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authorIlhan Ozgen <iozgen@lbl.gov>2021-04-06 12:29:09 -0700
committerIlhan Ozgen <iozgen@lbl.gov>2021-04-06 12:29:09 -0700
commitf6ec98980fae9b43d596d5c5d1f19e69dc9fc6a8 (patch)
treed0bfd5c62ab5b7624a9ef189378159ea8ffbec7d
initial commit
Diffstat
-rw-r--r--.gitignore4
-rw-r--r--Makefile40
-rw-r--r--header.h98
-rw-r--r--input/dem.asc561
-rw-r--r--input/test.input3
-rw-r--r--main.c610
6 files changed, 1316 insertions, 0 deletions
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ae1fdfa
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,4 @@
+output/
+*~
+mammoth
+*.o \ No newline at end of file
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..343d134
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,40 @@
+#
+# Makefile
+#
+
+PRG=mammoth
+SRC=main.c
+
+CC=/usr/local/bin/gcc-10
+
+CFLAGS=-g -Wall -Wextra -pedantic -std=c99
+LFLAGS=
+CPU=
+RUNFLAGS=
+INCLUDES=
+LIB=
+
+#
+#
+#
+
+OBJ=$(SRC:.c=.o)
+
+all: $(PRG)
+
+run: $(PRG)
+ $(RUNFLAGS) ./$(PRG)
+
+$(PRG): $(OBJ)
+ $(CC) $(LFLAGS) $(CFLAGS) $(OBJ) -o $@ $(LIB)
+
+%.o: %.c
+ $(CC) $(LFLAGS) $(CFLAGS) -c $< -o $@
+
+clean:
+ rm -vf $(PRG) $(OBJ) output/*
+ rm -vf $(P)
+
+.PHONY: all clean
+
+# eof
diff --git a/header.h b/header.h
new file mode 100644
index 0000000..55df416
--- /dev/null
+++ b/header.h
@@ -0,0 +1,98 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+#ifndef DEBUG_IO
+#define DEBUG_IO 0
+#endif
+
+/*
+ * ----------------------------------------------------------------------
+ */
+
+int get_metadata(char *datafilename, int *nrow, int *ncol, double *xllcorner, double *yllcorner, double *cellsize, double *nodata);
+
+int get_data(char *datafilename, int nrow, int ncol, int ncol_padded, double *data);
+
+int compress(double *data, double *m, int nrow, int ncol);
+
+int decompress(double *m, int nrow, int ncol);
+
+int hard_threshold(double *m, int *flag, int n, int nlevels, int nrow, int ncol, double threshold);
+
+/*
+ * ----------------------------------------------------------------------
+ */
+
+int ipow(int base, int exponent) {
+ int result = 1;
+ for (int i = exponent; i > 0; i--) {
+ result = result * base;
+ }
+ return result;
+}
+
+int get_wavelet_matrix(double *m, int dim)
+{
+ int len = (int) (dim / 2);
+
+ int r1[len]; /* rows for low frequency */
+ int r2[len]; /* rows for high frequency */
+ int c1[len]; /* columns */
+ int c2[len]; /* columns */
+
+ for (int i = 0; i < len; i ++) {
+ r1[i] = i;
+ r2[i] = len + i;
+ c1[i] = 2 * i;
+ c2[i] = 2 * i + 1;
+
+ m[c1[i] + dim * r1[i]] = 0.5 * sqrt(2.0);
+ m[c2[i] + dim * r1[i]] = 0.5 * sqrt(2.0);
+
+ m[c1[i] + dim * r2[i]] = 0.5 * sqrt(2.0);
+ m[c2[i] + dim * r2[i]] = - 0.5 * sqrt(2.0);
+ }
+
+ return 0;
+}
+
+int matmul(double* matrix1, int nrow1, int ncol1, double* matrix2, int nrow2, int ncol2, double* result) {
+
+ if (ncol1 != nrow2) {
+ fscanf(stderr, "[ERR] Dimensions of matrices don't match: %d-by%d with %d-by%d\n", &nrow1, &ncol1, &nrow2, &ncol2);
+ return -1;
+ }
+
+ double sum = 0.0;
+
+ for (int i = 0; i < nrow1; i ++) {
+ for (int j = 0; j < ncol2; j ++) {
+ for (int k = 0; k < ncol1; k ++) {
+ sum += matrix1[k + i * ncol1] * matrix2[j + k * ncol2];
+ }
+ result[j + ncol2 * i] = sum;
+ sum = 0.0;
+ }
+ }
+
+ return 0;
+}
+
+int transpose(double* matrix, int nrow, int ncol) {
+
+ double *_tmp = (double*) calloc(ncol * nrow, sizeof(double));
+
+ for (int j = 0; j < nrow; j ++) {
+ for (int i = 0; i < ncol; i ++) {
+ _tmp[j + nrow * i] = matrix[i + ncol * j];
+ }
+ }
