Actual source code: sbaijfact5.c


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

  5: /*
  6:       Version for when blocks are 4 by 4 Using natural ordering
  7: */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
  9: {
 10:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
 11:   PetscInt      i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
 12:   PetscInt     *ai, *aj, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
 13:   MatScalar    *ba = b->a, *aa, *ap, *dk, *uik;
 14:   MatScalar    *u, *diag, *rtmp, *rtmp_ptr;
 15:   PetscBool     pivotinblocks = b->pivotinblocks;
 16:   PetscReal     shift         = info->shiftamount;
 17:   PetscBool     allowzeropivot, zeropivotdetected = PETSC_FALSE;

 19:   PetscFunctionBegin;
 20:   /* initialization */
 21:   allowzeropivot = PetscNot(A->erroriffailure);
 22:   PetscCall(PetscCalloc1(16 * mbs, &rtmp));
 23:   PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
 24:   il[0] = 0;
 25:   for (i = 0; i < mbs; i++) jl[i] = mbs;

 27:   PetscCall(PetscMalloc2(16, &dk, 16, &uik));
 28:   ai = a->i;
 29:   aj = a->j;
 30:   aa = a->a;

 32:   /* for each row k */
 33:   for (k = 0; k < mbs; k++) {
 34:     /*initialize k-th row with elements nonzero in row k of A */
 35:     jmin = ai[k];
 36:     jmax = ai[k + 1];
 37:     if (jmin < jmax) {
 38:       ap = aa + jmin * 16;
 39:       for (j = jmin; j < jmax; j++) {
 40:         vj       = aj[j]; /* block col. index */
 41:         rtmp_ptr = rtmp + vj * 16;
 42:         for (i = 0; i < 16; i++) *rtmp_ptr++ = *ap++;
 43:       }
 44:     }

 46:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 47:     PetscCall(PetscArraycpy(dk, rtmp + k * 16, 16));
 48:     i = jl[k]; /* first row to be added to k_th row  */

 50:     while (i < mbs) {
 51:       nexti = jl[i]; /* next row to be added to k_th row */

 53:       /* compute multiplier */
 54:       ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */

 56:       /* uik = -inv(Di)*U_bar(i,k) */
 57:       diag = ba + i * 16;
 58:       u    = ba + ili * 16;

 60:       uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]);
 61:       uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]);
 62:       uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]);
 63:       uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]);

 65:       uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]);
 66:       uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]);
 67:       uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]);
 68:       uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]);

 70:       uik[8]  = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]);
 71:       uik[9]  = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]);
 72:       uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]);
 73:       uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]);

 75:       uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]);
 76:       uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]);
 77:       uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]);
 78:       uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]);

 80:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
 81:       dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
 82:       dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
 83:       dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
 84:       dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];

 86:       dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
 87:       dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
 88:       dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
 89:       dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];

 91:       dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
 92:       dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
 93:       dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
 94:       dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];

 96:       dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
 97:       dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
 98:       dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
 99:       dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];

101:       PetscCall(PetscLogFlops(64.0 * 4.0));

103:       /* update -U(i,k) */
104:       PetscCall(PetscArraycpy(ba + ili * 16, uik, 16));

106:       /* add multiple of row i to k-th row ... */
107:       jmin = ili + 1;
108:       jmax = bi[i + 1];
109:       if (jmin < jmax) {
110:         for (j = jmin; j < jmax; j++) {
111:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
112:           rtmp_ptr = rtmp + bj[j] * 16;
113:           u        = ba + j * 16;
114:           rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
115:           rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
116:           rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
117:           rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];

119:           rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
120:           rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
121:           rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
122:           rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];

124:           rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
125:           rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
126:           rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
127:           rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];

129:           rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
130:           rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
131:           rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
132:           rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
133:         }
134:         PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin)));

136:         /* ... add i to row list for next nonzero entry */
137:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
138:         j     = bj[jmin];
139:         jl[i] = jl[j];
140:         jl[j] = i; /* update jl */
141:       }
142:       i = nexti;
143:     }

145:     /* save nonzero entries in k-th row of U ... */

147:     /* invert diagonal block */
148:     diag = ba + k * 16;
149:     PetscCall(PetscArraycpy(diag, dk, 16));
150:     if (pivotinblocks) {
151:       PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
152:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
153:     } else {
154:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag));
155:     }

157:     jmin = bi[k];
158:     jmax = bi[k + 1];
159:     if (jmin < jmax) {
160:       for (j = jmin; j < jmax; j++) {
161:         vj       = bj[j]; /* block col. index of U */
162:         u        = ba + j * 16;
163:         rtmp_ptr = rtmp + vj * 16;
164:         for (k1 = 0; k1 < 16; k1++) {
165:           *u++        = *rtmp_ptr;
166:           *rtmp_ptr++ = 0.0;
167:         }
168:       }

170:       /* ... add k to row list for first nonzero entry in k-th row */
171:       il[k] = jmin;
172:       i     = bj[jmin];
173:       jl[k] = jl[i];
174:       jl[i] = k;
175:     }
176:   }

178:   PetscCall(PetscFree(rtmp));
179:   PetscCall(PetscFree2(il, jl));
180:   PetscCall(PetscFree2(dk, uik));

182:   C->ops->solve          = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
183:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
184:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
185:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;

187:   C->assembled    = PETSC_TRUE;
188:   C->preallocated = PETSC_TRUE;

190:   PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */
191:   PetscFunctionReturn(PETSC_SUCCESS);
192: }