| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
| 4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
| 5 | |||
| 6 | This file is part of SLEPc. | ||
| 7 | SLEPc is distributed under a 2-clause BSD license (see LICENSE). | ||
| 8 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 9 | */ | ||
| 10 | /* | ||
| 11 | BV private kernels that use the LAPACK | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/bvimpl.h> | ||
| 15 | #include <slepcblaslapack.h> | ||
| 16 | |||
| 17 | /* | ||
| 18 | Reduction operation to compute sqrt(x**2+y**2) when normalizing vectors | ||
| 19 | */ | ||
| 20 | 15246 | SLEPC_EXTERN void MPIAPI SlepcPythag(void *in,void *inout,PetscMPIInt *len,MPI_Datatype *datatype) | |
| 21 | { | ||
| 22 | 15246 | PetscBLASInt i,n=*len; | |
| 23 | 15246 | PetscReal *x = (PetscReal*)in,*y = (PetscReal*)inout; | |
| 24 | |||
| 25 |
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15246 | PetscFunctionBegin; |
| 26 |
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15246 | if (PetscUnlikely(*datatype!=MPIU_REAL)) { |
| 27 | ✗ | (void)(*PetscErrorPrintf)("Only implemented for MPIU_REAL data type"); | |
| 28 | ✗ | MPI_Abort(PETSC_COMM_WORLD,1); | |
| 29 | } | ||
| 30 |
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33222 | for (i=0;i<n;i++) y[i] = SlepcAbs(x[i],y[i]); |
| 31 |
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15246 | PetscFunctionReturnVoid(); |
| 32 | } | ||
| 33 | |||
| 34 | /* | ||
| 35 | Compute ||A|| for an mxn matrix | ||
| 36 | */ | ||
| 37 | 102569 | PetscErrorCode BVNorm_LAPACK_Private(BV bv,PetscInt m_,PetscInt n_,const PetscScalar *A,PetscInt lda_,NormType type,PetscReal *nrm,PetscBool mpi) | |
| 38 | { | ||
| 39 | 102569 | PetscBLASInt m,n,lda,i,j; | |
| 40 | 102569 | PetscMPIInt len; | |
| 41 | 102569 | PetscReal lnrm,*rwork=NULL,*rwork2=NULL; | |
| 42 | |||
| 43 |
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102569 | PetscFunctionBegin; |
| 44 |
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102569 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 45 |
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102569 | PetscCall(PetscBLASIntCast(m_,&m)); |
| 46 |
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102569 | PetscCall(PetscBLASIntCast(n_,&n)); |
| 47 |
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102569 | PetscCall(PetscBLASIntCast(lda_,&lda)); |
| 48 |
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102569 | if (type==NORM_FROBENIUS || type==NORM_2) { |
| 49 | 102465 | lnrm = LAPACKlange_("F",&m,&n,(PetscScalar*)A,&lda,rwork); | |
| 50 |
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102465 | if (mpi) PetscCallMPI(MPIU_Allreduce(&lnrm,nrm,1,MPIU_REAL,MPIU_LAPY2,PetscObjectComm((PetscObject)bv))); |
| 51 | 86657 | else *nrm = lnrm; | |
| 52 |
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102465 | PetscCall(PetscLogFlops(2.0*m*n)); |
| 53 |
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104 | } else if (type==NORM_1) { |
| 54 |
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104 | if (mpi) { |
| 55 | ✗ | PetscCall(BVAllocateWork_Private(bv,2*n_)); | |
| 56 | ✗ | rwork = (PetscReal*)bv->work; | |
| 57 | ✗ | rwork2 = rwork+n_; | |
| 58 | ✗ | PetscCall(PetscArrayzero(rwork,n_)); | |
| 59 | ✗ | PetscCall(PetscArrayzero(rwork2,n_)); | |
| 60 | ✗ | for (j=0;j<n_;j++) { | |
| 61 | ✗ | for (i=0;i<m_;i++) { | |
| 62 | ✗ | rwork[j] += PetscAbsScalar(A[i+j*lda_]); | |
| 63 | } | ||
| 64 | } | ||
| 65 | ✗ | PetscCall(PetscMPIIntCast(n_,&len)); | |
| 66 | ✗ | PetscCallMPI(MPIU_Allreduce(rwork,rwork2,len,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)bv))); | |
| 67 | ✗ | *nrm = 0.0; | |
| 68 | ✗ | for (j=0;j<n_;j++) if (rwork2[j] > *nrm) *nrm = rwork2[j]; | |
| 69 | } else { | ||
| 70 | 104 | *nrm = LAPACKlange_("O",&m,&n,(PetscScalar*)A,&lda,rwork); | |
| 71 | } | ||
| 72 |
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104 | PetscCall(PetscLogFlops(1.0*m*n)); |
| 73 | ✗ | } else if (type==NORM_INFINITY) { | |
| 74 | ✗ | PetscCall(BVAllocateWork_Private(bv,m_)); | |