+
+ memcpy(matrix, _tmp, nrow * ncol * sizeof(double));
+
+ free(_tmp);
+
+ return 0;
+}
diff --git a/input/dem.asc b/input/dem.asc
new file mode 100644
index 0000000..5ad851d
--- /dev/null
+++ b/input/dem.asc
@@ -0,0 +1,561 @@
+ncols 526
+nrows 555
+xllcorner 325922.99999999907
+yllcorner 4309187.000000004
+cellsize 10.0
+nodata_value -9999.0
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diff --git a/input/test.input b/input/test.input
new file mode 100644
index 0000000..de91967
--- /dev/null
+++ b/input/test.input
@@ -0,0 +1,3 @@
+datafile input/dem.asc
+N 8
+threshold 0.001 \ No newline at end of file
diff --git a/main.c b/main.c
new file mode 100644
index 0000000..dc46b64
--- /dev/null
+++ b/main.c
@@ -0,0 +1,610 @@
+/* -*- mode: c; style: linux -*- */
+
+/* Purpose: Given input data in the form of a 2D array, perform a
+ * discrete Haar wavelet transform.
+ *
+ * Author: Ilhan Ozgen-Xian, iozgen@lbl.gov
+ */
+
+#include "header.h"
+
+/* Main logic */
+
+int main(int argc, char** argv)
+{
+
+ FILE *fp;
+
+ char datafilename[255];
+ int nlevels;
+ double threshold;
+
+ int ncol;
+ int nrow;
+
+ double xllcorner;
+ double yllcorner;
+ double cellsize;
+ double nodata;
+
+ double *data;
+
+ if (argc < 2) {
+ fprintf(stderr, "[ERR] No input file provided.\n");
+ return -1;
+ }
+
+ printf("[OK] Reading in: %s\n", argv[1]);
+
+ fp = fopen(argv[1], "r");
+
+ if (fp == NULL) {
+ fprintf(stderr, "[ERR] Couldn't read input file: %s\n", argv[1]);
+ return -1;
+ }
+
+ char key[1024];
+
+ while (fscanf(fp, "%s", key) != EOF) {
+
+ if (strcmp(key, "datafile") == 0) {
+ fscanf(fp, "%s", datafilename);
+ printf("[OK] Data filename set: %s\n", datafilename);
+ } else if (strcmp(key, "N") == 0) {
+ fscanf(fp, "%d", &nlevels);
+ printf("[OK] # of resolution levels set: %d\n", nlevels);
+ } else if (strcmp(key, "threshold") == 0) {
+ fscanf(fp, "%lf", &threshold);
+ printf("[OK] Threshold set: %f\n", threshold);
+ } else {
+ printf("[!!] Key not recognised: %s\n", key);
+ printf("[!!] Continue until known key is encountered\n");
+ }
+
+ }
+
+ fclose(fp);
+
+ if (get_metadata(datafilename, &nrow, &ncol, &xllcorner, &yllcorner, &cellsize, &nodata)) {
+ return -1;
+ }
+
+ printf("[OK] Metadata of %s: nrow: %d, ncol: %d, xll: %lf, yll: %lf, dx: %lf, nodata: %lf\n", datafilename, nrow, ncol, xllcorner, yllcorner, cellsize, nodata);
+
+ int powx = (int) ceil(log2(ncol));
+ int powy = (int) ceil(log2(nrow));
+
+ int ncol_padded = ipow(2, powx);
+ int nrow_padded = ipow(2, powy);
+
+ /* read in data */
+ data = (double*) calloc(ncol_padded * nrow_padded, sizeof(double));
+ for (int i = 0; i < nrow_padded; i ++) {
+ for (int j = 0; j < ncol_padded; j ++) {
+ data[j + ncol_padded * i] = nodata;
+ }
+ }
+
+ if (get_data(datafilename, nrow, ncol, ncol_padded, data)) {
+ return -1;
+ }
+
+ /*
+ * ----------------------------------------------------------------------
+ * Compression step
+ * ----------------------------------------------------------------------
+ */
+
+ double *m = (double*) calloc(ncol_padded * nrow_padded, sizeof(double));
+ double *_data = (double*) calloc(ncol_padded * nrow_padded, sizeof(double));
+ double *_m = (double*) calloc(ncol_padded * nrow_padded, sizeof(double));
+
+ memcpy(_data, data, ncol_padded * nrow_padded * sizeof(double));
+
+ int _nrow = nrow_padded;
+ int _ncol = ncol_padded;
+
+ for (int n = 0; n < nlevels; n ++) {
+
+ /*
+ * If non-divisible by 2, DHT can't be applied since it depends on
+ * pair-wise comparisons. In this case, we exit with fail.
