Actual source code: aijhipsparseband.hip.cpp
1: /*
2: AIJHIPSPARSE methods implemented with HIP kernels. Uses hipSparse/Thrust maps from AIJHIPSPARSE
3: Portions of this code are under:
4: Copyright (c) 2022 Advanced Micro Devices, Inc. All rights reserved.
5: */
6: #define PETSC_SKIP_SPINLOCK
8: #include <petscconf.h>
9: #include <../src/mat/impls/aij/seq/aij.h>
10: #include <../src/mat/impls/sbaij/seq/sbaij.h>
11: #undef VecType
12: #include <../src/mat/impls/aij/seq/seqhipsparse/hipsparsematimpl.h>
13: #define AIJBANDUSEGROUPS 1
14: #if defined(AIJBANDUSEGROUPS)
15: #include <hip/hip_cooperative_groups.h>
16: #endif
18: /*
19: LU BAND factorization with optimization for block diagonal (Nf blocks) in natural order (-mat_no_inode -pc_factor_mat_ordering_type rcm with Nf>1 fields)
21: requires:
22: structurally symmetric: fix with transpose/column meta data
23: */
25: static PetscErrorCode MatLUFactorSymbolic_SeqAIJHIPSPARSEBAND(Mat, Mat, IS, IS, const MatFactorInfo *);
26: static PetscErrorCode MatLUFactorNumeric_SeqAIJHIPSPARSEBAND(Mat, Mat, const MatFactorInfo *);
27: static PetscErrorCode MatSolve_SeqAIJHIPSPARSEBAND(Mat, Vec, Vec);
29: /*
30: The GPU LU factor kernel
31: */
32: __global__ void __launch_bounds__(1024, 1) mat_lu_factor_band_init_set_i(const PetscInt n, const int bw, int bi_csr[])
33: {
34: const PetscInt Nf = gridDim.x, Nblk = gridDim.y, nloc = n / Nf;
35: const PetscInt field = blockIdx.x, blkIdx = blockIdx.y;
36: const PetscInt nloc_i = (nloc / Nblk + !!(nloc % Nblk)), start_i = field * nloc + blkIdx * nloc_i, end_i = (start_i + nloc_i) > (field + 1) * nloc ? (field + 1) * nloc : (start_i + nloc_i);
38: // set i (row+1)
39: if (threadIdx.x + threadIdx.y + blockIdx.x + blockIdx.y == 0) bi_csr[0] = 0; // dummy at zero
40: for (int rowb = start_i + threadIdx.y; rowb < end_i; rowb += blockDim.y) { // rows in block by thread y
41: if (rowb < end_i && threadIdx.x == 0) {
42: PetscInt i = rowb + 1, ni = (rowb > bw) ? bw + 1 : i, n1L = ni * (ni - 1) / 2, nug = i * bw, n2L = bw * ((rowb > bw) ? (rowb - bw) : 0), mi = bw + rowb + 1 - n, clip = (mi > 0) ? mi * (mi - 1) / 2 + mi : 0;
43: bi_csr[rowb + 1] = n1L + nug - clip + n2L + i;
44: }
45: }
46: }
47: // copy AIJ to AIJ_BAND
48: __global__ void __launch_bounds__(1024, 1) mat_lu_factor_band_copy_aij_aij(const PetscInt n, const int bw, const PetscInt r[], const PetscInt ic[], const int ai_d[], const int aj_d[], const PetscScalar aa_d[], const int bi_csr[], PetscScalar ba_csr[])
49: {
50: const PetscInt Nf = gridDim.x, Nblk = gridDim.y, nloc = n / Nf;
51: const PetscInt field = blockIdx.x, blkIdx = blockIdx.y;
52: const PetscInt nloc_i = (nloc / Nblk + !!(nloc % Nblk)), start_i = field * nloc + blkIdx * nloc_i, end_i = (start_i + nloc_i) > (field + 1) * nloc ? (field + 1) * nloc : (start_i + nloc_i);
54: // zero B
55: if (threadIdx.x + threadIdx.y + blockIdx.x + blockIdx.y == 0) ba_csr[bi_csr[n]] = 0; // flop count at end
56: for (int rowb = start_i + threadIdx.y; rowb < end_i; rowb += blockDim.y) { // rows in block by thread y
57: if (rowb < end_i) {
