Actual source code: baijsolvnat7.c

  1: #include <../src/mat/impls/baij/seq/baij.h>
  2: #include <petsc/private/kernels/blockinvert.h>

  4: PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
  5: {
  6:   Mat_SeqBAIJ       *a    = (Mat_SeqBAIJ *)A->data;
  7:   const PetscInt    *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
  8:   PetscInt           i, nz, idx, idt, jdx;
  9:   const MatScalar   *aa = a->a, *v;
 10:   PetscScalar       *x, s1, s2, s3, s4, s5, s6, s7, x1, x2, x3, x4, x5, x6, x7;
 11:   const PetscScalar *b;

 13:   VecGetArrayRead(bb, &b);
 14:   VecGetArray(xx, &x);
 15:   /* forward solve the lower triangular */
 16:   idx  = 0;
 17:   x[0] = b[idx];
 18:   x[1] = b[1 + idx];
 19:   x[2] = b[2 + idx];
 20:   x[3] = b[3 + idx];
 21:   x[4] = b[4 + idx];
 22:   x[5] = b[5 + idx];
 23:   x[6] = b[6 + idx];
 24:   for (i = 1; i < n; i++) {
 25:     v   = aa + 49 * ai[i];
 26:     vi  = aj + ai[i];
 27:     nz  = diag[i] - ai[i];
 28:     idx = 7 * i;
 29:     s1  = b[idx];
 30:     s2  = b[1 + idx];
 31:     s3  = b[2 + idx];
 32:     s4  = b[3 + idx];
 33:     s5  = b[4 + idx];
 34:     s6  = b[5 + idx];
 35:     s7  = b[6 + idx];
 36:     while (nz--) {
 37:       jdx = 7 * (*vi++);
 38:       x1  = x[jdx];
 39:       x2  = x[1 + jdx];
 40:       x3  = x[2 + jdx];
 41:       x4  = x[3 + jdx];
 42:       x5  = x[4 + jdx];
 43:       x6  = x[5 + jdx];
 44:       x7  = x[6 + jdx];
 45:       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
 46:       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
 47:       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
 48:       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
 49:       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
 50:       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
 51:       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
 52:       v += 49;
 53:     }
 54:     x[idx]     = s1;
 55:     x[1 + idx] = s2;
 56:     x[2 + idx] = s3;
 57:     x[3 + idx] = s4;
 58:     x[4 + idx] = s5;
 59:     x[5 + idx] = s6;
 60:     x[6 + idx] = s7;
 61:   }
 62:   /* backward solve the upper triangular */
 63:   for (i = n - 1; i >= 0; i--) {
 64:     v   = aa + 49 * diag[i] + 49;
 65:     vi  = aj + diag[i] + 1;
 66:     nz  = ai[i + 1] - diag[i] - 1;
 67:     idt = 7 * i;
 68:     s1  = x[idt];
 69:     s2  = x[1 + idt];
 70:     s3  = x[2 + idt];
 71:     s4  = x[3 + idt];
 72:     s5  = x[4 + idt];
 73:     s6  = x[5 + idt];
 74:     s7  = x[6 + idt];
 75:     while (nz--) {
 76:       idx = 7 * (*vi++);
 77:       x1  = x[idx];
 78:       x2  = x[1 + idx];
 79:       x3  = x[2 + idx];
 80:       x4  = x[3 + idx];
 81:       x5  = x[4 + idx];
 82:       x6  = x[5 + idx];
 83:       x7  = x[6 + idx];
 84:       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
 85:       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
 86:       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
 87:       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
 88:       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
 89:       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
 90:       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
 91:       v += 49;
 92:     }
 93:     v          = aa + 49 * diag[i];
 94:     x[idt]     = v[0] * s1 + v[7] * s2 + v[14] * s3 + v[21] * s4 + v[28] * s5 + v[35] * s6 + v[42] * s7;
 95:     x[1 + idt] = v[1] * s1 + v[8] * s2 + v[15] * s3 + v[22] * s4 + v[29] * s5 + v[36] * s6 + v[43] * s7;
 96:     x[2 + idt] = v[2] * s1 + v[9] * s2 + v[16] * s3 + v[23] * s4 + v[30] * s5 + v[37] * s6 + v[44] * s7;
 97:     x[3 + idt] = v[3] * s1 + v[10] * s2 + v[17] * s3 + v[24] * s4 + v[31] * s5 + v[38] * s6 + v[45] * s7;
 98:     x[4 + idt] = v[4] * s1 + v[11] * s2 + v[18] * s3 + v[25] * s4 + v[32] * s5 + v[39] * s6 + v[46] * s7;
 99:     x[5 + idt] = v[5] * s1 + v[12] * s2 + v[19] * s3 + v[26] * s4 + v[33] * s5 + v[40] * s6 + v[47] * s7;
100:     x[6 + idt] = v[6] * s1 + v[13] * s2 + v[20] * s3 + v[27] * s4 + v[34] * s5 + v[41] * s6 + v[48] * s7;
101:   }

