From 457d8274fde5d20dc5694576b99c5541e55b4f40 Mon Sep 17 00:00:00 2001
From: Anton Khirnov <anton@khirnov.net>
Date: Mon, 18 Mar 2019 10:33:46 +0100
Subject: ell_grid_solve: use BiCGSTAB to speed up exact solves

---
 ell_grid_solve.c | 63 +++++++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 55 insertions(+), 8 deletions(-)

(limited to 'ell_grid_solve.c')

diff --git a/ell_grid_solve.c b/ell_grid_solve.c
index cbb7d68..550f305 100644
--- a/ell_grid_solve.c
+++ b/ell_grid_solve.c
@@ -27,6 +27,7 @@
 
 #include <lapacke.h>
 
+#include "bicgstab.h"
 #include "common.h"
 #include "ell_grid_solve.h"
 #include "log.h"
@@ -51,9 +52,13 @@ typedef struct EGSExactInternal {
     size_t N_ghosts;
 
     double *mat;
+    double *mat_f;
     double *rhs;
+    double *x;
     double *scratch_line;
     int    *ipiv;
+
+    BiCGStabContext *bicgstab;
 } EGSExactInternal;
 
 struct EGSInternal {
@@ -511,23 +516,48 @@ static int solve_exact(EGSContext *ctx)
         }
     }
 
+    for (int i = 0; i < e->N; i++)
+        for (int j = i + 1; j < e->N; j++) {
+            double tmp = e->mat[j * e->N + i];
+            e->mat[j * e->N + i] = e->mat[i * e->N + j];
+            e->mat[i * e->N + j] = tmp;
+        }
     ec->time_mat_construct += gettime() - start;
     ec->count_mat_construct++;
 
     start = gettime();
-    ret = LAPACKE_dgesv(LAPACK_ROW_MAJOR, e->N, 1, e->mat, e->N, e->ipiv, e->rhs, 1);
-    if (ret != 0) {
-        mg2di_log(&ctx->logger, MG2D_LOG_ERROR,
-                  "Error solving the linear system: %d\n", ret);
-        return -EDOM;
+
+    ret = mg2di_bicgstab_solve(e->bicgstab, e->mat, e->rhs, e->x);
+    if (ret < 0) {
+        char equed = 'N';
+        double cond, ferr, berr, rpivot;
+
+        ret = LAPACKE_dgesvx(LAPACK_COL_MAJOR, 'N', 'N', e->N, 1,
+                             e->mat, e->N, e->mat_f, e->N, e->ipiv, &equed, NULL, NULL,
+                             e->rhs, e->N, e->x, e->N, &cond, &ferr, &berr, &rpivot);
+        if (ret == 0)
+            ret = LAPACKE_dgetri(LAPACK_COL_MAJOR, e->N, e->mat_f, e->N, e->ipiv);
+        if (ret != 0) {
+            mg2di_log(&ctx->logger, MG2D_LOG_ERROR,
+                      "Error solving the linear system: %d\n", ret);
+            return -EDOM;
+        }
+        mg2di_log(&ctx->logger, MG2D_LOG_DEBUG,
+                  "LU factorization solution to a %zdx%zd matrix: "
+                  "condition number %16.16g; forward error %16.16g backward error %16.16g\n",
+                  e->N, e->N, cond, ferr, berr);
+
+        ret = mg2di_bicgstab_init(e->bicgstab, e->mat_f, e->x);
+        if (ret < 0)
+            return ret;
     }
 
+    for (size_t idx1 = 0; idx1 < ctx->domain_size[1]; idx1++)
+        memcpy(ctx->u + idx1 * ctx->u_stride, e->x + idx1 * ctx->domain_size[0], ctx->domain_size[0] * sizeof(*e->x));
+
     ec->time_lin_solve += gettime() - start;
     ec->count_lin_solve++;
 
-    for (size_t idx1 = 0; idx1 < ctx->domain_size[1]; idx1++)
-        memcpy(ctx->u + idx1 * ctx->u_stride, e->rhs + idx1 * ctx->domain_size[0], ctx->domain_size[0] * sizeof(*e->rhs));
-
     boundaries_apply(ctx);
     residual_calc(ctx);
 
@@ -692,10 +722,23 @@ static int arrays_alloc(EGSContext *ctx, const size_t domain_size[2])
 
         e->scratch_line = calloc(e->N_ghosts, sizeof(*e->scratch_line));
         e->mat          = calloc(SQR(e->N),   sizeof(*e->mat));
+        e->mat_f        = calloc(SQR(e->N),   sizeof(*e->mat_f));
         e->rhs          = calloc(e->N,        sizeof(*e->rhs));
+        e->x            = calloc(e->N,        sizeof(*e->x));
         e->ipiv         = calloc(e->N,        sizeof(*e->ipiv));
         if (!e->scratch_line || !e->mat || !e->rhs || !e->ipiv)
             return -ENOMEM;
+
+        ret = mg2di_bicgstab_context_alloc(&e->bicgstab, e->N, 64);
+        if (ret < 0)
+            return ret;
+
+        for (int i = 0; i < e->N; i++)
+            e->mat[i * e->N + i] = 1.0;
+
+        ret = mg2di_bicgstab_init(e->bicgstab, e->mat, e->x);
+        if (ret < 0)
+            return ret;
     }
 
     return 0;
@@ -766,8 +809,12 @@ void mg2di_egs_free(EGSContext **pctx)
 
         free(e->scratch_line);
         free(e->mat);
+        free(e->mat_f);
         free(e->rhs);
+        free(e->x);
         free(e->ipiv);
+
+        mg2di_bicgstab_context_free(&e->bicgstab);
     }
 
     free(ctx->priv->u_base);
-- 
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