+ */
+ if (_ncol % 2 != 0 || _nrow % 2 != 0) {
+ fprintf(stderr, "[ERR] %d-by-%d matrix can't be compressed by DHT.\n", _ncol, _nrow);
+ return -1;
+ }
+
+ /*
+ * carry out the DHT
+ */
+
+ compress(_data, _m, _nrow, _ncol);
+
+ /*
+ * Now get the new image matrix. We know that it is located at the
+ * upper left corner of the compressed image M, and has dimensions
+ * ncol/2 x nrow/2.
+ */
+
+ _nrow = _nrow / 2;
+ _ncol = _ncol / 2;
+
+ /* Resize _data */
+ _data = (double*) realloc(_data, _ncol * _nrow * sizeof(double));
+
+ printf("[OK] Data is resized\n");
+
+ /* Transfer _data */
+ for (int i = 0; i < _nrow; i ++) {
+ for (int j = 0; j < _ncol; j ++) {
+ _data[j + i * _ncol] = _m[j + i * 2 * _ncol];
+ }
+ }
+
+ printf("[OK] Data is transferred\n");
+
+ /* Transfer m */
+ for (int i = 0; i < 2 * _nrow; i ++) {
+ for (int j = 0; j < 2 * _ncol; j ++) {
+ m[j + i * ncol_padded] = _m[j + i * 2 * _ncol];
+ }
+ }
+
+#if DEBUG_IO
+
+ char filename[1024];
+ sprintf(filename, "output/m-%d.asc", n);
+
+ FILE *fp = fopen(filename, "w");
+
+ for (int i = 0; i < 2 * _nrow; i ++) {
+ for (int j = 0; j < 2 * _ncol; j ++) {
+ fprintf(fp, "%f ", _m[j + i * 2 * _ncol]);
+ }
+ fprintf(fp, "\n");
+ }
+
+ fclose(fp);
+
+#endif
+
+ printf("[OK] M is transferred\n");
+
+ /* Resize _m */
+ _m = (double*) realloc(_m, _ncol * _nrow * sizeof(double));
+
+ printf("[OK] M is resized\n");
+
+ }
+
+ /*
+ * ----------------------------------------------------------------------
+ * Decompression step
+ * ----------------------------------------------------------------------
+ * Decompressing the DHT, in each level we look at the details and
+ * see if they are significant. i = 0 is the coarsest level, and
+ * the subsequent finer levels are i = 1, 2, ... , N - 1,
+ * respectively.