| 75 | ✗ | rwork = (PetscReal*)bv->work; | |
| 76 | ✗ | lnrm = LAPACKlange_("I",&m,&n,(PetscScalar*)A,&lda,rwork); | |
| 77 | ✗ | if (mpi) PetscCallMPI(MPIU_Allreduce(&lnrm,nrm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)bv))); | |
| 78 | ✗ | else *nrm = lnrm; | |
| 79 | ✗ | PetscCall(PetscLogFlops(1.0*m*n)); | |
| 80 | } | ||
| 81 |
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102569 | PetscCall(PetscFPTrapPop()); |
| 82 |
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19421 | PetscFunctionReturn(PETSC_SUCCESS); |
| 83 | } | ||
| 84 | |||
| 85 | /* | ||
| 86 | Normalize the columns of an mxn matrix A | ||
| 87 | */ | ||
| 88 | 37441 | PetscErrorCode BVNormalize_LAPACK_Private(BV bv,PetscInt m_,PetscInt n_,const PetscScalar *A,PetscInt lda_,PetscScalar *eigi,PetscBool mpi) | |
| 89 | { | ||
| 90 | 37441 | PetscBLASInt m,lda,j,k,info,zero=0; | |
| 91 | 37441 | PetscMPIInt len; | |
| 92 | 37441 | PetscReal *norms,*rwork=NULL,*rwork2=NULL,done=1.0; | |
| 93 | |||
| 94 |
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37441 | PetscFunctionBegin; |
| 95 |
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37441 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 96 |
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37441 | PetscCall(PetscBLASIntCast(m_,&m)); |
| 97 |
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37441 | PetscCall(PetscBLASIntCast(lda_,&lda)); |
| 98 |
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37441 | PetscCall(BVAllocateWork_Private(bv,2*n_)); |
| 99 | 37441 | rwork = (PetscReal*)bv->work; | |
| 100 | 37441 | rwork2 = rwork+n_; | |
| 101 | /* compute local norms */ | ||
| 102 |
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407895 | for (j=0;j<n_;j++) { |
| 103 | 370454 | k = 1; | |
| 104 | #if !defined(PETSC_USE_COMPLEX) | ||
| 105 |
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172077 | if (eigi && eigi[j] != 0.0) k = 2; |
| 106 | #endif | ||
| 107 | 370454 | rwork[j] = LAPACKlange_("F",&m,&k,(PetscScalar*)(A+j*lda_),&lda,rwork2); | |
| 108 |
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370454 | if (k==2) { rwork[j+1] = rwork[j]; j++; } |
| 109 | } | ||
| 110 | /* reduction to get global norms */ | ||
| 111 |
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37441 | if (mpi) { |
| 112 |
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996 | PetscCall(PetscMPIIntCast(n_,&len)); |
| 113 |
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996 | PetscCall(PetscArrayzero(rwork2,n_)); |
| 114 |
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996 | PetscCallMPI(MPIU_Allreduce(rwork,rwork2,len,MPIU_REAL,MPIU_LAPY2,PetscObjectComm((PetscObject)bv))); |
| 115 | 180 | norms = rwork2; | |
| 116 | } else norms = rwork; | ||
| 117 | /* scale columns */ | ||
| 118 |
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407895 | for (j=0;j<n_;j++) { |
| 119 | 370454 | k = 1; | |
| 120 | #if !defined(PETSC_USE_COMPLEX) | ||
| 121 |
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172077 | if (eigi && eigi[j] != 0.0) k = 2; |
| 122 | #endif | ||
| 123 |
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370454 | PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,norms+j,&done,&m,&k,(PetscScalar*)(A+j*lda_),&lda,&info)); |
| 124 |
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370454 | SlepcCheckLapackInfo("lascl",info); |
| 125 |
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370454 | if (k==2) j++; |
| 126 | } | ||
| 127 |
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37441 | PetscCall(PetscLogFlops(3.0*m*n_)); |
| 128 |
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37441 | PetscCall(PetscFPTrapPop()); |
| 129 |
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7465 | PetscFunctionReturn(PETSC_SUCCESS); |
| 130 | } | ||
| 131 | |||
| 132 | /* | ||
| 133 | Compute the upper Cholesky factor in R and its inverse in S. | ||
| 134 | If S == R then the inverse overwrites the Cholesky factor. | ||
| 135 | */ | ||
| 136 | 1178 | PetscErrorCode BVMatCholInv_LAPACK_Private(BV bv,Mat R,Mat S) | |