103:   VecRestoreArrayRead(bb, &b);
104:   VecRestoreArray(xx, &x);
105:   PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n);
106:   return 0;
107: }

109: PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering(Mat A, Vec bb, Vec xx)
110: {
111:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
112:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *adiag = a->diag;
113:   PetscInt           i, k, nz, idx, jdx, idt;
114:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
115:   const MatScalar   *aa = a->a, *v;
116:   PetscScalar       *x;
117:   const PetscScalar *b;
118:   PetscScalar        s1, s2, s3, s4, s5, s6, s7, x1, x2, x3, x4, x5, x6, x7;

120:   VecGetArrayRead(bb, &b);
121:   VecGetArray(xx, &x);
122:   /* forward solve the lower triangular */
123:   idx  = 0;
124:   x[0] = b[idx];
125:   x[1] = b[1 + idx];
126:   x[2] = b[2 + idx];
127:   x[3] = b[3 + idx];
128:   x[4] = b[4 + idx];
129:   x[5] = b[5 + idx];
130:   x[6] = b[6 + idx];
131:   for (i = 1; i < n; i++) {
132:     v   = aa + bs2 * ai[i];
133:     vi  = aj + ai[i];
134:     nz  = ai[i + 1] - ai[i];
135:     idx = bs * i;
136:     s1  = b[idx];
137:     s2  = b[1 + idx];
138:     s3  = b[2 + idx];
139:     s4  = b[3 + idx];
140:     s5  = b[4 + idx];
141:     s6  = b[5 + idx];
142:     s7  = b[6 + idx];
143:     for (k = 0; k < nz; k++) {
144:       jdx = bs * vi[k];
145:       x1  = x[jdx];
146:       x2  = x[1 + jdx];
147:       x3  = x[2 + jdx];
148:       x4  = x[3 + jdx];
149:       x5  = x[4 + jdx];
150:       x6  = x[5 + jdx];
151:       x7  = x[6 + jdx];
152:       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
153:       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
154:       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
155:       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
156:       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
157:       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
158:       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
159:       v += bs2;
160:     }

162:     x[idx]     = s1;
163:     x[1 + idx] = s2;
164:     x[2 + idx] = s3;
165:     x[3 + idx] = s4;
166:     x[4 + idx] = s5;
167:     x[5 + idx] = s6;
168:     x[6 + idx] = s7;
169:   }

171:   /* backward solve the upper triangular */
172:   for (i = n - 1; i >= 0; i--) {
173:     v   = aa + bs2 * (adiag[i + 1] + 1);
174:     vi  = aj + adiag[i + 1] + 1;
175:     nz  = adiag[i] - adiag[i + 1] - 1;
176:     idt = bs * i;
177:     s1  = x[idt];
178:     s2  = x[1 + idt];
179:     s3  = x[2 + idt];
180:     s4  = x[3 + idt];
181:     s5  = x[4 + idt];
182:     s6  = x[5 + idt];
183:     s7  = x[6 + idt];
184:     for (k = 0; k < nz; k++) {
185:       idx = bs * vi[k];
186:       x1  = x[idx];
187:       x2  = x[1 + idx];
188:       x3  = x[2 + idx];
189:       x4  = x[3 + idx];
190:       x5  = x[4 + idx];
191:       x6  = x[5 + idx];
192:       x7  = x[6 + idx];
193:       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
194:       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
195:       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
196:       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
197:       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
198:       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
199:       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
200:       v += bs2;
201:     }
202:     /* x = inv_diagonal*x */
203:     x[idt]     = v[0] * s1 + v[7] * s2 + v[14] * s3 + v[21] * s4 + v[28] * s5 + v[35] * s6 + v[42] * s7;
204:     x[1 + idt] = v[1] * s1 + v[8] * s2 + v[15] * s3 + v[22] * s4 + v[29] * s5 + v[36] * s6 + v[43] * s7;
205:     x[2 + idt] = v[2] * s1 + v[9] * s2 + v[16] * s3 + v[23] * s4 + v[30] * s5 + v[37] * s6 + v[44] * s7;
206:     x[3 + idt] = v[3] * s1 + v[10] * s2 + v[17] * s3 + v[24] * s4 + v[31] * s5 + v[38] * s6 + v[45] * s7;
207:     x[4 + idt] = v[4] * s1 + v[11] * s2 + v[18] * s3 + v[25] * s4 + v[32] * s5 + v[39] * s6 + v[46] * s7;
208:     x[5 + idt] = v[5] * s1 + v[12] * s2 + v[19] * s3 + v[26] * s4 + v[33] * s5 + v[40] * s6 + v[47] * s7;
209:     x[6 + idt] = v[6] * s1 + v[13] * s2 + v[20] * s3 + v[27] * s4 + v[34] * s5 + v[41] * s6 + v[48] * s7;
210:   }

212:   VecRestoreArrayRead(bb, &b);
213:   VecRestoreArray(xx, &x);
214:   PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n);
215:   return 0;
216: }