+ * ----------------------------------------------------------------------
+ */
+
+ int *levels = (int*) calloc(nrow_padded * ncol_padded, sizeof(int));
+
+ /* Set resolution level to highest at the beginning */
+ for (int i = 0; i < nrow_padded; i ++) {
+ for (int j = 0; j < ncol_padded; j ++) {
+ levels[j + ncol_padded * i] = nlevels - 1;
+ }
+ }
+
+ _nrow = nrow_padded / ipow(2, nlevels - 1);
+ _ncol = ncol_padded / ipow(2, nlevels - 1);
+
+ _m = (double*) realloc(_m, _ncol * _nrow * sizeof(double));
+
+ for (int i = 0; i < _nrow; i ++) {
+ for (int j = 0; j < _ncol; j ++) {
+ _m[j + _ncol * i] = m[j + i * ncol_padded];
+ }
+ }
+
+ int *flag = (int*) calloc(_nrow * _ncol / 4, sizeof(double));
+
+ for (int n = 0; n < nlevels; n ++) {
+
+ printf("[OK] Thresholding image at level %d\n", n);
+
+ /* Perform hard thresholding to predict refinement levels */
+ hard_threshold(_m, flag, n, nlevels, _nrow, _ncol, threshold);
+
+ /* Tag cells that are sufficiently refined */
+ for (int i = 0; i < _nrow/2; i ++) {
+ for (int j = 0; j < _ncol/2; j ++) {
+
+ if (flag[j + i * _ncol/2] == 1) {
+
+ int coef = ipow(2, nlevels - n);
+
+ if (levels[coef * j + coef * i * ncol_padded] > n) {
+
+ for (int m = coef * i; m < coef * i + coef; m ++) {
+ for (int p = coef * j; p < coef * j + coef; p ++) {
+ levels[p + m * ncol_padded] = n;
+ }
+ }
+
+ }
+
+ }
+
+ }
+ }
+
+#if DEBUG_IO
+
+ char filename[1024];
+ sprintf(filename, "f-%d.asc", n);
+
+ FILE *fp = fopen(filename, "w");
+
+ for (int i = 0; i < _nrow/2; i ++) {
+ for (int j = 0; j < _ncol/2; j ++) {
+ fprintf(fp, "%d ", flag[j + i * _ncol/2]);
+ }
+ fprintf(fp, "\n");
+ }
+
+ fclose(fp);
+
+#endif
+
+ /* Decompress the blur image to move to the next refinement level */
+ decompress(_m, _nrow, _ncol);
+
+ /* Transfer m */
+ for (int i = 0; i < _nrow; i ++) {
+ for (int j = 0; j < _ncol; j ++) {
+ m[j + i * ncol_padded] = _m[j + i * _ncol];
+ }
+ }
+
+ printf("[OK] M is transferred\n");
+
+ /*
+ * Adjust the dimensions. We are now refining so _ncol and _nrow
+ * need to be doubled
+ */
+ _ncol = 2 * _ncol;
+ _nrow = 2 * _nrow;
+
+ /* Resize _m */
+ _m = (double*) realloc(_m, _ncol * _nrow * sizeof(double));
+
+ printf("[OK] M is resized\n");
+
+ /* Transfer m back */
+ for (int i = 0; i < _nrow; i ++) {
+ for (int j = 0; j < _ncol; j ++) {
+ _m[j + i * _ncol] = m[j + i * ncol_padded];
+ }
+ }
+
+ printf("[OK] M is transferred back\n");
+
+ /* Resize flag */
+ flag = (int*) realloc(flag, (_nrow * _ncol / 4) * sizeof(double));
+
+ printf("[OK] Flag is resized\n");
+
+ }
+
+ /*
+ * ----------------------------------------------------------------------
+ * I/O
+ * ----------------------------------------------------------------------
+ */
+
+#if DEBUG_IO
+ FILE *mptr; /* Terrain data */
+ mptr = fopen("output/m.asc", "w");
+#endif
+
+ FILE *lptr; /* Level data */
+ lptr = fopen("output/l.asc", "w");
+
+ for (int i = 0; i < nrow_padded; i ++) {
+ for (int j = 0; j < ncol_padded; j ++) {
+#if DEBUG_IO
+ fprintf(mptr, "%f ", m[j + ncol_padded * i]);
+#endif
+ fprintf(lptr, "%d ", levels[j + ncol_padded * i]);
+ }
+#if DEBUG_IO
+ fprintf(mptr, "\n");
+#endif
+ fprintf(lptr, "\n");
+ }
+
+ /*
+ * ----------------------------------------------------------------------
+ * Housekeeping
