├── .gitignore
├── LICENSE
├── README.md
├── simpleProblem.mps
└── src
├── cudaCheck.cuh
├── lpProblem.cu
├── lpProblem.cuh
├── main.cu
├── print.cu
├── print.cuh
├── simplex.cu
└── simplex.cuh
/.gitignore:
--------------------------------------------------------------------------------
1 | # build
2 | *.d
3 | *.i
4 | *.o
5 | *.ii
6 | *.gpu
7 | *.ptx
8 | *.cubin
9 | *.fatbin
10 |
11 | # IDE
12 | .project
13 | .cproject
14 | Debug/
15 | Release/
16 |
--------------------------------------------------------------------------------
/LICENSE:
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/README.md:
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1 | # cuda-revised-simplex
2 |
3 | An implementation of the revised simplex algorithm in CUDA for solving linear optimization problems in the form `max{c*x | A*x=b, l<=x<=u}`. The LP problem is read from an MPS file by GLPK.
4 |
5 | The implementations uses the following data structures. The coefficient matrix and objective function values are splitted in two parts. One contains the basic variables and the other the nonbasic variables. The matrices are stored in array format and CSR format. The CSR format is used for calculations and the array format for copying of columns. The CSR representation is updated at the end of each iteration. Temporary variables are allocated once at the beginning and reused throughout the iterations. All values are stored in double precision.
6 |
7 | The LP problem is transformed into standard form. Lower bounds are eliminated via a shift. Upper bounds are integrated by addition of new equations. Negative right hand size are eliminated by multiplication of the row with -1.
8 |
9 | The implemented simplex algorithm is as follows. The current basis solution is calculated by solving the system of linear equations `A_B*x_B=b` with a QR decomposition from the cuSolver library. The basis solution can also be calculated by updating the old basis solution via `x_B_i=x_B_i-s_i*x_B_row/s_row, x_B_row=x_B_row/s_row$`. Afterwards reduced costs are calculated in two steps. First the system of linear equations `A_B^T*s=c_B` is solved with QR decomposition. The routine can't handle matrix transpose implicitly, so the CSR matrix is transposed explicitly by converting it into a CSC format and reinterpreting it as CSR format. Afterwards the reduced costs are calculated with a matrix-vector product with cuSparse library `g=A_NB^T*s-c_NB`. The outgoing variable is chosen via Dantzig's or steepest-edge rule. Dantzig's rule chooses the variable with the most negative reduced cost `column={i|min{g_i}, g_i<0}`. This is implemented as a parallel reduction over the values of `g`. The values aren't compared directly to zero but rather to a small tolerance like `-10^-12`. This is necessary because of numerical inaccuracy whereas very small values can arise that would be zero when solved exactly. The steepest-edge rule scales the values of `g` with the norm of the corresponding column of the basis matrix `g_i=g_i/||A_NB_i||`. The norm is calculated as the square root of the sum of squares `||v||=sum_i v_i^2` with the CSR representation. For this purpose the square of each element is added atomically on the corresponding position. After all elements are processed the values of the vector `g` are divided by the square root of the calculated values. The steepest edge rule has in general a better convergence behaviour and therefore takes less iterations. Here the smallest negative value is also used which is calculated by a parallel reduction. The current solution is optimal if such a value isn't found. The entering variable is calculated with the minimum ratio test. Therefore the equation system `A_B*s=A_NB_column` is solved by with a QR decomposition from the cuSolver library. The needed column of the non nonbasic matrix is copied from the array representation. The entering column is calculated by a parallel reduction of the ratio of basic variable and the corresponding values of `s`: `row={i|min{x_B_i/s_i}, s_i>0}`. The values of `s` are also not directly checked for positivity but rather if they are above a certain tolerance like `10^-12`. The lp problem is unbounded if such a value isn't found. After choosing entering and leaving variable, the data structures need to be updated. For this the corresponding columns in the array format of basic and nonbasic matrix are swapped. Afterwards the CSR representation is updated. Also the corresponding entries in basic and nonbasic objective function values are swapped.
10 |
11 | ## Build
12 |
13 | ```
14 | nvcc -o cuda-revised-simplex src/*.cu -lcusolver -lcusparse -lglpk -arch=sm_35 --relocatable-device-code=true -O3
15 | ```
16 |
17 | ## Run
18 |
19 | ```
20 | ./cuda-revised-simplex simpleProblem.mps
21 | ```
22 |
23 | The solution for the simple example should be 3.3333 for X8 (index [7]) (the objective function). Different values are possible for other variables because the problem has multiple optimal solutions.
24 |
--------------------------------------------------------------------------------
/simpleProblem.mps:
--------------------------------------------------------------------------------
1 | NAME MINIEXAMPLE
2 | ROWS
3 | N COST
4 | E EQ1
5 | E EQ2
6 | E EQ3
7 | E EQ4
8 | COLUMNS
9 | X1 EQ1 1
10 | X2 EQ1 -2 EQ2 1
11 | X3 EQ2 -1 EQ4 1
12 | X4 EQ1 -2 EQ3 1
13 | X5 EQ3 -1 EQ4 1
14 | X6 EQ3 1 EQ4 -1
15 | X7 EQ4 1
16 | X8 COST 1 EQ1 -1
17 | X8 EQ3 -2 EQ4 -2
18 | RHS
19 | BOUNDS
20 | UP BND1 X1 10
21 | UP BND1 X2 1000
22 | UP BND1 X3 1000
23 | UP BND1 X4 1000
24 | UP BND1 X5 1000
25 | LO BND1 X6 -1000
26 | UP BND1 X6 1000
27 | LO BND1 X7 -1000
28 | UP BND1 X7 10
29 | UP BND1 X8 1000
30 | ENDATA
31 |
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/src/cudaCheck.cuh:
--------------------------------------------------------------------------------
1 | /**
2 | * Defines CUDA runtime error checking
3 | */
4 |
5 | #ifndef CUDACHECK_CUH_