58: PetscScalar *batmp = ba_csr + bi_csr[rowb];
59: const PetscInt nzb = bi_csr[rowb + 1] - bi_csr[rowb];
60: for (int j = threadIdx.x; j < nzb; j += blockDim.x) {
61: if (j < nzb) { batmp[j] = 0; }
62: }
63: }
64: }
66: // copy A into B with CSR format -- these two loops can be fused
67: for (int rowb = start_i + threadIdx.y; rowb < end_i; rowb += blockDim.y) { // rows in block by thread y
68: if (rowb < end_i) {
69: const PetscInt rowa = r[rowb], nza = ai_d[rowa + 1] - ai_d[rowa];
70: const int *ajtmp = aj_d + ai_d[rowa], bjStart = (rowb > bw) ? rowb - bw : 0;
71: const PetscScalar *av = aa_d + ai_d[rowa];
72: PetscScalar *batmp = ba_csr + bi_csr[rowb];
73: /* load in initial (unfactored row) */
74: for (int j = threadIdx.x; j < nza; j += blockDim.x) {
75: if (j < nza) {
76: PetscInt colb = ic[ajtmp[j]], idx = colb - bjStart;
77: PetscScalar vala = av[j];
78: batmp[idx] = vala;
79: }
80: }
81: }
82: }
83: }
84: // print AIJ_BAND
85: __global__ void print_mat_aij_band(const PetscInt n, const int bi_csr[], const PetscScalar ba_csr[])
86: {
87: // debug
88: if (threadIdx.x + threadIdx.y + blockIdx.x + blockIdx.y == 0) {
89: printf("B (AIJ) n=%d:\n", (int)n);
90: for (int rowb = 0; rowb < n; rowb++) {
91: const PetscInt nz = bi_csr[rowb + 1] - bi_csr[rowb];
92: const PetscScalar *batmp = ba_csr + bi_csr[rowb];
93: for (int j = 0; j < nz; j++) printf("(%13.6e) ", PetscRealPart(batmp[j]));
94: printf(" bi=%d\n", bi_csr[rowb + 1]);
95: }
96: }
97: }
98: // Band LU kernel --- ba_csr bi_csr
99: __global__ void __launch_bounds__(1024, 1) mat_lu_factor_band(const PetscInt n, const PetscInt bw, const int bi_csr[], PetscScalar ba_csr[], int *use_group_sync)
100: {
101: const PetscInt Nf = gridDim.x, Nblk = gridDim.y, nloc = n / Nf;
102: const PetscInt field = blockIdx.x, blkIdx = blockIdx.y;
103: const PetscInt start = field * nloc, end = start + nloc;
104: #if defined(AIJBANDUSEGROUPS)
105: auto g = cooperative_groups::this_grid();
106: #endif
107: // A22 panel update for each row A(1,:) and col A(:,1)
108: for (int glbDD = start, locDD = 0; glbDD < end; glbDD++, locDD++) {
109: PetscInt tnzUd = bw, maxU = end - 1 - glbDD; // we are chopping off the inter ears
110: const PetscInt nzUd = (tnzUd > maxU) ? maxU : tnzUd, dOffset = (glbDD > bw) ? bw : glbDD; // global to go past ears after first
111: PetscScalar *pBdd = ba_csr + bi_csr[glbDD] + dOffset;
112: const PetscScalar *baUd = pBdd + 1; // vector of data U(i,i+1:end)
113: const PetscScalar Bdd = *pBdd;
114: const PetscInt offset = blkIdx * blockDim.y + threadIdx.y, inc = Nblk * blockDim.y;
115: if (threadIdx.x == 0) {
116: for (int idx = offset, myi = glbDD + offset + 1; idx < nzUd; idx += inc, myi += inc) { /* assuming symmetric structure */
117: const PetscInt bwi = myi > bw ? bw : myi, kIdx = bwi - (myi - glbDD); // cuts off just the first (global) block
118: PetscScalar *Aid = ba_csr + bi_csr[myi] + kIdx;
119: *Aid = *Aid / Bdd;
120: }
121: }
122: __syncthreads(); // synch on threadIdx.x only
123: for (int idx = offset, myi = glbDD + offset + 1; idx < nzUd; idx += inc, myi += inc) {