+ * ----------------------------------------------------------------------
+ */
+
+#if DEBUG_IO
+ fclose(mptr);
+#endif
+
+ fclose(lptr);
+
+ free(levels);
+ free(flag);
+ free(_data);
+ free(m);
+ free(data);
+
+ printf("[OK] Finished successfully\n");
+
+ return 0;
+
+}
+
+/*
+ * Functions related to reading in the data set
+ */
+
+int get_metadata(char *datafilename, int *nrow, int *ncol, double *xllcorner, double *yllcorner, double *cellsize, double *nodata)
+{
+
+ FILE *dp;
+
+ printf("[OK] Reading in: %s\n", datafilename);
+ dp = fopen(datafilename, "r");
+
+ if (dp == NULL) {
+ fprintf(stderr, "[ERR] Couldn't read data file: %s\n", datafilename);
+ return -1;
+ }
+
+ char key[1024];
+
+ while (fscanf(dp, "%s", key) != EOF) {
+
+ if (strcmp(key, "ncols") == 0) {
+ fscanf(dp, "%d", ncol);
+ printf("[OK] # of columns set: %d\n", *ncol);
+ } else if (strcmp(key, "nrows") == 0) {
+ fscanf(dp, "%d", nrow);
+ printf("[OK] # of rows set: %d\n", *nrow);
+ } else if (strcmp(key, "xllcorner") == 0) {
+ fscanf(dp, "%lf", xllcorner);
+ printf("[OK] x-coordinate of lower left corner set: %lf\n", *xllcorner);
+ } else if (strcmp(key, "yllcorner") == 0) {
+ fscanf(dp, "%lf", yllcorner);
+ printf("[OK] y-coordinate of lower left corner set: %lf\n", *yllcorner);
+ } else if (strcmp(key, "cellsize") == 0) {
+ fscanf(dp, "%lf", cellsize);
+ printf("[OK] cell size set: %lf\n", *cellsize);
+ } else if (strcmp(key, "nodata_value") == 0) {
+ fscanf(dp, "%lf", nodata);
+ printf("[OK] No data value set: %lf\n", *nodata);
+ return 0;
+ } else {
+ printf("[!!] Key not recognised: %s\n", key);
+ printf("[!!] Continue until known key is encountered\n");
+ }
+
+ }
+
+ fclose(dp);
+
+ return 0;
+}
+
+int get_data(char *datafilename, int nrow, int ncol, int ncol_padded, double *data) {
+
+ FILE *dp;
+ dp = fopen(datafilename, "r");
+
+ if (dp == NULL) {
+ fprintf(stderr, "[ERR] Couldn't read data file: %s\n", datafilename);
+ return -1;
+ }
+
+ double nodata;
+ char key[1024];
+
+ while (fscanf(dp, "%s", key) != EOF) {
+
+ if (strcmp(key, "nodata_value") == 0) {
+
+ fscanf(dp, "%lf", &nodata);
+ printf("[OK] Starting to read data\n");
+
+ for (int i = 0; i < nrow; i ++) {
+ for (int j = 0; j < ncol; j ++) {
+ fscanf(dp, "%lf", &data[j + ncol_padded * i]);
+ }
+ }
+
+ }
+
+ }
+
+ return 0;
+
+}
+
+/*
+ * Functions related to discrete Haar wavelet transform
+ */
+
+int compress(double* data, double *m, int nrow, int ncol)
+{
+ /*
+ * | B : V |
+ * M = |-------|
+ * | H : D |
+ *
+ * where B is the blur image, V is the vertical detail, H is the
+ * horizontal detail, and D is the diagonal detail.
+ */
+
+ printf("[OK] Compressing a %d-by-%d matrix\n", nrow, ncol);
+
+ /*
+ * Get the coefficient matrix for left matrix multiplication:
+ *
+ * C = Wm A
+ *
+ * This matrix needs to have dimension `nrow x nrow'. After that,
+ * carry out the matrix multiplication to get the column-compressed
+ * matrix C.
+ */
+
+ double *wm;
+ wm = (double*) calloc(nrow * nrow, sizeof(double));
+
+ get_wavelet_matrix(wm, nrow);
+
+ double *c;
+ c = (double*) calloc(nrow * ncol, sizeof(double));
+
+ matmul(wm, nrow, nrow, data, nrow, ncol, c);
+
+ /*
+ * Carry out the row compression. We need a coefficient matrix with
+ * dimension `ncol x ncol' to multiply:
+ *
+ * M = C Wn^T
+ *
+ * This will compress the image one level.