6 | #define CUDACHECK_CUH_
7 |
8 | #include
9 | #include
10 | #include
11 | #include
12 |
13 | //#define NDEBUG // include to remove asserts and cudaCheck
14 | #define cudaCheck(call) __cudaCheck(call, __FILE__, __LINE__)
15 |
16 | inline void __cudaCheck(cudaError err, const char* file, int line) {
17 | #ifndef NDEBUG
18 | if (err != cudaSuccess) {
19 | fprintf(stderr, "%s(%d): CUDA error: %s\n", file, line,
20 | cudaGetErrorString(err));
21 | exit(EXIT_FAILURE);
22 | }
23 | #endif
24 | }
25 |
26 | #define cuSparseCheck(call) __cuSparseCheck(call, __FILE__, __LINE__)
27 |
28 | inline void __cuSparseCheck(cusparseStatus_t err, const char* file, int line) {
29 | #ifndef NDEBUG
30 | if (err != CUSPARSE_STATUS_SUCCESS) {
31 | fprintf(stderr, "%s(%d): CUSPARSE error: %s\n", file, line, err);
32 | exit(EXIT_FAILURE);
33 | }
34 | #endif
35 | }
36 |
37 | #define cuSolverCheck(call) __cuSolverCheck(call, __FILE__, __LINE__)
38 |
39 | inline void __cuSolverCheck(cusolverStatus_t err, const char* file, int line) {
40 | #ifndef NDEBUG
41 | if (err != CUSOLVER_STATUS_SUCCESS) {
42 | fprintf(stderr, "%s(%d): CUSOLVER error: %s\n", file, line, err);
43 | exit(EXIT_FAILURE);
44 | }
45 | #endif
46 | }
47 |
48 | #endif /* CUDACHECK_CUH_ */
49 |
--------------------------------------------------------------------------------
/src/lpProblem.cu:
--------------------------------------------------------------------------------
1 | /**
2 | * Implements LP problem
3 | */
4 |
5 | #include
6 | #include
7 |
8 | #include "cudaCheck.cuh"
9 | #include "lpProblem.cuh"
10 | #include "print.cuh"
11 |
12 | void readMPS(char *mpsFile, LPProblem *lpProblem) {
13 | glp_prob *lp = glp_create_prob();
14 | glp_read_mps(lp, GLP_MPS_FILE, NULL, mpsFile);
15 | lpProblem->rows = glp_get_num_rows(lp);
16 | lpProblem->columns = glp_get_num_cols(lp);
17 | lpProblem->nnz = glp_get_num_nz(lp);
18 | lpProblem->isBasisAllocated = false;
19 |
20 |
21 | cudaCheck(
22 | cudaMallocManaged(&lpProblem->A, lpProblem->rows * lpProblem->columns * sizeof(double)));
23 | cudaCheck(cudaMallocManaged(&lpProblem->b, lpProblem->rows * sizeof(double)));
24 | cudaCheck(cudaMallocManaged(&lpProblem->c, lpProblem->columns * sizeof(double)));
25 | cudaCheck(
26 | cudaMallocManaged(&lpProblem->lowerBound,
27 | lpProblem->columns * sizeof(double)));
28 | cudaCheck(
29 | cudaMallocManaged(&lpProblem->upperBound,
30 | lpProblem->columns * sizeof(double)));
31 |
32 | for (int32_t i = 0; i < lpProblem->rows * lpProblem->columns; i++) {
33 | lpProblem->A[i] = 0.;
34 | }
35 | int32_t *indices = (int32_t *) malloc(lpProblem->columns * sizeof(int32_t));
36 | double *values = (double *) malloc(lpProblem->columns * sizeof(double));
37 | // for glpk i + 1 (indices one-based)
38 | for (int32_t i = 0; i < lpProblem->rows; i++) {
39 | if (glp_get_row_type(lp, i + 1) == GLP_FR) {
40 | // ignore cost row
41 | printf("shouldn't be here!!\n");
42 | continue;
43 | }
44 | int32_t numberValues = glp_get_mat_row(lp, i + 1, indices, values);
45 | for (uint32_t j = 0; j < numberValues; j++) {
46 | lpProblem->A[i * lpProblem->columns + indices[j + 1] - 1] = values[j + 1];
47 | }
48 | }
49 | free(indices);
50 | free(values);
51 |
52 | for (int32_t i = 0; i < lpProblem->rows; i++) {
53 | // constraints are expected to be in form A*x=b
54 | if (glp_get_row_type(lp, i + 1) == GLP_FX) {
55 | lpProblem->b[i] = glp_get_row_lb(lp, i + 1);
56 | } else {
57 | printf("Can only handle constraints in form A*x=b!");
58 | exit(EXIT_FAILURE);
59 | }
60 | }
61 |
62 | for (uint32_t i = 0; i < lpProblem->columns; i++) {
63 | lpProblem->c[i] = glp_get_obj_coef(lp, i + 1);
64 | }
65 |
66 | for (int32_t i = 0; i < lpProblem->columns; i++) {
67 | lpProblem->lowerBound[i] = glp_get_col_lb(lp, i + 1);
68 | lpProblem->upperBound[i] = glp_get_col_ub(lp, i + 1);
69 | }
70 |
71 | glp_delete_prob(lp);
72 | glp_free_env();
73 | }
74 |
75 | void convertToStandardform(LPProblem *source, LPProblem *converted) {
76 | converted->isBasisAllocated = source->isBasisAllocated;
77 | converted->rows= source->rows + source->columns;
78 | converted->columns = source->columns * 2;
79 | converted->nnz = source->nnz + source->columns * 2;
80 | cudaCheck(cudaMallocManaged(&converted->A, converted->rows * converted->columns * sizeof(double)));
81 | for (int32_t i = 0; i < converted->rows; i++) {
82 | for (int32_t j = 0; j < converted->columns; j++) {
83 | if (i < source->rows && j < source->columns) {
84 | converted->A[i * converted->columns + j] = source->A[i * source->columns + j];
85 | } else if(i < source->rows) {
86 | converted->A[i * converted->columns + j] = 0;
87 | } else if(j < source->columns) {
88 | if (i - source->rows == j) {
89 | converted->A[i * converted->columns + j] = 1;
90 | } else {
91 | converted->A[i * converted->columns + j] = 0;
92 | }
93 | } else {
94 | if (i - source->rows == j - source->columns) {
95 | converted->A[i * converted->columns + j] = 1;
96 | } else {
97 | converted->A[i * converted->columns + j] = 0;
98 | }
99 | }
100 | }
101 | }
102 | cudaCheck(cudaMallocManaged(&converted->b, converted->rows * sizeof(double)));
103 | for (int32_t i = 0; i < converted->rows; i++) {
104 | if (i < source->rows) {
105 | converted->b[i] = source->b[i];
106 | for (int32_t j = 0; j < source->columns; j++) {
107 | converted->b[i] -= source->A[i * source->columns + j] * source->lowerBound[j];
108 | }
109 | } else {
110 | converted->b[i] = source->upperBound[i - source->rows] - source->lowerBound[i - source->rows];
111 | }
112 | if (converted->b[i] < 0) {
113 | converted->b[i] = -converted->b[i];
114 | for (int j = 0; j < converted->columns; j++) {
115 | converted->A[i * converted->columns + j] = -converted->A[i * converted->columns + j];
116 | }
117 | }
118 | }
119 | cudaCheck(cudaMallocManaged(&converted->c, converted->columns * sizeof(double)));
120 | for (int32_t i = 0; i < converted->columns; i++) {
121 | if (i < source->columns) {
122 | converted->c[i] = source->c[i];
123 | } else {