124: const PetscInt bwi = myi > bw ? bw : myi, kIdx = bwi - (myi - glbDD); // cuts off just the first (global) block
125: PetscScalar *Aid = ba_csr + bi_csr[myi] + kIdx;
126: PetscScalar *Aij = Aid + 1;
127: const PetscScalar Lid = *Aid;
128: for (int jIdx = threadIdx.x; jIdx < nzUd; jIdx += blockDim.x) { Aij[jIdx] -= Lid * baUd[jIdx]; }
129: }
130: #if defined(AIJBANDUSEGROUPS)
131: if (use_group_sync) {
132: g.sync();
133: } else {
134: __syncthreads();
135: }
136: #else
137: __syncthreads();
138: #endif
139: } /* endof for (i=0; i<n; i++) { */
140: }
142: static PetscErrorCode MatLUFactorNumeric_SeqAIJHIPSPARSEBAND(Mat B, Mat A, const MatFactorInfo *info)
143: {
144: Mat_SeqAIJ *b = (Mat_SeqAIJ *)B->data;
145: Mat_SeqAIJHIPSPARSETriFactors *hipsparseTriFactors = (Mat_SeqAIJHIPSPARSETriFactors *)B->spptr;
148: Mat_SeqAIJHIPSPARSE *hipsparsestructA = (Mat_SeqAIJHIPSPARSE *)A->spptr;
149: Mat_SeqAIJHIPSPARSEMultStruct *matstructA;
150: CsrMatrix *matrixA;
151: const PetscInt n = A->rmap->n, *ic, *r;
152: const int *ai_d, *aj_d;
153: const PetscScalar *aa_d;
154: PetscScalar *ba_t = hipsparseTriFactors->a_band_d;
155: int *bi_t = hipsparseTriFactors->i_band_d;
156: int Ni = 10, team_size = 9, Nf = 1, nVec = 56, nconcurrent = 1, nsm = -1; // Nf is batch size - not used
158: if (A->rmap->n == 0) return 0;
159: // hipsparse setup
161: matstructA = (Mat_SeqAIJHIPSPARSEMultStruct *)hipsparsestructA->mat; // matstruct->cprowIndices
163: matrixA = (CsrMatrix *)matstructA->mat;
166: // get data
167: ic = thrust::raw_pointer_cast(hipsparseTriFactors->cpermIndices->data());
168: ai_d = thrust::raw_pointer_cast(matrixA->row_offsets->data());
169: aj_d = thrust::raw_pointer_cast(matrixA->column_indices->data());
170: aa_d = thrust::raw_pointer_cast(matrixA->values->data().get());
171: r = thrust::raw_pointer_cast(hipsparseTriFactors->rpermIndices->data());
173: WaitForHIP();
174: PetscLogGpuTimeBegin();
175: {
176: int bw = (int)(2. * (double)n - 1. - (double)(PetscSqrtReal(1. + 4. * ((double)n * (double)n - (double)b->nz)) + PETSC_MACHINE_EPSILON)) / 2, bm1 = bw - 1, nl = n / Nf;
177: #if !defined(AIJBANDUSEGROUPS)
178: Ni = 1 / nconcurrent;
179: Ni = 1;
180: #else
181: if (!hipsparseTriFactors->init_dev_prop) {
182: int gpuid;
183: hipsparseTriFactors->init_dev_prop = PETSC_TRUE;
184: hipGetDevice(&gpuid);
185: hipGetDeviceProperties(&hipsparseTriFactors->dev_prop, gpuid);
186: }
187: nsm = hipsparseTriFactors->dev_prop.multiProcessorCount;
188: Ni = nsm / Nf / nconcurrent;
189: #endif
190: team_size = bw / Ni + !!(bw % Ni);
191: nVec = PetscMin(bw, 1024 / team_size);
192: PetscInfo(A, "Matrix Bandwidth = %d, number SMs/block = %d, num concurrency = %d, num fields = %d, numSMs/GPU = %d, thread group size = %d,%d\n", bw, Ni, nconcurrent, Nf, nsm, team_size, nVec);
193: {
194: dim3 dimBlockTeam(nVec, team_size);
195: dim3 dimBlockLeague(Nf, Ni);
196: hipLaunchKernelGGL(mat_lu_factor_band_copy_aij_aij, dim3(dimBlockLeague), dim3(dimBlockTeam), 0, 0, n, bw, r, ic, ai_d, aj_d, aa_d, bi_t, ba_t);
197: PetscHIPCheckLaunch; // does a sync