| 137 | { | ||
| 138 | 1178 | PetscInt i,k,l,n,m,ld,lds; | |
| 139 | 1178 | PetscScalar *pR,*pS; | |
| 140 | 1178 | PetscBLASInt info,n_ = 0,m_ = 0,ld_,lds_; | |
| 141 | |||
| 142 |
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1178 | PetscFunctionBegin; |
| 143 | 1178 | l = bv->l; | |
| 144 | 1178 | k = bv->k; | |
| 145 |
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1178 | PetscCall(MatGetSize(R,&m,NULL)); |
| 146 | 1178 | n = k-l; | |
| 147 |
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1178 | PetscCall(PetscBLASIntCast(m,&m_)); |
| 148 |
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1178 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 149 | 1178 | ld = m; | |
| 150 | 1178 | ld_ = m_; | |
| 151 |
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1178 | PetscCall(MatDenseGetArray(R,&pR)); |
| 152 | |||
| 153 |
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1178 | if (S==R) { |
| 154 |
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794 | PetscCall(BVAllocateWork_Private(bv,m*k)); |
| 155 | 794 | pS = bv->work; | |
| 156 | 794 | lds = ld; | |
| 157 | 794 | lds_ = ld_; | |
| 158 | } else { | ||
| 159 |
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384 | PetscCall(MatDenseGetArray(S,&pS)); |
| 160 |
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384 | PetscCall(MatGetSize(S,&lds,NULL)); |
| 161 |
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384 | PetscCall(PetscBLASIntCast(lds,&lds_)); |
| 162 | } | ||
| 163 | |||
| 164 | /* save a copy of matrix in S */ | ||
| 165 |
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10810 | for (i=l;i<k;i++) PetscCall(PetscArraycpy(pS+i*lds+l,pR+i*ld+l,n)); |
| 166 | |||
| 167 | /* compute upper Cholesky factor in R */ | ||
| 168 |
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1178 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 169 |
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1178 | PetscCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info)); |
| 170 |
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1178 | PetscCall(PetscLogFlops((1.0*n*n*n)/3.0)); |
| 171 | |||
| 172 |
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1178 | if (info) { /* LAPACKpotrf failed, retry on diagonally perturbed matrix */ |
| 173 | ✗ | for (i=l;i<k;i++) { | |
| 174 | ✗ | PetscCall(PetscArraycpy(pR+i*ld+l,pS+i*lds+l,n)); | |
| 175 | ✗ | pR[i+i*ld] += 50.0*PETSC_MACHINE_EPSILON; | |
| 176 | } | ||
| 177 | ✗ | PetscCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&n_,pR+l*ld+l,&ld_,&info)); | |
| 178 | ✗ | SlepcCheckLapackInfo("potrf",info); | |
| 179 | ✗ | PetscCall(PetscLogFlops((1.0*n*n*n)/3.0)); | |
| 180 | } | ||
| 181 | |||
| 182 | /* compute S = inv(R) */ | ||
| 183 |
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1178 | if (S==R) { |
| 184 |
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794 | PetscCallBLAS("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pR+l*ld+l,&ld_,&info)); |
| 185 | } else { | ||
| 186 |
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384 | PetscCall(PetscArrayzero(pS+l*lds,(k-l)*k)); |
| 187 |
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1920 | for (i=l;i<k;i++) PetscCall(PetscArraycpy(pS+i*lds+l,pR+i*ld+l,n)); |
| 188 |
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384 | PetscCallBLAS("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pS+l*lds+l,&lds_,&info)); |
| 189 | } | ||
| 190 |
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1178 | SlepcCheckLapackInfo("trtri",info); |
| 191 |
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1178 | PetscCall(PetscFPTrapPop()); |
| 192 |
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1178 | PetscCall(PetscLogFlops(0.33*n*n*n)); |
| 193 | |||
| 194 | /* Zero out entries below the diagonal */ | ||
| 195 |
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9632 | for (i=l;i<k-1;i++) { |
| 196 |
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8454 | PetscCall(PetscArrayzero(pR+i*ld+i+1,(k-i-1))); |
| 197 |