124 | converted->c[i] = 0;
125 | }
126 | }
127 | }
128 |
129 | void copyLPProblem(LPProblem *source, LPProblem *destination) {
130 | if (source->isBasisAllocated) {
131 | initializeLPProblem(destination, source->rows, source->columns, source->nnz);
132 | destination->isBasisAllocated = true;
133 | destination->rows = source->rows;
134 | destination->columns = source->columns;
135 | destination->nnz = source->nnz;
136 | cudaCheck(cudaMemcpy(destination->A, source->A, destination->rows * destination->columns * sizeof(double), cudaMemcpyDeviceToDevice));
137 | cudaCheck(cudaMemcpy(destination->b, source->b, destination->rows * sizeof(double), cudaMemcpyDeviceToDevice));
138 | cudaCheck(cudaMemcpy(destination->c, source->c, destination->columns * sizeof(double), cudaMemcpyDeviceToDevice));
139 |
140 | destination->nnzAB = source->nnzAB;
141 | cudaCheck(cudaMemcpy(destination->AB, source->AB, destination->rows * destination->rows * sizeof(double), cudaMemcpyDeviceToDevice));
142 | cudaCheck(cudaMemcpy(destination->ABRowPointer, source->ABRowPointer, (destination->rows + 1) * sizeof(int32_t), cudaMemcpyDeviceToDevice));
143 | cudaCheck(cudaMemcpy(destination->ABColumnIndices, source->ABColumnIndices, destination->nnz * sizeof(int32_t), cudaMemcpyDeviceToDevice));
144 | cudaCheck(cudaMemcpy(destination->ABValues, source->ABValues, destination->nnz * sizeof(double), cudaMemcpyDeviceToDevice));
145 |
146 | cudaCheck(cudaMemcpy(destination->ABTRowPointer, source->ABTRowPointer, (destination->rows + 1) * sizeof(int32_t), cudaMemcpyDeviceToDevice));
147 | cudaCheck(cudaMemcpy(destination->ABTColumnIndices, source->ABTColumnIndices, destination->nnz * sizeof(int32_t), cudaMemcpyDeviceToDevice));
148 | cudaCheck(cudaMemcpy(destination->ABTValues, source->ABTValues, destination->nnz * sizeof(double), cudaMemcpyDeviceToDevice));
149 |
150 | destination->nnzANB = source->nnzANB;
151 | cudaCheck(cudaMemcpy(destination->ANB, source->ANB, destination->rows * (destination->columns - destination->rows) * sizeof(double), cudaMemcpyDeviceToDevice));
152 | cudaCheck(cudaMemcpy(destination->ANBRowPointer, source->ANBRowPointer, (destination->rows + 1) * sizeof(int32_t), cudaMemcpyDeviceToDevice));
153 | cudaCheck(cudaMemcpy(destination->ANBColumnIndices, source->ANBColumnIndices, destination->nnz * sizeof(int32_t), cudaMemcpyDeviceToDevice));
154 | cudaCheck(cudaMemcpy(destination->ANBValues, source->ANBValues, destination->nnz * sizeof(double), cudaMemcpyDeviceToDevice));
155 |
156 | cudaCheck(cudaMemcpy(destination->cB, source->cB, destination->rows * sizeof(double), cudaMemcpyDeviceToDevice));
157 | cudaCheck(cudaMemcpy(destination->cBIndex, source->cBIndex, destination->rows * sizeof(int32_t), cudaMemcpyDeviceToDevice));
158 | cudaCheck(cudaMemcpy(destination->cNB, source->cNB, (destination->columns - destination->rows) * sizeof(double), cudaMemcpyDeviceToDevice));
159 | cudaCheck(cudaMemcpy(destination->cNBIndex, source->cNBIndex, (destination->columns - destination->rows) * sizeof(int32_t), cudaMemcpyDeviceToDevice));
160 |
161 |
162 | cudaCheck(cudaMemcpy(destination->xB, source->xB, destination->rows * sizeof(double), cudaMemcpyDeviceToDevice));
163 | cudaCheck(cudaMemcpy(destination->xIndex, source->xIndex, destination->columns * sizeof(int32_t), cudaMemcpyDeviceToDevice));
164 | cudaCheck(cudaMemcpy(destination->lowerBound, source->lowerBound, destination->columns * sizeof(double), cudaMemcpyDeviceToDevice));
165 | cudaCheck(cudaMemcpy(destination->upperBound, source->upperBound, destination->columns * sizeof(double), cudaMemcpyDeviceToDevice));
166 | } else {
167 | destination->isBasisAllocated = false;
168 | destination->rows = source->rows;
169 | destination->columns = source->columns;
170 | destination->nnz = source->nnz;
171 | cudaCheck(cudaMallocManaged(&destination->A, destination->rows * destination->columns * sizeof(double)));
172 | cudaCheck(cudaMemcpy(destination->A, source->A, destination->rows * destination->columns * sizeof(double), cudaMemcpyDeviceToDevice));
173 | cudaCheck(cudaMallocManaged(&destination->b, destination->rows * sizeof(double)));
174 | cudaCheck(cudaMemcpy(destination->b, source->b, destination->rows * sizeof(double), cudaMemcpyDeviceToDevice));
175 | cudaCheck(cudaMallocManaged(&destination->c, destination->columns * sizeof(double)));
176 | cudaCheck(cudaMemcpy(destination->c, source->c, destination->columns * sizeof(double), cudaMemcpyDeviceToDevice));
177 | }
178 | }
179 |
180 | void deleteLPProblem(LPProblem *lpProblem) {
181 | cudaFree(lpProblem->A);
182 | cudaFree(lpProblem->b);
183 | cudaFree(lpProblem->c);
184 | cudaFree(lpProblem->lowerBound);
185 | cudaFree(lpProblem->upperBound);
186 | if (lpProblem->isBasisAllocated) {
187 | cudaFree(lpProblem->AB);
188 | cudaFree(lpProblem->ABRowPointer);
189 | cudaFree(lpProblem->ABColumnIndices);
190 | cudaFree(lpProblem->ABValues);
191 | cudaFree(lpProblem->ABTRowPointer);
192 | cudaFree(lpProblem->ABTColumnIndices);
193 | cudaFree(lpProblem->ABTValues);
194 | cudaFree(lpProblem->ANB);
195 | cudaFree(lpProblem->ANBRowPointer);
196 | cudaFree(lpProblem->ANBColumnIndices);
197 | cudaFree(lpProblem->ANBValues);
198 | cudaFree(lpProblem->cB);
199 | cudaFree(lpProblem->cBIndex);
200 | cudaFree(lpProblem->cNB);
201 | cudaFree(lpProblem->cNBIndex);
202 | cudaFree(lpProblem->xB);
203 | cudaFree(lpProblem->xIndex);
204 | cudaFree(lpProblem->s);
205 | cudaFree(lpProblem->g);
206 | cudaFree(lpProblem->gTemp);
207 | cudaFree(lpProblem->ANBColumn);
208 | cudaFree(lpProblem->nnzPerRow);
209 | cudaFree(lpProblem->row);
210 | cudaFree(lpProblem->column);
211 | }
212 | free(lpProblem);
213 | }
214 |
215 | void initializeLPProblem(LPProblem *lpProblem, int32_t rows, int32_t columns,
216 | int32_t nnz) {
217 | lpProblem->isBasisAllocated = true;
218 | lpProblem->rows = rows;
219 | lpProblem->columns = columns;
220 | lpProblem->nnz = nnz;
221 | cudaCheck(
222 | cudaMallocManaged(&lpProblem->A, rows * columns * sizeof(double)));