198: #if defined(AIJBANDUSEGROUPS)
199: if (Ni > 1) {
200: void *kernelArgs[] = {(void *)&n, (void *)&bw, (void *)&bi_t, (void *)&ba_t, (void *)&nsm};
201: hipLaunchCooperativeKernel((void *)mat_lu_factor_band, dimBlockLeague, dimBlockTeam, kernelArgs, 0, NULL);
202: } else {
203: hipLaunchKernelGGL(mat_lu_factor_band, dim3(dimBlockLeague), dim3(dimBlockTeam), 0, 0, n, bw, bi_t, ba_t, NULL);
204: }
205: #else
206: hipLaunchKernelGGL(mat_lu_factor_band, dim3(dimBlockLeague), dim3(dimBlockTeam), 0, 0, n, bw, bi_t, ba_t, NULL);
207: #endif
208: PetscHIPCheckLaunch; // does a sync
209: #if defined(PETSC_USE_LOG)
210: PetscLogGpuFlops((PetscLogDouble)Nf * (bm1 * (bm1 + 1) * (PetscLogDouble)(2 * bm1 + 1) / 3 + (PetscLogDouble)2 * (nl - bw) * bw * bw + (PetscLogDouble)nl * (nl + 1) / 2));
211: #endif
212: }
213: }
214: PetscLogGpuTimeEnd();
215: /* determine which version of MatSolve needs to be used. from MatLUFactorNumeric_AIJ_SeqAIJHIPSPARSE */
216: B->ops->solve = MatSolve_SeqAIJHIPSPARSEBAND;
217: B->ops->solvetranspose = NULL; /* need transpose */
218: B->ops->matsolve = NULL;
219: B->ops->matsolvetranspose = NULL;
220: return 0;
221: }
223: PetscErrorCode MatLUFactorSymbolic_SeqAIJHIPSPARSEBAND(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
224: {
225: Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data, *b;
226: IS isicol;
227: const PetscInt *ic, *ai = a->i, *aj = a->j;
228: PetscScalar *ba_t;
229: int *bi_t;
230: PetscInt i, n = A->rmap->n, Nf = 1; /* Nf batch size - not used */
231: PetscInt nzBcsr, bwL, bwU;
232: PetscBool missing;
233: Mat_SeqAIJHIPSPARSETriFactors *hipsparseTriFactors = (Mat_SeqAIJHIPSPARSETriFactors *)B->spptr;
236: MatMissingDiagonal(A, &missing, &i);
239: MatGetOption(A, MAT_STRUCTURALLY_SYMMETRIC, &missing);
241: ISInvertPermutation(iscol, PETSC_DECIDE, &isicol);
242: ISGetIndices(isicol, &ic);
243: MatSeqAIJSetPreallocation_SeqAIJ(B, MAT_SKIP_ALLOCATION, NULL);
244: PetscLogObjectParent((PetscObject)B, (PetscObject)isicol);
245: b = (Mat_SeqAIJ *)(B)->data;
247: /* get band widths, MatComputeBandwidth should take a reordering ic and do this */
248: bwL = bwU = 0;
249: for (int rwb = 0; rwb < n; rwb++) {
250: const PetscInt rwa = ic[rwb], anz = ai[rwb + 1] - ai[rwb], *ajtmp = aj + ai[rwb];
251: for (int j = 0; j < anz; j++) {
252: PetscInt colb = ic[ajtmp[j]];
253: if (colb < rwa) { // L
254: if (rwa - colb > bwL) bwL = rwa - colb;
255: } else {
256: if (colb - rwa > bwU) bwU = colb - rwa;
257: }
258: }
259: }
260: ISRestoreIndices(isicol, &ic);
261: /* only support structurally symmetric, but it might work */
263: MatSeqAIJHIPSPARSETriFactors_Reset(&hipsparseTriFactors);
264: nzBcsr = n + (2 * n - 1) * bwU - bwU * bwU;
265: b->maxnz = b->nz = nzBcsr;
266: hipsparseTriFactors->nnz = b->nz; // only meta data needed: n & nz
267: PetscInfo(A, "Matrix Bandwidth = %" PetscInt_FMT ", nnz = %" PetscInt_FMT "\n", bwL, b->nz);
268: if (!hipsparseTriFactors->workVector) hipsparseTriFactors->workVector = new THRUSTARRAY(n);
269: hipMalloc(&ba_t, (b->nz + 1) * sizeof(PetscScalar)); // include a place for flops
