned int idx);
+    /**
+     * Get the idx-th collocation point for the specified order.
+     * idx runs from 0 to order - 1 (inclusive)
+     */
+    double (*colloc_point)(const MDBasisSetContext *s, unsigned int order, unsigned int idx);
+} BasisSet;
+
+struct MDBasisSetContext {
+    const BasisSet *bs;
+    double sf;
+};
+
+/*
+ * The basis of even (n = 2 * idx) SB functions (Boyd 2000, Ch 17.9)
+ * SB(x, n) = sin((n + 1) arccot(|x| / L))
+ * They are symmetric wrt origin and decay as 1/x in infinity.
+ */
+static double sb_even_eval(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    double val = atan2(s->sf, coord);
+
+    idx *= 2;   // even only
+
+    return sin((idx + 1) * val);
+}
+
+static double sb_even_eval_diff1(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    double val = atan2(s->sf, coord);
+
+    idx *= 2;   // even only
+
+    return -s->sf * (idx + 1) * cos((idx + 1) * val) / (SQR(s->sf) + SQR(coord));
+}
+
+static double sb_even_eval_diff2(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    const double sf = s->sf;
+    double val = atan2(sf, coord);
+
+    idx *= 2;   // even only
+
+    return sf * (idx + 1) * (2 * coord * cos((idx + 1) * val) - sf * (idx + 1) * sin((idx + 1) * val)) / SQR(SQR(sf) + SQR(coord));
+}
+
+static double sb_even_colloc_point(const MDBasisSetContext *s, unsigned int order, unsigned int idx)
+{
+    double t;
+
+    idx = order - idx - 1;
+    //order *= 2;
+
+    //t = (idx + 2) * M_PI / (order + 4);
+#if MD_POLAR
+    t = (idx + 2) * M_PI / (2 * order + 3);
+#else
+    t = (idx + 2) * M_PI / (2 * order + 2);
+#endif
+    return s->sf / tan(t);
+}
+
+static const BasisSet sb_even_basis = {
+    .eval         = sb_even_eval,
+    .eval_diff1   = sb_even_eval_diff1,
+    .eval_diff2   = sb_even_eval_diff2,
+    .colloc_point = sb_even_colloc_point,
+};
+
+static double sb_odd_eval(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    double val = atan2(s->sf, coord);
+
+    idx = 2 * idx + 2;   // odd only
+
+    return sin((idx) * val);
+}
+
+static double sb_odd_eval_diff1(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    double val = atan2(s->sf, coord);
+
+    idx = 2 * idx + 2;   // odd only
+
+    return -s->sf * (idx) * cos((idx) * val) / (SQR(s->sf) + SQR(coord));
+}
+
+static double sb_odd_eval_diff2(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    const double sf = s->sf;
+    double val = atan2(sf, coord);
+
+    idx = 2 * idx + 2;   // odd only
+
+    return sf * (idx) * (2 * coord * cos((idx) * val) - sf * (idx) * sin((idx) * val)) / SQR(SQR(sf) + SQR(coord));
+}
+
+static double sb_odd_colloc_point(const MDBasisSetContext *s, unsigned int order, unsigned int idx)
+{
+    double t;
+
+    idx = order - idx - 1;
+    //order *= 2;
+
+    //t = (idx + 2) * M_PI / (order + 4);
+#if MD_POLAR
+    t = (idx + 2) * M_PI / (2 * order + 3);
+#else
+    t = (idx + 2) * M_PI / (2 * order + 3);
+#endif
+    return s->sf / tan(t);
+}
+
+static const BasisSet sb_odd_basis = {
+    .eval         = sb_odd_eval,
+    .eval_diff1   = sb_odd_eval_diff1,
+    .eval_diff2   = sb_odd_eval_diff2,
+    .colloc_point = sb_odd_colloc_point,
+};
+
+static double tb_even_eval(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    double val = (coord == 0.0) ? M_PI_2 : atan(s->sf / fabs(coord));
+
+    idx++;
+    idx *= 2;   // even only
+
+    return cos(idx * val) - 1.0;