223 | cudaCheck(cudaMallocManaged(&lpProblem->b, rows * sizeof(double)));
224 | cudaCheck(cudaMallocManaged(&lpProblem->c, columns * sizeof(double)));
225 | cudaCheck(
226 | cudaMallocManaged(&lpProblem->lowerBound,
227 | columns * sizeof(double)));
228 | cudaCheck(
229 | cudaMallocManaged(&lpProblem->upperBound,
230 | columns * sizeof(double)));
231 |
232 | cudaCheck(cudaMallocManaged(&lpProblem->AB, rows * rows * sizeof(double)));
233 | cudaCheck(
234 | cudaMallocManaged(&lpProblem->ABRowPointer,
235 | (rows + 1) * sizeof(int32_t)));
236 | cudaCheck(
237 | cudaMallocManaged(&lpProblem->ABColumnIndices,
238 | nnz * sizeof(int32_t)));
239 | cudaCheck(cudaMallocManaged(&lpProblem->ABValues, nnz * sizeof(double)));
240 |
241 | cudaCheck(
242 | cudaMallocManaged(&lpProblem->ABTRowPointer,
243 | (rows + 1) * sizeof(int32_t)));
244 | cudaCheck(
245 | cudaMallocManaged(&lpProblem->ABTColumnIndices,
246 | nnz * sizeof(int32_t)));
247 | cudaCheck(cudaMallocManaged(&lpProblem->ABTValues, nnz * sizeof(double)));
248 |
249 | cudaCheck(
250 | cudaMallocManaged(&lpProblem->ANB,
251 | rows * (columns - rows) * sizeof(double)));
252 | cudaCheck(
253 | cudaMallocManaged(&lpProblem->ANBRowPointer,
254 | (rows + 1) * sizeof(int32_t)));
255 | cudaCheck(
256 | cudaMallocManaged(&lpProblem->ANBColumnIndices,
257 | nnz * sizeof(int32_t)));
258 | cudaCheck(cudaMallocManaged(&lpProblem->ANBValues, nnz * sizeof(double)));
259 |
260 | cudaCheck(cudaMallocManaged(&lpProblem->cB, rows * sizeof(double)));
261 | cudaCheck(cudaMallocManaged(&lpProblem->cBIndex, rows * sizeof(int32_t)));
262 | cudaCheck(
263 | cudaMallocManaged(&lpProblem->cNB,
264 | (columns - rows) * sizeof(double)));
265 | cudaCheck(
266 | cudaMallocManaged(&lpProblem->cNBIndex,
267 | (columns - rows) * sizeof(int32_t)));
268 |
269 | cudaCheck(cudaMallocManaged(&lpProblem->xB, rows * sizeof(double)));
270 | cudaCheck(cudaMallocManaged(&lpProblem->xIndex, columns * sizeof(int32_t)));
271 | cudaCheck(cudaMallocManaged(&lpProblem->s, rows * sizeof(double)));
272 | cudaCheck(
273 | cudaMallocManaged(&lpProblem->g,
274 | (columns - rows) * sizeof(double)));
275 | cudaCheck(
276 | cudaMallocManaged(&lpProblem->gTemp,
277 | (columns - rows) * sizeof(double)));
278 | cudaCheck(cudaMallocManaged(&lpProblem->ANBColumn, rows * sizeof(double)));
279 | cudaCheck(cudaMallocManaged(&lpProblem->nnzPerRow, rows * sizeof(int32_t)));
280 |
281 | cudaCheck(cudaMallocManaged(&lpProblem->row, sizeof(int32_t)));
282 | cudaCheck(cudaMallocManaged(&lpProblem->column, sizeof(int32_t)));
283 | }
284 |
--------------------------------------------------------------------------------
/src/lpProblem.cuh:
--------------------------------------------------------------------------------
1 | /**
2 | * Defines LP Problem.
3 | */
4 |
5 | #ifndef LPPROBLEM_CUH_
6 | #define LPPROBLEM_CUH_
7 |
8 | #include
9 | #include
10 |
11 | typedef struct LPProblem {
12 | bool isBasisAllocated;
13 | bool isOptimal;
14 | bool isUnbounded;
15 | bool isSolution;
16 |
17 | int32_t rows;
18 | int32_t columns;
19 | int32_t nnz;
20 | double *A;
21 |
22 | int32_t nnzAB;
23 | double *AB;
24 | int32_t *ABRowPointer;
25 | int32_t *ABColumnIndices;
26 | double *ABValues;
27 |
28 | int32_t *ABTRowPointer;
29 | int32_t *ABTColumnIndices;
30 | double *ABTValues;
31 |
32 | int32_t nnzANB;
33 | double *ANB;
34 | int32_t *ANBRowPointer;
35 | int32_t *ANBColumnIndices;
36 | double *ANBValues;
37 |
38 | double *b;
39 |
40 | double *c;
41 | double *cB;
42 | int32_t *cBIndex;
43 | double *cNB;
44 | int32_t *cNBIndex;
45 |
46 | double *xB;
47 | int32_t *xIndex;
48 | double *lowerBound;
49 | double *upperBound;
50 |
51 | double *s;
52 | double *g;
53 | double *gTemp;
54 | double *ANBColumn;
55 | int32_t *nnzPerRow;
56 | int32_t *row;
57 | int32_t *column;
58 | } LPProblem;
59 |
60 | void readMPS(char *mpsFile, LPProblem *lpProblem);
61 |
62 | void convertToStandardform(LPProblem *source, LPProblem *converted);
63 |
64 | void copyLPProblem(LPProblem *source, LPProblem *destination);
65 |
66 | void deleteLPProblem(LPProblem *lpProblem);
67 |
68 | void initializeLPProblem(LPProblem *lpProblem, int32_t rows, int32_t columns,
69 | int32_t nnz);
70 |
71 | #endif /* LPPROBLEM_CUH_ */
72 |
--------------------------------------------------------------------------------
/src/main.cu:
--------------------------------------------------------------------------------
1 | #include
2 | #include
3 | #include
4 |
5 | #include "cudaCheck.cuh"
6 | #include "lpProblem.cuh"
7 | #include "print.cuh"
8 | #include "simplex.cuh"
9 |
10 | int32_t main(int32_t argc, char *argv[]) {
11 | cusolverSpHandle_t cusolverHandle;
12 | cuSolverCheck(cusolverSpCreate(&cusolverHandle));
13 | cusparseHandle_t cusparseHandle;
14 | cuSparseCheck(cusparseCreate(&cusparseHandle));
15 |
16 | cusparseMatDescr_t matrixDescriptor;
17 | cuSparseCheck(cusparseCreateMatDescr(&matrixDescriptor));
18 | cuSparseCheck(
19 | cusparseSetMatType(matrixDescriptor, CUSPARSE_MATRIX_TYPE_GENERAL));
20 | cuSparseCheck(
21 | cusparseSetMatIndexBase(matrixDescriptor,
22 | CUSPARSE_INDEX_BASE_ZERO));
23 |
24 | LPProblem *lpProblem = (LPProblem *) malloc(sizeof(LPProblem));
25 | readMPS(argv[1], lpProblem);
26 | LPProblem *lpProblemMod = (LPProblem *) malloc(sizeof(LPProblem));
27 | convertToStandardform(lpProblem, lpProblemMod);
28 | findBFS(lpProblemMod, cusolverHandle, cusparseHandle, matrixDescriptor);
29 | LPProblem *lpProblemCopy = (LPProblem *) malloc(sizeof(LPProblem));
30 | copyLPProblem(lpProblemMod, lpProblemCopy);
31 | deleteLPProblem(lpProblem);
32 | deleteLPProblem(lpProblemMod);
33 | deleteLPProblem(lpProblemCopy);
34 |
35 | cudaCheck(cudaDeviceReset());
36 |
37 | return EXIT_SUCCESS;
38 | }
39 |
--------------------------------------------------------------------------------
/src/print.cu:
--------------------------------------------------------------------------------
1 | /**
2 | * Implements print.