270: hipMalloc(&bi_t, (n + 1) * sizeof(int));
271: hipsparseTriFactors->a_band_d = ba_t;
272: hipsparseTriFactors->i_band_d = bi_t;
273: /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */
274: PetscLogObjectMemory((PetscObject)B, (nzBcsr + 1) * (sizeof(PetscInt) + sizeof(PetscScalar)));
275: {
276: dim3 dimBlockTeam(1, 128);
277: dim3 dimBlockLeague(Nf, 1);
278: hipLaunchKernelGGL(mat_lu_factor_band_init_set_i, dim3(dimBlockLeague), dim3(dimBlockTeam), 0, 0, n, bwU, bi_t);
279: }
280: PetscHIPCheckLaunch; // does a sync
282: // setup data
283: if (!hipsparseTriFactors->rpermIndices) {
284: const PetscInt *r;
285: ISGetIndices(isrow, &r);
286: hipsparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
287: hipsparseTriFactors->rpermIndices->assign(r, r + n);
288: ISRestoreIndices(isrow, &r);
289: PetscLogCpuToGpu(n * sizeof(PetscInt));
290: }
291: /* upper triangular indices */
292: if (!hipsparseTriFactors->cpermIndices) {
293: const PetscInt *c;
294: ISGetIndices(isicol, &c);
295: hipsparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
296: hipsparseTriFactors->cpermIndices->assign(c, c + n);
297: ISRestoreIndices(isicol, &c);
298: PetscLogCpuToGpu(n * sizeof(PetscInt));
299: }
301: /* put together the new matrix */
302: b->free_a = PETSC_FALSE;
303: b->free_ij = PETSC_FALSE;
304: b->singlemalloc = PETSC_FALSE;
305: b->ilen = NULL;
306: b->imax = NULL;
307: b->row = isrow;
308: b->col = iscol;
309: PetscObjectReference((PetscObject)isrow);
310: PetscObjectReference((PetscObject)iscol);
311: b->icol = isicol;
312: PetscMalloc1(n + 1, &b->solve_work);
314: B->factortype = MAT_FACTOR_LU;
315: B->info.factor_mallocs = 0;
316: B->info.fill_ratio_given = 0;
318: if (ai[n]) B->info.fill_ratio_needed = ((PetscReal)(nzBcsr)) / ((PetscReal)ai[n]);
319: else B->info.fill_ratio_needed = 0.0;
320: #if defined(PETSC_USE_INFO)
321: if (ai[n] != 0) {
322: PetscReal af = B->info.fill_ratio_needed;
323: PetscInfo(A, "Band fill ratio %g\n", (double)af);
324: } else PetscInfo(A, "Empty matrix\n");
325: #endif
326: if (a->inode.size) PetscInfo(A, "Warning: using inodes in band solver.\n");
327: MatSeqAIJCheckInode_FactorLU(B);
328: B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJHIPSPARSEBAND;
329: B->offloadmask = PETSC_OFFLOAD_GPU;
331: return 0;
332: }
334: /* Use -pc_factor_mat_solver_type hipsparseband */
335: PetscErrorCode MatFactorGetSolverType_seqaij_hipsparse_band(Mat A, MatSolverType *type)
336: {
337: *type = MATSOLVERHIPSPARSEBAND;
338: return 0;
339: }
341: PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijhipsparse_hipsparse_band(Mat A, MatFactorType ftype, Mat *B)
342: {
343: PetscInt n = A->rmap->n;
345: MatCreate(PetscObjectComm((PetscObject)A), B);
346: MatSetSizes(*B, n, n, n, n);
347: (*B)->factortype = ftype;
348: (*B)->canuseordering = PETSC_TRUE;
349: MatSetType(*B, MATSEQAIJHIPSPARSE);
351: if (ftype == MAT_FACTOR_LU) {
352: MatSetBlockSizesFromMats(*B, A, A);
353: (*B)->ops->ilufactorsymbolic = NULL; // MatILUFactorSymbolic_SeqAIJHIPSPARSE;
354: (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJHIPSPARSEBAND;
