1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* 6 Version for when blocks are 5 by 5 Using natural ordering 7 */ 8 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_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,ipvt[5]; 13 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 14 MatScalar *u,*d,*rtmp,*rtmp_ptr,work[25]; 15 PetscReal shift = info->shiftamount; 16 PetscBool allowzeropivot,zeropivotdetected; 17 18 PetscFunctionBegin; 19 /* initialization */ 20 allowzeropivot = PetscNot(A->erroriffailure); 21 PetscCall(PetscCalloc1(25*mbs,&rtmp)); 22 PetscCall(PetscMalloc2(mbs,&il,mbs,&jl)); 23 il[0] = 0; 24 for (i=0; i<mbs; i++) jl[i] = mbs; 25 26 PetscCall(PetscMalloc2(25,&dk,25,&uik)); 27 ai = a->i; aj = a->j; aa = a->a; 28 29 /* for each row k */ 30 for (k = 0; k<mbs; k++) { 31 32 /*initialize k-th row with elements nonzero in row k of A */ 33 jmin = ai[k]; jmax = ai[k+1]; 34 if (jmin < jmax) { 35 ap = aa + jmin*25; 36 for (j = jmin; j < jmax; j++) { 37 vj = aj[j]; /* block col. index */ 38 rtmp_ptr = rtmp + vj*25; 39 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 40 } 41 } 42 43 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 44 PetscCall(PetscArraycpy(dk,rtmp+k*25,25)); 45 i = jl[k]; /* first row to be added to k_th row */ 46 47 while (i < mbs) { 48 nexti = jl[i]; /* next row to be added to k_th row */ 49 50 /* compute multiplier */ 51 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 52 53 /* uik = -inv(Di)*U_bar(i,k) */ 54 d = ba + i*25; 55 u = ba + ili*25; 56 57 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 58 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 59 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 60 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 61 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 62 63 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 64 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 65 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 66 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 67 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 68 69 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 70 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 71 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 72 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 73 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 74 75 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 76 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 77 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 78 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 79 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 80 81 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 82 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 83 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 84 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 85 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 86 87 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 88 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 89 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 90 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 91 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 92 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 93 94 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 95 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 96 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 97 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 98 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 99 100 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 101 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 102 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 103 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 104 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 105 106 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 107 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 108 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 109 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 110 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 111 112 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 113 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 114 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 115 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 116 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 117 118 PetscCall(PetscLogFlops(125.0*4.0)); 119 120 /* update -U(i,k) */ 121 PetscCall(PetscArraycpy(ba+ili*25,uik,25)); 122 123 /* add multiple of row i to k-th row ... */ 124 jmin = ili + 1; jmax = bi[i+1]; 125 if (jmin < jmax) { 126 for (j=jmin; j<jmax; j++) { 127 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 128 rtmp_ptr = rtmp + bj[j]*25; 129 u = ba + j*25; 130 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 131 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 132 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 133 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 134 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 135 136 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 137 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 138 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 139 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 140 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 141 142 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 143 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 144 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 145 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 146 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 147 148 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 149 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 150 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 151 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 152 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 153 154 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 155 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 156 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 157 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 158 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 159 } 160 PetscCall(PetscLogFlops(2.0*125.0*(jmax-jmin))); 161 162 /* ... add i to row list for next nonzero entry */ 163 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 164 j = bj[jmin]; 165 jl[i] = jl[j]; jl[j] = i; /* update jl */ 166 } 167 i = nexti; 168 } 169 170 /* save nonzero entries in k-th row of U ... */ 171 172 /* invert diagonal block */ 173 d = ba+k*25; 174 PetscCall(PetscArraycpy(d,dk,25)); 175 PetscCall(PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected)); 176 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 177 178 jmin = bi[k]; jmax = bi[k+1]; 179 if (jmin < jmax) { 180 for (j=jmin; j<jmax; j++) { 181 vj = bj[j]; /* block col. index of U */ 182 u = ba + j*25; 183 rtmp_ptr = rtmp + vj*25; 184 for (k1=0; k1<25; k1++) { 185 *u++ = *rtmp_ptr; 186 *rtmp_ptr++ = 0.0; 187 } 188 } 189 190 /* ... add k to row list for first nonzero entry in k-th row */ 191 il[k] = jmin; 192 i = bj[jmin]; 193 jl[k] = jl[i]; jl[i] = k; 194 } 195 } 196 197 PetscCall(PetscFree(rtmp)); 198 PetscCall(PetscFree2(il,jl)); 199 PetscCall(PetscFree2(dk,uik)); 200 201 C->ops->solve = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace; 202 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace; 203 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace; 204 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace; 205 C->assembled = PETSC_TRUE; 206 C->preallocated = PETSC_TRUE; 207 208 PetscCall(PetscLogFlops(1.3333*125*b->mbs)); /* from inverting diagonal blocks */ 209 PetscFunctionReturn(0); 210 } 211