3 | */
4 |
5 | #include
6 |
7 | void printIntArray(int32_t *array, int32_t length) {
8 | for (int32_t i = 0; i < length; i++) {
9 | printf("%d,", array[i]);
10 | }
11 | printf("\n");
12 | }
13 |
14 | void printDoubleArray(double *array, int32_t length) {
15 | for (int32_t i = 0; i < length; i++) {
16 | printf("%g,", array[i]);
17 | }
18 | printf("\n");
19 | }
20 |
21 | void printCSRMatrix(int32_t *RowPointer, int32_t *ColumnIndices, double *Values,
22 | int32_t rows) {
23 | for (int32_t i = 0; i <= rows; i++) {
24 | printf("%d,", RowPointer[i]);
25 | }
26 | printf("\n");
27 | for (int32_t i = 0; i < RowPointer[rows]; i++) {
28 | printf("%d,", ColumnIndices[i]);
29 | }
30 | printf("\n");
31 | for (int32_t i = 0; i < RowPointer[rows]; i++) {
32 | printf("%g,", Values[i]);
33 | }
34 | printf("\n");
35 | }
36 |
37 | void printMatrix(double *matrix, int32_t rows, int32_t columns) {
38 | for (int32_t row = 0; row < rows; row++) {
39 | for (int32_t column = 0; column < columns; column++) {
40 | printf("%g,", matrix[row * columns + column]);
41 | }
42 | printf("\n");
43 | }
44 | }
45 |
--------------------------------------------------------------------------------
/src/print.cuh:
--------------------------------------------------------------------------------
1 | /**
2 | * Defines print.
3 | */
4 |
5 | #ifndef PRINT_CUH_
6 | #define PRINT_CUH_
7 |
8 | void printIntArray(int32_t *array, int32_t length);
9 |
10 | void printDoubleArray(double *array, int32_t length);
11 |
12 | void printCSRMatrix(int32_t *RowPointer, int32_t *ColumnIndices, double *Values,
13 | int32_t rows);
14 |
15 | void printMatrix(double *matrix, int32_t rows, int32_t columns);
16 |
17 | #endif /* PRINT_CUH_ */
18 |
--------------------------------------------------------------------------------
/src/simplex.cu:
--------------------------------------------------------------------------------
1 | /**
2 | * Implements simplex algorithm.
3 | */
4 |
5 | #include "simplex.cuh"
6 |
7 | #include
8 | #include
9 |
10 | #include "cudaCheck.cuh"
11 | #include "print.cuh"
12 |
13 | __device__ double atomicAdd(double *address, double val) {
14 | unsigned long long int* address_as_ull = (unsigned long long int*) address;
15 | unsigned long long int old = *address_as_ull, assumed;
16 | if (val == 0.0)
17 | return __longlong_as_double(old);
18 | do {
19 | assumed = old;
20 | old = atomicCAS(address_as_ull, assumed,
21 | __double_as_longlong(val + __longlong_as_double(assumed)));
22 | } while (assumed != old);
23 | return __longlong_as_double(old);
24 | }
25 |
26 | __device__ void minimumIndex(double *value1, int32_t *index1, double value2,
27 | int32_t index2) {
28 | if (*value1 > value2) {
29 | *value1 = value2;
30 | *index1 = index2;
31 | }
32 | }
33 |
34 | __device__ void warpReduceMinIndex(double *value, int32_t *index) {
35 | // see https://devblogs.nvidia.com/parallelforall/faster-parallel-reductions-kepler/
36 | for (int32_t offset = warpSize / 2; offset > 0; offset /= 2) {
37 | double shuffleValue = __shfl_down(*value, offset, warpSize);
38 | double shuffleIndex = __shfl_down(*index, offset, warpSize);
39 | minimumIndex(value, index, shuffleValue, shuffleIndex);
40 | };
41 | }
42 |
43 | __device__ void blockReduceMinGIndex(double *g, int32_t columns,
44 | double *blockData, int32_t *blockIndex, double *localData,
45 | int32_t *localIndex) {
46 | // see https://devblogs.nvidia.com/parallelforall/faster-parallel-reductions-kepler/
47 | int32_t warpIndex = threadIdx.x / warpSize;
48 | int32_t warpLane = threadIdx.x % warpSize;
49 |
50 | *localData = DBL_MAX;
51 | *localIndex = -1;
52 | for (int32_t i = threadIdx.x; i < columns; i += blockDim.x) {
53 | // not 0 because of numerical errors
54 | if (g[i] < -1.e-4) {
55 | minimumIndex(localData, localIndex, g[i], i);
56 | }
57 | }
58 | warpReduceMinIndex(localData, localIndex);
59 | if (warpLane == 0) {
60 | blockData[warpIndex] = *localData;
61 | blockIndex[warpIndex] = *localIndex;
62 | }
63 |
64 | __syncthreads();
65 |
66 | if (threadIdx.x < blockDim.x / warpSize) {
67 | *localData = blockData[warpLane];
68 | *localIndex = blockIndex[warpLane];
69 | } else {
70 | *localData = DBL_MAX;
71 | *localIndex = -1;
72 | }
73 | if (warpIndex == 0) {
74 | warpReduceMinIndex(localData, localIndex);
75 | }
76 | }
77 |
78 | __device__ void blockReduceMinSIndex(double *s, double *xB, int32_t rows,
79 | double *blockData, int32_t *blockIndex, double *localData,
80 | int32_t *localIndex) {
81 | // see https://devblogs.nvidia.com/parallelforall/faster-parallel-reductions-kepler/
82 | int32_t warpIndex = threadIdx.x / warpSize;
83 | int32_t warpLane = threadIdx.x % warpSize;
84 |
85 | *localData = DBL_MAX;
86 | *localIndex = -1;
87 | for (int32_t i = threadIdx.x; i < rows; i += blockDim.x) {
88 | // not 0 because of numerical errors
89 | if (s[i] > 1.e-4) {
90 | minimumIndex(localData, localIndex, xB[i] / s[i], i);
91 | }
92 | }
93 | warpReduceMinIndex(localData, localIndex);
94 | if (warpLane == 0) {
95 | blockData[warpIndex] = *localData;
96 | blockIndex[warpIndex] = *localIndex;
97 | }
98 |
99 | __syncthreads();
100 |
101 | if (threadIdx.x < blockDim.x / warpSize) {
102 | *localData = blockData[warpLane];
103 | *localIndex = blockIndex[warpLane];
104 | } else {
105 | *localData = DBL_MAX;
106 | *localIndex = -1;
107 | }
108 | if (warpIndex == 0) {
109 | warpReduceMinIndex(localData, localIndex);