+ */
+
+ double *wn;
+ wn = (double*) calloc(ncol * ncol, sizeof(double));
+
+ get_wavelet_matrix(wn, ncol);
+ transpose(wn, nrow, ncol);
+
+ matmul(c, nrow, ncol, wn, ncol, ncol, m);
+
+ free(wn);
+ free(c);
+ free(wm);
+
+ return 0;
+}
+
+int decompress(double *data, int nrow, int ncol) {
+
+ printf("[OK] Decompressing a %d-by-%d matrix\n", nrow, ncol);
+
+ double *wm = (double*) calloc(nrow * nrow, sizeof(double));
+ double *wn = (double*) calloc(ncol * ncol, sizeof(double));
+
+ double *c1 = (double*) calloc(nrow * ncol, sizeof(double));
+ double *c2 = (double*) calloc(nrow * ncol, sizeof(double));
+
+ /* Reconstruct the DHT to move to finer resolution */
+
+ get_wavelet_matrix(wm, nrow);
+ get_wavelet_matrix(wn, ncol);
+
+ transpose(wm, nrow, nrow);
+
+ matmul(wm, nrow, nrow, data, nrow, ncol, c1);
+ matmul(c1, nrow, ncol, wn, ncol, ncol, c2);
+
+ for (int i = 0; i < nrow; i ++) {
+ for (int j = 0; j < ncol; j ++) {
+ data[j + ncol * i] = c2[j + i * ncol];
+ }
+ }
+
+ free(wm);
+ free(wn);
+ free(c1);
+ free(c2);
+
+ return 0;
+}
+
+int hard_threshold(double *m, int *flag, int n, int nlevels, int nrow, int ncol, double threshold) {
+ /*
+ * Hard thresholding as explained in (Caviedes-Voullieme and
+ * Kesserwani, 2015: Benchmarking a multi-resolution discontinuous
+ * Galerkin shallow water model, Advances in Water Resources,
+ * 86:14-31).
+ */
+
+ /*
+ * | B : V |
+ * M = |-------|
+ * | H : D |
+ */
+
+ double _b;
+ double _v;
+ double _h;
+ double _d;
+
+ double _err = ipow(2, n - nlevels) * threshold;
+
+ for (int i = 0; i < nrow/2; i ++) {
+ for (int j = 0; j < ncol/2; j++) {
+
+ double max_b = 0.0;
+ double max_v = 0.0;
+ double max_h = 0.0;
+ double max_d = 0.0;
+
+ double max_hvd = 0.0;
+
+ double abs_b = 0.0;
+ double abs_v = 0.0;
+ double abs_h = 0.0;
+ double abs_d = 0.0;
+
+ _b = m[j + ncol * i];
+ _v = m[(j + ncol/2) + ncol * i];
+ _h = m[j + ncol * (nrow/2 + i)];
+ _d = m[(j + ncol/2) + ncol * (nrow/2 + i)];
+
+ /* printf(">>> %d %d %f %f %f %f\n", j, i, _b, _v, _h, _d); */
+
+ abs_b = fabs(_b);
+ max_b = (max_b < abs_b) ? abs_b : max_b;
+
+ abs_v = fabs(_v);
+ max_v = (max_v < abs_v) ? abs_v : max_v;
+
+ abs_h = fabs(_h);
+ max_h = (max_h < abs_h) ? abs_h : max_h;
+
+ abs_d = fabs(_d);
+ max_d = (max_d < abs_d) ? abs_d : max_d;
+
+ max_hvd = (max_v > max_h) ? max_v : max_h;
+ max_hvd = (max_hvd > max_d) ? max_hvd : max_d;
+
+ /* normalise */
+ if (max_b > 1.0) {
+ max_hvd = max_hvd / max_b;
+ }
+
+ if (max_hvd < _err) {
+ /* Can be coarsened */
+ flag[j + (ncol/2) * i] = 1;
+ /* printf(">>> coarsen: %d %d %f %f %f %f\n", j, i, max_v, ); */
+ } else {
+ /* Can't be coarsened */
+ flag[j + (ncol/2) * i] = -1;
+ }
+
+ }
+ }
+
+ return 0;
+}
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