355: PetscStrallocpy(MATORDERINGRCM, (char **)&(*B)->preferredordering[MAT_FACTOR_LU]);
356: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor type not supported for HIPSPARSEBAND Matrix Types");
358: MatSeqAIJSetPreallocation(*B, MAT_SKIP_ALLOCATION, NULL);
359: PetscObjectComposeFunction((PetscObject)(*B), "MatFactorGetSolverType_C", MatFactorGetSolverType_seqaij_hipsparse_band);
360: return 0;
361: }
363: #define WARP_SIZE 32 // to be consistent with Nvidia terminology. WARP == Wavefront
364: template <typename T>
365: __forceinline__ __device__ T wreduce(T a)
366: {
367: T b;
368: #pragma unroll
369: for (int i = WARP_SIZE / 2; i >= 1; i = i >> 1) {
370: b = __shfl_down(0xffffffff, a, i);
371: a += b;
372: }
373: return a;
374: }
375: // reduce in a block, returns result in thread 0
376: template <typename T, int BLOCK_SIZE>
377: __device__ T breduce(T a)
378: {
379: constexpr int NWARP = BLOCK_SIZE / WARP_SIZE;
380: __shared__ double buf[NWARP];
381: int wid = threadIdx.x / WARP_SIZE;
382: int laneid = threadIdx.x % WARP_SIZE;
383: T b = wreduce<T>(a);
384: if (laneid == 0) buf[wid] = b;
385: __syncthreads();
386: if (wid == 0) {
387: if (threadIdx.x < NWARP) a = buf[threadIdx.x];
388: else a = 0;
389: for (int i = (NWARP + 1) / 2; i >= 1; i = i >> 1) { a += __shfl_down(0xffffffff, a, i); }
390: }
391: return a;
392: }
394: // Band LU kernel --- ba_csr bi_csr
395: template <int BLOCK_SIZE>
396: __global__ void __launch_bounds__(256, 1) mat_solve_band(const PetscInt n, const PetscInt bw, const PetscScalar ba_csr[], PetscScalar x[])
397: {
398: const PetscInt Nf = gridDim.x, nloc = n / Nf, field = blockIdx.x, start = field * nloc, end = start + nloc, chopnz = bw * (bw + 1) / 2, blocknz = (2 * bw + 1) * nloc, blocknz_0 = blocknz - chopnz;
399: const PetscScalar *pLi;
400: const int tid = threadIdx.x;
402: /* Next, solve L */
403: pLi = ba_csr + (field == 0 ? 0 : blocknz_0 + (field - 1) * blocknz + bw); // diagonal (0,0) in field
404: for (int glbDD = start, locDD = 0; glbDD < end; glbDD++, locDD++) {
405: const PetscInt col = locDD < bw ? start : (glbDD - bw);
406: PetscScalar t = 0;
407: for (int j = col + tid, idx = tid; j < glbDD; j += blockDim.x, idx += blockDim.x) { t += pLi[idx] * x[j]; }
408: #if defined(PETSC_USE_COMPLEX)
409: PetscReal tr = PetscRealPartComplex(t), ti = PetscImaginaryPartComplex(t);
410: PetscScalar tt(breduce<PetscReal, BLOCK_SIZE>(tr), breduce<PetscReal, BLOCK_SIZE>(ti));
411: t = tt;
412: #else
413: t = breduce<PetscReal, BLOCK_SIZE>(t);
414: #endif
415: if (threadIdx.x == 0) x[glbDD] -= t; // /1.0
416: __syncthreads();
417: // inc
418: pLi += glbDD - col; // get to diagonal
419: if (glbDD > n - 1 - bw) pLi += n - 1 - glbDD; // skip over U, only last block has funny offset
420: else pLi += bw;
421: pLi += 1; // skip to next row
422: if (field > 0 && (locDD + 1) < bw) pLi += bw - (locDD + 1); // skip padding at beginning (ear)
423: }
424: /* Then, solve U */
425: pLi = ba_csr + Nf * blocknz - 2 * chopnz - 1; // end of real data on block (diagonal)