110 | }
111 | }
112 |
113 | __global__ void copyColumnDouble(double *fromMatrix, double *to, int32_t rows,
114 | int32_t columns, int32_t column) {
115 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
116 | for (int32_t i = id; i < rows; i += gridDim.x * blockDim.x) {
117 | to[i] = fromMatrix[i * columns + column];
118 | }
119 | }
120 |
121 | __global__ void copyColumnDouble2(double *fromANB, double *toANB, int32_t rows,
122 | int32_t fromColumns, int32_t toColumns, double *fromCNB, double *toCNB,
123 | int32_t *fromCNBIndex, int32_t *toCNBIndex, int32_t fromColumn, int32_t toColumn) {
124 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
125 | for (int32_t i = id; i < rows; i += gridDim.x * blockDim.x) {
126 | toANB[i * toColumns + toColumn] = fromANB[i * fromColumns + fromColumn];
127 | }
128 | if (id == 0) {
129 | toCNB[toColumn] = fromCNB[fromColumn];
130 | toCNBIndex[toColumn] = fromCNBIndex[fromColumn];
131 | }
132 | }
133 |
134 | __global__ void copyNegativeDouble(double *from, double *to, int32_t elements) {
135 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
136 | for (int32_t i = id; i < elements; i += gridDim.x * blockDim.x) {
137 | to[i] = -from[i];
138 | }
139 | }
140 |
141 | __global__ void minG(double *g, int32_t columns, int32_t *column) {
142 | extern __shared__ double blockData[];
143 | int32_t *blockIndex = (int32_t *) &blockData[blockDim.x / 32];
144 |
145 | double localData;
146 | int32_t localIndex;
147 | blockReduceMinGIndex(g, columns, blockData, blockIndex, &localData,
148 | &localIndex);
149 |
150 | if (threadIdx.x == 0) {
151 | *column = localIndex;
152 | }
153 | }
154 |
155 | __global__ void minS(double *s, double *xB, int32_t columns, int32_t *row) {
156 | extern __shared__ double blockData[];
157 | int32_t *blockIndex = (int32_t *) &blockData[blockDim.x / 32];
158 |
159 | double localData;
160 | int32_t localIndex;
161 | blockReduceMinSIndex(s, xB, columns, blockData, blockIndex, &localData,
162 | &localIndex);
163 |
164 | if (threadIdx.x == 0) {
165 | *row = localIndex;
166 | }
167 | }
168 |
169 | __global__ void steepestEdge(double *gTemp, int32_t *ANBColumnIndices,
170 | double *ANBValues, int32_t columns, int32_t nnz) {
171 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
172 | for (int32_t i = id; i < nnz; i += gridDim.x * blockDim.x) {
173 | atomicAdd(&gTemp[ANBColumnIndices[i]],
174 | ANBValues[ANBColumnIndices[i]]
175 | * ANBValues[ANBColumnIndices[i]]);
176 | }
177 | }
178 |
179 | __global__ void steepestEdge2(double *g, double *gTemp, int32_t columns) {
180 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
181 | for (int32_t i = id; i < columns; i += gridDim.x * blockDim.x) {
182 | g[i] *= rsqrt(gTemp[i]);
183 | }
184 | }
185 |
186 | __global__ void swapColumnDouble(double *AB, double *ANB, int32_t rows,
187 | int32_t columnsAB, int32_t columnsANB, int32_t columnAB, int32_t columnANB,
188 | double *cB, int32_t *cBIndex, double *cNB, int32_t *cNBIndex,
189 | int32_t *xIndex) {
190 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
191 | for (int32_t i = id; i < rows; i += gridDim.x * blockDim.x) {
192 | double temp = AB[i * columnsAB + columnAB];
193 | AB[i * columnsAB + columnAB] = ANB[i * columnsANB + columnANB];
194 | ANB[i * columnsANB + columnANB] = temp;
195 | }
196 |
197 | if (id == 0) {
198 | double tempValue = cB[columnAB];
199 | cB[columnAB] = cNB[columnANB];
200 | cNB[columnANB] = tempValue;
201 |
202 | int32_t tempIndex = cBIndex[columnAB];
203 | cBIndex[columnAB] = cNBIndex[columnANB];
204 | cNBIndex[columnANB] = tempIndex;
205 |
206 | tempIndex = xIndex[columnAB + columnsANB];
207 | xIndex[columnAB + columnsANB] = xIndex[columnANB];
208 | xIndex[columnANB] = tempIndex;
209 | }
210 | }
211 |
212 | __global__ void updateXB(double *xB, double *s, int32_t rows, int32_t row) {
213 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
214 | //xBi=xBi-si*xBrow/srow xBrow=xBrow/srow
215 | for (int32_t i = id; i < rows; i += gridDim.x * blockDim.x) {
216 | if (i == row) {
217 | xB[i] /= s[i];
218 | } else {
219 | xB[i] -= s[i] * xB[row] / s[row];
220 | }
221 | }
222 | }
223 |
224 | __global__ void zero(double *pointer, int32_t length) {
225 | int32_t id = blockIdx.x * blockDim.x + threadIdx.x;
226 | for (int32_t i = id; i < length; i += gridDim.x * blockDim.x) {
227 | pointer[i] = 0.;
228 | }
229 | }
230 |
231 | void findBFS(LPProblem *lpProblem, cusolverSpHandle_t cusolverHandle,
232 | cusparseHandle_t cusparseHandle, cusparseMatDescr_t matrixDescriptor) {
233 | LPProblem *lpTemp = (LPProblem *) malloc(sizeof(LPProblem));
234 | initializeLPProblem(lpTemp, lpProblem->rows, lpProblem->columns + lpProblem->rows, lpProblem->nnz + lpProblem->rows);
235 |
236 | lpTemp->isBasisAllocated = false;
237 | lpTemp->rows = lpProblem->rows;
238 | lpTemp->columns = lpProblem->columns + lpProblem->rows;
239 | lpTemp->nnz = lpProblem->nnz + lpProblem->rows;
240 | cudaCheck(cudaMemcpy(lpTemp->ANB, lpProblem->A, lpTemp->rows * (lpTemp->columns - lpTemp->rows)* sizeof(double), cudaMemcpyDeviceToDevice));
241 | cuSparseCheck(
242 | cusparseDnnz(cusparseHandle, CUSPARSE_DIRECTION_COLUMN, lpTemp->columns - lpTemp->rows, lpTemp->rows,
243 | matrixDescriptor, lpTemp->ANB, lpTemp->columns - lpTemp->rows, lpTemp->nnzPerRow,
244 | &lpTemp->nnzANB));
245 | cuSparseCheck(
246 | cusparseDdense2csc(cusparseHandle, lpTemp->columns - lpTemp->rows, lpTemp->rows,