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8838 | if (S!=R) PetscCall(PetscArrayzero(pS+i*lds+i+1,(k-i-1))); |
| 198 | } | ||
| 199 |
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1178 | PetscCall(MatDenseRestoreArray(R,&pR)); |
| 200 |
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1178 | if (S!=R) PetscCall(MatDenseRestoreArray(S,&pS)); |
| 201 |
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210 | PetscFunctionReturn(PETSC_SUCCESS); |
| 202 | } | ||
| 203 | |||
| 204 | /* | ||
| 205 | Compute the inverse of an upper triangular matrix R, store it in S. | ||
| 206 | If S == R then the inverse overwrites R. | ||
| 207 | */ | ||
| 208 | 794 | PetscErrorCode BVMatTriInv_LAPACK_Private(BV bv,Mat R,Mat S) | |
| 209 | { | ||
| 210 | 794 | PetscInt i,k,l,n,m,ld,lds; | |
| 211 | 794 | PetscScalar *pR,*pS; | |
| 212 | 794 | PetscBLASInt info,n_,m_ = 0,ld_,lds_; | |
| 213 | |||
| 214 |
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794 | PetscFunctionBegin; |
| 215 | 794 | l = bv->l; | |
| 216 | 794 | k = bv->k; | |
| 217 |
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794 | PetscCall(MatGetSize(R,&m,NULL)); |
| 218 | 794 | n = k-l; | |
| 219 |
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794 | PetscCall(PetscBLASIntCast(m,&m_)); |
| 220 |
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794 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 221 | 794 | ld = m; | |
| 222 | 794 | ld_ = m_; | |
| 223 |
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794 | PetscCall(MatDenseGetArray(R,&pR)); |
| 224 | |||
| 225 |
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794 | if (S==R) { |
| 226 |
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602 | PetscCall(BVAllocateWork_Private(bv,m*k)); |
| 227 | 602 | pS = bv->work; | |
| 228 | 602 | lds = ld; | |
| 229 | 602 | lds_ = ld_; | |
| 230 | } else { | ||
| 231 |
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192 | PetscCall(MatDenseGetArray(S,&pS)); |
| 232 |
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192 | PetscCall(MatGetSize(S,&lds,NULL)); |
| 233 |
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192 | PetscCall(PetscBLASIntCast(lds,&lds_)); |
| 234 | } | ||
| 235 | |||
| 236 | /* compute S = inv(R) */ | ||
| 237 |
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794 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 238 |
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794 | if (S==R) { |
| 239 |
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602 | PetscCallBLAS("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pR+l*ld+l,&ld_,&info)); |
| 240 | } else { | ||
| 241 |
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192 | PetscCall(PetscArrayzero(pS+l*lds,(k-l)*k)); |
| 242 |
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960 | for (i=l;i<k;i++) PetscCall(PetscArraycpy(pS+i*lds+l,pR+i*ld+l,n)); |
| 243 |
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192 | PetscCallBLAS("LAPACKtrtri",LAPACKtrtri_("U","N",&n_,pS+l*lds+l,&lds_,&info)); |
| 244 | } | ||
| 245 |
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794 | SlepcCheckLapackInfo("trtri",info); |
| 246 |
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794 | PetscCall(PetscFPTrapPop()); |
| 247 |
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794 | PetscCall(PetscLogFlops(0.33*n*n*n)); |
| 248 | |||
| 249 |
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794 | PetscCall(MatDenseRestoreArray(R,&pR)); |
| 250 |
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794 | if (S!=R) PetscCall(MatDenseRestoreArray(S,&pS)); |
| 251 |
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146 | PetscFunctionReturn(PETSC_SUCCESS); |
| 252 | } | ||
| 253 | |||
| 254 | /* | ||
| 255 | Compute the matrix to be used for post-multiplying the basis in the SVQB | ||
| 256 | block orthogonalization method. | ||
| 257 | On input R = V'*V, on output S = D*U*Lambda^{-1/2} where (U,Lambda) is | ||
| 258 | the eigendecomposition of D*R*D with D=diag(R)^{-1/2}. | ||
| 259 | If S == R then the result overwrites R. | ||
| 260 | */ | ||