426: if (field != Nf - 1) pLi -= blocknz_0 + (Nf - 2 - field) * blocknz + bw; // diagonal of last local row
428: for (int glbDD = end - 1, locDD = 0; glbDD >= start; glbDD--, locDD++) {
429: const PetscInt col = (locDD < bw) ? end - 1 : glbDD + bw; // end of row in U
430: PetscScalar t = 0;
431: for (int j = col - tid, idx = tid; j > glbDD; j -= blockDim.x, idx += blockDim.x) { t += pLi[-idx] * x[j]; }
432: #if defined(PETSC_USE_COMPLEX)
433: PetscReal tr = PetscRealPartComplex(t), ti = PetscImaginaryPartComplex(t);
434: PetscScalar tt(breduce<PetscReal, BLOCK_SIZE>(tr), breduce<PetscReal, BLOCK_SIZE>(ti));
435: t = tt;
436: #else
437: t = breduce<PetscReal, BLOCK_SIZE>(PetscRealPart(t));
438: #endif
439: pLi -= col - glbDD; // diagonal
440: if (threadIdx.x == 0) {
441: x[glbDD] -= t;
442: x[glbDD] /= pLi[0];
443: }
444: __syncthreads();
445: // inc past L to start of previous U
446: pLi -= bw + 1;
447: if (glbDD < bw) pLi += bw - glbDD; // overshot in top left corner
448: if (((locDD + 1) < bw) && field != Nf - 1) pLi -= (bw - (locDD + 1)); // skip past right corner
449: }
450: }
452: static PetscErrorCode MatSolve_SeqAIJHIPSPARSEBAND(Mat A, Vec bb, Vec xx)
453: {
454: const PetscScalar *barray;
455: PetscScalar *xarray;
456: thrust::device_ptr<const PetscScalar> bGPU;
457: thrust::device_ptr<PetscScalar> xGPU;
458: Mat_SeqAIJHIPSPARSETriFactors *hipsparseTriFactors = (Mat_SeqAIJHIPSPARSETriFactors *)A->spptr;
459: THRUSTARRAY *tempGPU = (THRUSTARRAY *)hipsparseTriFactors->workVector;
460: PetscInt n = A->rmap->n, nz = hipsparseTriFactors->nnz, Nf = 1; // Nf is batch size - not used
461: PetscInt bw = (int)(2. * (double)n - 1. - (double)(PetscSqrtReal(1. + 4. * ((double)n * (double)n - (double)nz)) + PETSC_MACHINE_EPSILON)) / 2; // quadric formula for bandwidth
463: if (A->rmap->n == 0) return 0;
465: /* Get the GPU pointers */
466: VecHIPGetArrayWrite(xx, &xarray);
467: VecHIPGetArrayRead(bb, &barray);
468: xGPU = thrust::device_pointer_cast(xarray);
469: bGPU = thrust::device_pointer_cast(barray);
471: PetscLogGpuTimeBegin();
472: /* First, reorder with the row permutation */
473: thrust::copy(thrust::hip::par.on(PetscDefaultHipStream), thrust::make_permutation_iterator(bGPU, hipsparseTriFactors->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, hipsparseTriFactors->rpermIndices->end()), tempGPU->begin());
474: constexpr int block = 128;
475: hipLaunchKernelGGL(HIP_KERNEL_NAME(mat_solve_band<block>), dim3(Nf), dim3(block), 0, 0, n, bw, hipsparseTriFactors->a_band_d, tempGPU->data().get());
476: PetscHIPCheckLaunch; // does a sync
478: /* Last, reorder with the column permutation */
479: thrust::copy(thrust::hip::par.on(PetscDefaultHipStream), thrust::make_permutation_iterator(tempGPU->begin(), hipsparseTriFactors->cpermIndices->begin()), thrust::make_permutation_iterator(tempGPU->begin(), hipsparseTriFactors->cpermIndices->end()), xGPU);
481: VecHIPRestoreArrayRead(bb, &barray);
482: VecHIPRestoreArrayWrite(xx, &xarray);
483: PetscLogGpuFlops(2.0 * hipsparseTriFactors->nnz - A->cmap->n);
484: PetscLogGpuTimeEnd();
486: return 0;
487: }