+}
+
+static double tb_even_eval_diff1(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    double val = (coord == 0.0) ? M_PI_2 : atan(s->sf / fabs(coord));
+
+    idx++;
+    idx *= 2;   // even only
+
+    return s->sf * idx * SGN(coord) * sin(idx * val) / (SQR(s->sf) + SQR(coord));
+}
+
+static double tb_even_eval_diff2(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    const double sf = s->sf;
+    double val = (coord == 0.0) ? M_PI_2 : atan(sf / fabs(coord));
+
+    idx++;
+    idx *= 2;   // even only
+
+    return -sf * idx * SGN(coord) * (2 * fabs(coord) * sin(idx * val) + sf * idx * cos(idx * val)) / SQR(SQR(sf) + SQR(coord));
+}
+
+static double tb_even_colloc_point(const MDBasisSetContext *s, unsigned int order, unsigned int idx)
+{
+    double t;
+
+    idx = order - idx - 1;
+    //order *= 2;
+
+    //t = (idx + 2) * M_PI / (order + 4);
+    t = (idx + 2) * M_PI / (2 * order + 4);
+    return s->sf / tan(t);
+}
+
+static const BasisSet tb_even_basis = {
+    .eval         = tb_even_eval,
+    .eval_diff1   = tb_even_eval_diff1,
+    .eval_diff2   = tb_even_eval_diff2,
+    .colloc_point = tb_even_colloc_point,
+};
+
+static double cos_even_eval(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    return cos(2 * idx * coord);
+}
+
+static double cos_even_eval_diff1(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    return -2 * idx * sin(2 * idx * coord);
+}
+
+static double cos_even_eval_diff2(const MDBasisSetContext *s, double coord, unsigned int idx)
+{
+    return -4 * SQR(idx) * cos(2 * idx * coord);
+}
+
+static double cos_even_colloc_point(const MDBasisSetContext *s, unsigned int order, unsigned int idx)
+{
+    return M_PI * idx / (2 * order - 0);
+}
+
+static const BasisSet cos_even_basis = {
+    .eval         = cos_even_eval,
+    .eval_diff1   = cos_even_eval_diff1,
+    .eval_diff2   = cos_even_eval_diff2,
+    .colloc_point = cos_even_colloc_point,
+};
+
+double md_basis_eval(const MDBasisSetContext *s, enum MDBasisEvalType type,
+                     double coord, unsigned int order)
+{
+    double (*eval)(const MDBasisSetContext *, double, unsigned int) = NULL;
+
+    switch (type) {
+    case MD_BASIS_EVAL_TYPE_VALUE: eval = s->bs->eval;       break;
+    case MD_BASIS_EVAL_TYPE_DIFF1: eval = s->bs->eval_diff1; break;
+    case MD_BASIS_EVAL_TYPE_DIFF2: eval = s->bs->eval_diff2; break;
+    }
+
+    return eval(s, coord, order);
+}
+
+double md_basis_colloc_point(const MDBasisSetContext *s, unsigned int order,
+                             unsigned int idx)
+{
+    return s->bs->colloc_point(s, order, idx);
+}
+
+void md_basis_free(MDBasisSetContext **pctx)
+{
+    MDBasisSetContext *ctx = *pctx;
+
+    if (!ctx)
+        return;
+
+    free(ctx);
+    *pctx = NULL;
+}
+
+int md_basis_init(MDBasisSetContext **pctx, enum MDBasisFamily family, double sf)
+{
+    MDBasisSetContext *ctx;
+
+    ctx = calloc(1, sizeof(*ctx));
+    if (!ctx)
+        return -ENOMEM;
+
+    switch (family) {
+    case MD_BASIS_FAMILY_TB_EVEN:   ctx->bs = &tb_even_basis;   break;
+    case MD_BASIS_FAMILY_SB_EVEN:   ctx->bs = &sb_even_basis;   break;
+    case MD_BASIS_FAMILY_SB_ODD:    ctx->bs = &sb_odd_basis;    break;
+    case MD_BASIS_FAMILY_COS_EVEN:  ctx->bs = &cos_even_basis;  break;
+    default:
+        free(ctx);
+        return -EINVAL;        
+    }
+
+    ctx->sf = sf;
+
+    *pctx = ctx;
+    return 0;
+}