| 261 | 1178 | PetscErrorCode BVMatSVQB_LAPACK_Private(BV bv,Mat R,Mat S) | |
| 262 | { | ||
| 263 | 1178 | PetscInt i,j,k,l,n,m,ld,lds; | |
| 264 | 1178 | PetscScalar *pR,*pS,*D,*work,a; | |
| 265 | 1178 | PetscReal *eig,dummy; | |
| 266 | 1178 | PetscBLASInt info,lwork,n_,m_ = 0,ld_,lds_; | |
| 267 | #if defined(PETSC_USE_COMPLEX) | ||
| 268 | 589 | PetscReal *rwork,rdummy; | |
| 269 | #endif | ||
| 270 | |||
| 271 |
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1178 | PetscFunctionBegin; |
| 272 | 1178 | l = bv->l; | |
| 273 | 1178 | k = bv->k; | |
| 274 |
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1178 | PetscCall(MatGetSize(R,&m,NULL)); |
| 275 |
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1178 | PetscCall(MatDenseGetLDA(R,&ld)); |
| 276 | 1178 | n = k-l; | |
| 277 |
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1178 | PetscCall(PetscBLASIntCast(m,&m_)); |
| 278 |
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1178 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 279 | 1178 | ld_ = m_; | |
| 280 |
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1178 | PetscCall(MatDenseGetArray(R,&pR)); |
| 281 | |||
| 282 |
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1178 | if (S==R) { |
| 283 | 794 | pS = pR; | |
| 284 | 794 | lds = ld; | |
| 285 | 794 | lds_ = ld_; | |
| 286 | } else { | ||
| 287 |
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384 | PetscCall(MatDenseGetArray(S,&pS)); |
| 288 |
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384 | PetscCall(MatDenseGetLDA(S,&lds)); |
| 289 |
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384 | PetscCall(PetscBLASIntCast(lds,&lds_)); |
| 290 | } | ||
| 291 |
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1178 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 292 | |||
| 293 | /* workspace query and memory allocation */ | ||
| 294 | 1178 | lwork = -1; | |
| 295 | #if defined(PETSC_USE_COMPLEX) | ||
| 296 |
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589 | PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS,&lds_,&dummy,&a,&lwork,&rdummy,&info)); |
| 297 |
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589 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork)); |
| 298 |
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589 | PetscCall(PetscMalloc4(n,&eig,n,&D,lwork,&work,PetscMax(1,3*n-2),&rwork)); |
| 299 | #else | ||
| 300 |
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589 | PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS,&lds_,&dummy,&a,&lwork,&info)); |
| 301 |
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589 | PetscCall(PetscBLASIntCast((PetscInt)a,&lwork)); |
| 302 |
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589 | PetscCall(PetscMalloc3(n,&eig,n,&D,lwork,&work)); |
| 303 | #endif | ||
| 304 | |||
| 305 | /* copy and scale matrix */ | ||
| 306 |
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10810 | for (i=l;i<k;i++) D[i-l] = 1.0/PetscSqrtReal(PetscRealPart(pR[i+i*ld])); |
| 307 |
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131130 | for (i=l;i<k;i++) for (j=l;j<k;j++) pS[i+j*lds] = pR[i+j*ld]*D[i-l]; |
| 308 |
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131130 | for (j=l;j<k;j++) for (i=l;i<k;i++) pS[i+j*lds] *= D[j-l]; |
| 309 | |||
| 310 | /* compute eigendecomposition */ | ||
| 311 | #if defined(PETSC_USE_COMPLEX) | ||
| 312 |
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589 | PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS+l*lds+l,&lds_,eig,work,&lwork,rwork,&info)); |
| 313 | #else | ||
| 314 |
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589 | PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n_,pS+l*lds+l,&lds_,eig,work,&lwork,&info)); |
| 315 | #endif | ||
| 316 |
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1178 | SlepcCheckLapackInfo("syev",info); |
| 317 | |||
| 318 |
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1178 | if (S!=R) { /* R = U' */ |
| 319 |
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9600 | for (i=l;i<k;i++) for (j=l;j<k;j++) pR[i+j*ld] = pS[j+i*lds]; |