247 | matrixDescriptor, lpTemp->ANB, lpTemp->columns - lpTemp->rows, lpTemp->nnzPerRow, lpTemp->ANBValues,
248 | lpTemp->ANBColumnIndices, lpTemp->ANBRowPointer));
249 | cudaCheck(cudaDeviceSynchronize());
250 | for (int32_t i = 0; i < lpTemp->rows; i++) {
251 | for (int32_t j = 0; j < lpTemp->rows; j++) {
252 | if (i == j) {
253 | lpTemp->AB[i * lpTemp->rows + j] = 1;
254 | } else {
255 | lpTemp->AB[i * lpTemp->rows + j] = 0;
256 | }
257 | }
258 | }
259 | cuSparseCheck(
260 | cusparseDnnz(cusparseHandle, CUSPARSE_DIRECTION_COLUMN, lpTemp->rows, lpTemp->rows,
261 | matrixDescriptor, lpTemp->AB, lpTemp->rows, lpTemp->nnzPerRow, &lpTemp->nnzAB));
262 | cuSparseCheck(
263 | cusparseDdense2csc(cusparseHandle, lpTemp->rows, lpTemp->rows, matrixDescriptor,
264 | lpTemp->AB, lpTemp->rows, lpTemp->nnzPerRow, lpTemp->ABValues, lpTemp->ABColumnIndices,
265 | lpTemp->ABRowPointer));
266 | cudaCheck(cudaMemcpy(lpTemp->b, lpProblem->b, lpTemp->rows * sizeof(double), cudaMemcpyDeviceToDevice));
267 | cudaCheck(cudaMemcpy(lpTemp->cNB, lpProblem->c, (lpTemp->columns - lpTemp->rows) * sizeof(double), cudaMemcpyDeviceToDevice));
268 | for (int32_t i = 0; i < lpTemp->columns - lpTemp->rows; i++) {
269 | lpTemp->cNBIndex[i] = i;
270 | }
271 | for (int32_t i = 0; i < lpTemp->rows; i++) {
272 | lpTemp->cBIndex[i] = i + lpTemp->columns - lpTemp->rows;
273 | lpTemp->cB[i] = -1000;
274 | }
275 | for (int32_t i = 0; i < lpTemp->columns; i++) {
276 | lpTemp->xIndex[i] = i;
277 | }
278 |
279 | simplex(cusolverHandle, cusparseHandle, matrixDescriptor, lpTemp->rows,
280 | lpTemp->columns, lpTemp->nnz, &lpTemp->nnzAB, lpTemp->AB,
281 | lpTemp->ABRowPointer, lpTemp->ABColumnIndices, lpTemp->ABValues,
282 | lpTemp->ABTRowPointer, lpTemp->ABTColumnIndices, lpTemp->ABTValues,
283 | &lpTemp->nnzANB, lpTemp->ANB, lpTemp->ANBRowPointer,
284 | lpTemp->ANBColumnIndices, lpTemp->ANBValues, lpTemp->b, lpTemp->cB,
285 | lpTemp->cBIndex, lpTemp->cNB, lpTemp->cNBIndex, lpTemp->xB,
286 | lpTemp->xIndex, lpTemp->s, lpTemp->g, lpTemp->gTemp,
287 | lpTemp->ANBColumn, lpTemp->nnzPerRow, lpTemp->row, lpTemp->column);
288 |
289 | for (int32_t i = 0; i < lpTemp->rows; i++) {
290 | if (lpTemp->cBIndex[i] < lpProblem->columns) {
291 | printf("[%d]%g(%d),", lpTemp->cBIndex[i], lpTemp->xB[i], lpProblem->columns);
292 | }
293 | }
294 | printf("\n");
295 |
296 | lpProblem->isSolution = true;
297 | for (int32_t i = 0; i < lpTemp->rows; i++) {
298 | if (lpTemp->cBIndex[i] >= lpProblem->columns) {
299 | lpProblem->isSolution = false;
300 | break;
301 | }
302 | }
303 |
304 | deleteLPProblem(lpTemp);
305 | }
306 |
307 | void simplex(cusolverSpHandle_t cusolverHandle, cusparseHandle_t cusparseHandle,
308 | cusparseMatDescr_t matrixDescriptor, int32_t rows, int32_t columns,
309 | int32_t nnz, int32_t *nnzAB, double *AB, int32_t *ABRowPointer,
310 | int32_t *ABColumnIndices, double *ABValues, int32_t *ABTRowPointer,
311 | int32_t *ABTColumnIndices, double *ABTValues, int32_t *nnzANB,
312 | double *ANB, int32_t *ANBRowPointer, int32_t *ANBColumnIndices,
313 | double *ANBValues, double *b, double *cB, int32_t *cBIndex, double *cNB,
314 | int32_t *cNBIndex, double *xB, int32_t *xIndex, double *s, double *g,
315 | double *gTemp, double *ANBColumn, int32_t *nnzPerRow, int32_t *row,
316 | int32_t *column) {
317 | double tolerance = 1.e-15;
318 | int32_t reorder = 0;
319 | int32_t singularity;
320 | double one = 1.;
321 |
322 | int32_t blockSize = 384;
323 | int32_t gridSize = 16;
324 |
325 | int32_t iteration = 0;
326 | while (true) {
327 | // AB*xB=b or xB_i=xB_i-s_i*xB_row/s_row xB_row=xB_row/s_row
328 | if (1) {//iteration % 10 == 0) {
329 | cuSolverCheck(
330 | cusolverSpDcsrlsvqr(cusolverHandle, rows, *nnzAB,
331 | matrixDescriptor, ABValues, ABRowPointer,
332 | ABColumnIndices, b, tolerance, reorder, xB,
333 | &singularity));
334 | if (singularity != -1) {
335 | printf("singularity at %d\n", singularity);
336 | }
337 | } else {
338 | cudaDeviceSynchronize();
339 | updateXB<<>>(xB, s, rows, *row);
340 | }
341 |
342 | // y*AB=cB (als ABT*s=cB)
343 | cuSparseCheck(
344 | cusparseDcsr2csc(cusparseHandle, rows, rows, *nnzAB, ABValues,
345 | ABRowPointer, ABColumnIndices, ABTValues,
346 | ABTColumnIndices, ABTRowPointer,
347 | CUSPARSE_ACTION_NUMERIC,
348 | cusparseGetMatIndexBase(matrixDescriptor)));
349 | cudaDeviceSynchronize();
350 | cuSolverCheck(
351 | cusolverSpDcsrlsvqr(cusolverHandle, rows, *nnzAB,
352 | matrixDescriptor, ABTValues, ABTRowPointer,
353 | ABTColumnIndices, cB, tolerance, reorder, s,
354 | &singularity));
355 | if (singularity != -1) {
356 | printf("singularity at %d\n", singularity);
357 | break;
358 | }
359 |
360 | // g=y*ANB-cNB (als g=ANBT*s-cNB)
361 | copyNegativeDouble<<>>(cNB, g, columns - rows);
362 | cuSparseCheck(
363 | cusparseDcsrmv(cusparseHandle, CUSPARSE_OPERATION_TRANSPOSE,
364 | rows, columns - rows, *nnzANB, &one, matrixDescriptor,
365 | ANBValues, ANBRowPointer, ANBColumnIndices, s, &one,
366 | g));
367 | // steepest edge g_i=g_i/||ANB_i||
368 | zero<<>>(gTemp, columns - rows);
369 | steepestEdge<<>>(gTemp, ANBColumnIndices,
370 | ANBValues, columns - rows, *nnzANB);
371 | steepestEdge2<<>>(g, gTemp, columns - rows);
372 |
373 | // column={i|min{g_i},g_i<0}
374 | minG<<<1, blockSize, blockSize / 32 * 2 * sizeof(double)>>>(g,
375 | columns - rows, column);