| 320 | } | ||
| 321 | |||
| 322 | /* compute S = D*U*Lambda^{-1/2} */ | ||
| 323 |
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131130 | for (i=l;i<k;i++) for (j=l;j<k;j++) pS[i+j*lds] *= D[i-l]; |
| 324 |
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131130 | for (j=l;j<k;j++) for (i=l;i<k;i++) pS[i+j*lds] /= PetscSqrtReal(eig[j-l]); |
| 325 | |||
| 326 |
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1178 | if (S!=R) { /* compute R = inv(S) = Lambda^{1/2}*U'/D */ |
| 327 |
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9600 | for (i=l;i<k;i++) for (j=l;j<k;j++) pR[i+j*ld] *= PetscSqrtReal(eig[i-l]); |
| 328 |
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9600 | for (j=l;j<k;j++) for (i=l;i<k;i++) pR[i+j*ld] /= D[j-l]; |
| 329 | } | ||
| 330 | |||
| 331 | #if defined(PETSC_USE_COMPLEX) | ||
| 332 |
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589 | PetscCall(PetscFree4(eig,D,work,rwork)); |
| 333 | #else | ||
| 334 |
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589 | PetscCall(PetscFree3(eig,D,work)); |
| 335 | #endif | ||
| 336 |
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1178 | PetscCall(PetscLogFlops(9.0*n*n*n)); |
| 337 |
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1178 | PetscCall(PetscFPTrapPop()); |
| 338 | |||
| 339 |
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1178 | PetscCall(MatDenseRestoreArray(R,&pR)); |
| 340 |
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1178 | if (S!=R) PetscCall(MatDenseRestoreArray(S,&pS)); |
| 341 |
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210 | PetscFunctionReturn(PETSC_SUCCESS); |
| 342 | } | ||
| 343 | |||
| 344 | /* | ||
| 345 | QR factorization of an mxn matrix via parallel TSQR | ||
| 346 | */ | ||
| 347 | 2101 | PetscErrorCode BVOrthogonalize_LAPACK_TSQR(BV bv,PetscInt m_,PetscInt n_,PetscScalar *Q,PetscInt ldq_,PetscScalar *R,PetscInt ldr) | |
| 348 | { | ||
| 349 | 2101 | PetscInt level,plevel,nlevels,lda,worklen; | |
| 350 | 2101 | PetscBLASInt m,n,ldq,i,j,k,l,nb,sz,lwork,info; | |
| 351 | 2101 | PetscScalar *tau,*work,*A=NULL,*QQ=NULL,*Qhalf,*C=NULL,one=1.0,zero=0.0; | |
| 352 | 2101 | PetscMPIInt rank,size,count,stride,powtwo,s = 0; | |
| 353 | 2101 | MPI_Datatype tmat; | |
| 354 | |||
| 355 |
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2101 | PetscFunctionBegin; |
| 356 |
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2101 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 357 |
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2101 | PetscCall(PetscBLASIntCast(m_,&m)); |
| 358 |
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2101 | PetscCall(PetscBLASIntCast(n_,&n)); |
| 359 |
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2101 | PetscCall(PetscBLASIntCast(ldq_,&ldq)); |
| 360 | 2101 | k = PetscMin(m,n); | |
| 361 | 2101 | nb = 16; | |
| 362 | 2101 | lda = 2*n; | |
| 363 |
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2101 | PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)bv),&size)); |
| 364 |
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2101 | PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)bv),&rank)); |
| 365 | 2101 | nlevels = (PetscInt)PetscCeilReal(PetscLog2Real((PetscReal)size)); | |
| 366 |
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4202 | PetscCall(PetscMPIIntCast(PetscPowInt(2,(PetscInt)PetscFloorReal(PetscLog2Real((PetscReal)size))),&powtwo)); |
| 367 | 2101 | worklen = n+n*nb; | |
| 368 |
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2101 | if (nlevels) worklen += n*lda+n*lda*nlevels+n*lda; |
| 369 |
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2101 | PetscCall(BVAllocateWork_Private(bv,worklen)); |
| 370 | 2101 | tau = bv->work; | |
| 371 | 2101 | work = bv->work+n; | |
| 372 |
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2101 | PetscCall(PetscBLASIntCast(n*nb,&lwork)); |
| 373 |
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2101 | if (nlevels) { |
| 374 | 1224 | A = bv->work+n+n*nb; | |
| 375 | 1224 | QQ = bv->work+n+n*nb+n*lda; | |