376 | cudaCheck(cudaDeviceSynchronize());
377 |
378 | // !column -> optimal
379 | if (*column == -1) {
380 | printf("optimal\n");
381 | break;
382 | }
383 |
384 | // AB*s=ANB_column
385 | copyColumnDouble<<>>(ANB, ANBColumn, rows,
386 | columns - rows, *column);
387 | cuSolverCheck(
388 | cusolverSpDcsrlsvqr(cusolverHandle, rows, *nnzAB,
389 | matrixDescriptor, ABValues, ABRowPointer,
390 | ABColumnIndices, ANBColumn, tolerance, reorder, s,
391 | &singularity));
392 | if (singularity != -1) {
393 | printf("singularity at %d\n", singularity);
394 | break;
395 | }
396 |
397 | // row={i|min{xB_i/s_i},s_i>0}
398 | minS<<<1, blockSize, blockSize / 32 * 2 * sizeof(double)>>>(s, xB, rows,
399 | row);
400 | cudaCheck(cudaDeviceSynchronize());
401 |
402 | // !row -> unbounded
403 | if (*row == -1) {
404 | printf("unbounded\n");
405 | break;
406 | }
407 |
408 | // swap/update variables
409 | // dense matrix is assumed to be stored in column-major format, need to transpose (implicitly via conversion to CSC format and reinterpreting as CSR)
410 | swapColumnDouble<<>>(AB, ANB, rows, rows, columns - rows, *row, *column, cB, cBIndex, cNB, cNBIndex,xIndex);
411 | cuSparseCheck(
412 | cusparseDnnz(cusparseHandle, CUSPARSE_DIRECTION_COLUMN, rows, rows,
413 | matrixDescriptor, AB, rows, nnzPerRow, nnzAB));
414 | cuSparseCheck(
415 | cusparseDdense2csc(cusparseHandle, rows, rows, matrixDescriptor,
416 | AB, rows, nnzPerRow, ABValues, ABColumnIndices,
417 | ABRowPointer));
418 | cuSparseCheck(
419 | cusparseDnnz(cusparseHandle, CUSPARSE_DIRECTION_COLUMN, columns - rows, rows,
420 | matrixDescriptor, ANB, columns - rows, nnzPerRow,
421 | nnzANB));
422 | cuSparseCheck(
423 | cusparseDdense2csc(cusparseHandle, columns - rows, rows,
424 | matrixDescriptor, ANB, columns - rows, nnzPerRow, ANBValues,
425 | ANBColumnIndices, ANBRowPointer));
426 |
427 | iteration++;
428 | }
429 |
430 | // solve exact
431 | cuSolverCheck(
432 | cusolverSpDcsrlsvqr(cusolverHandle, rows, *nnzAB,
433 | matrixDescriptor, ABValues, ABRowPointer,
434 | ABColumnIndices, b, tolerance, reorder, xB,
435 | &singularity));
436 | if (singularity != -1) {
437 | printf("singularity at %d\n", singularity);
438 | }
439 | }
440 |
--------------------------------------------------------------------------------
/src/simplex.cuh:
--------------------------------------------------------------------------------
1 | /**
2 | * Defines simplex algorithm.
3 | */
4 |
5 | #ifndef SIMPLEX_CUH_
6 | #define SIMPLEX_CUH_
7 |
8 | #include
9 | #include
10 | #include
11 |
12 | #include "lpProblem.cuh"
13 |
14 | __device__ double atomicAdd(double *address, double val);
15 |
16 | __device__ void minimumIndex(double *value1, int32_t *index1, double value2,
17 | int32_t index2);
18 |
19 | __device__ void warpReduceMinIndex(double *value, int32_t *index);
20 |
21 | __device__ void blockReduceMinGIndex(double *g, int32_t columns,
22 | double *blockData, int32_t *blockIndex, double *localData,
23 | int32_t *localIndex);
24 |
25 | __device__ void blockReduceMinSIndex(double *s, double *xB, int32_t rows,
26 | double *blockData, int32_t *blockIndex, double *localData,
27 | int32_t *localIndex);
28 |
29 | __global__ void copyColumnDouble(double *fromMatrix, double *to, int32_t rows,
30 | int32_t columns, int32_t column);
31 |
32 | __global__ void copyColumnDouble2(double *fromANB, double *toANB, int32_t rows,
33 | int32_t fromColumns, int32_t toColumns, double *fromCNB, double *toCNB,
34 | double *fromCNBIndex, double *toCNBIndex, int32_t fromColumn, int32_t toColumn);
35 |
36 | __global__ void copyNegativeDouble(double *from, double *to, int32_t elements);
37 |
38 | __global__ void minG(double *g, int32_t columns, int32_t *column);
39 |
40 | __global__ void minS(double *s, double *xB, int32_t columns, int32_t *row);
41 |
42 | __global__ void steepestEdge(double *gTemp, int32_t *ANBColumnIndices,
43 | double *ANBValues, int32_t columns, int32_t nnz);
44 |
45 | __global__ void steepestEdge2(double *g, double *gTemp, int32_t columns);
46 |
47 | __global__ void swapColumnDouble(double *AB, double *ANB, int32_t rows,
48 | int32_t columnsAB, int32_t columnsANB, int32_t columnAB, int32_t columnANB,
49 | double *cB, int32_t *cBIndex, double *cNB, int32_t *cNBIndex,
50 | int32_t *xIndex);
51 |
52 | __global__ void updateXB(double *xB, double *s, int32_t rows, int32_t row);
53 |
54 | __global__ void zero(double *pointer, int32_t length);
55 |
56 | void findBFS(LPProblem *lpProblem, cusolverSpHandle_t cusolverHandle,
57 | cusparseHandle_t cusparseHandle, cusparseMatDescr_t matrixDescriptor);
58 |
59 | void simplex(cusolverSpHandle_t cusolverHandle, cusparseHandle_t cusparseHandle,
60 | cusparseMatDescr_t matrixDescriptor, int32_t rows, int32_t columns,
61 | int32_t nnz, int32_t *nnzAB, double *AB, int32_t *ABRowPointer,
62 | int32_t *ABColumnIndices, double *ABValues, int32_t *ABTRowPointer,
63 | int32_t *ABTColumnIndices, double *ABTValues, int32_t *nnzANB,
64 | double *ANB, int32_t *ANBRowPointer, int32_t *ANBColumnIndices,
65 | double *ANBValues, double *b, double *cB, int32_t *cBIndex, double *cNB,
66 | int32_t *cNBIndex, double *xB, int32_t *xIndex, double *s, double *g,
67 | double *gTemp, double *ANBColumn, int32_t *nnzPerRow, int32_t *row,
68 | int32_t *column);
69 |
70 | #endif /* SIMPLEX_CUH_ */
71 |
--------------------------------------------------------------------------------