| 376 | 1224 | C = bv->work+n+n*nb+n*lda+n*lda*nlevels; | |
| 377 | } | ||
| 378 | |||
| 379 | /* Compute QR */ | ||
| 380 |
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2101 | PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&m,&n,Q,&ldq,tau,work,&lwork,&info)); |
| 381 |
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2101 | SlepcCheckLapackInfo("geqrf",info); |
| 382 | |||
| 383 | /* Extract R */ | ||
| 384 |
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2101 | if (R || nlevels) { |
| 385 |
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26697 | for (j=0;j<n;j++) { |
| 386 |
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273234 | for (i=0;i<=PetscMin(j,m-1);i++) { |
| 387 |
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248638 | if (nlevels) A[i+j*lda] = Q[i+j*ldq]; |
| 388 | 231310 | else R[i+j*ldr] = Q[i+j*ldq]; | |
| 389 | } | ||
| 390 |
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252318 | for (i=PetscMin(j,m-1)+1;i<n;i++) { |
| 391 |
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227722 | if (nlevels) A[i+j*lda] = 0.0; |
| 392 | 212450 | else R[i+j*ldr] = 0.0; | |
| 393 | } | ||
| 394 | } | ||
| 395 | } | ||
| 396 | |||
| 397 | /* Compute orthogonal matrix in Q */ | ||
| 398 |
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2101 | PetscCallBLAS("LAPACKorgqr",LAPACKorgqr_(&m,&k,&k,Q,&ldq,tau,work,&lwork,&info)); |
| 399 |
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2101 | SlepcCheckLapackInfo("orgqr",info); |
| 400 | |||
| 401 |
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2101 | if (nlevels) { |
| 402 | |||
| 403 |
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1224 | PetscCall(PetscMPIIntCast(n,&count)); |
| 404 |
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1224 | PetscCall(PetscMPIIntCast(lda,&stride)); |
| 405 |
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1224 | PetscCall(PetscBLASIntCast(lda,&l)); |
| 406 |
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1224 | PetscCallMPI(MPI_Type_vector(count,count,stride,MPIU_SCALAR,&tmat)); |
| 407 |
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1224 | PetscCallMPI(MPI_Type_commit(&tmat)); |
| 408 | |||
| 409 |
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4128 | for (level=nlevels;level>=1;level--) { |
| 410 | |||
| 411 | 2904 | plevel = PetscPowInt(2,level); | |
| 412 |
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5808 | PetscCall(PetscMPIIntCast(plevel*PetscFloorReal(rank/(PetscReal)plevel)+(rank+PetscPowInt(2,level-1))%plevel,&s)); |
| 413 | |||
| 414 | /* Stack triangular matrices */ | ||
| 415 |
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2904 | if (rank<s && s<size) { /* send top part, receive bottom part */ |
| 416 |
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1272 | PetscCallMPI(MPI_Sendrecv(A,1,tmat,s,111,A+n,1,tmat,s,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE)); |
| 417 |
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1632 | } else if (s<size) { /* copy top to bottom, receive top part */ |
| 418 |
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1272 | PetscCallMPI(MPI_Sendrecv(A,1,tmat,rank,111,A+n,1,tmat,rank,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE)); |
| 419 |
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1272 | PetscCallMPI(MPI_Sendrecv(A+n,1,tmat,s,111,A,1,tmat,s,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE)); |
| 420 | } | ||
| 421 |
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2904 | if (level<nlevels && size!=powtwo) { /* for cases when size is not a power of 2 */ |
| 422 |
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1680 | if (rank<size-powtwo) { /* send bottom part */ |
| 423 |
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720 | PetscCallMPI(MPI_Send(A+n,1,tmat,rank+powtwo,111,PetscObjectComm((PetscObject)bv))); |
| 424 |
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960 | } else if (rank>=powtwo) { /* receive bottom part */ |
| 425 |
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720 | PetscCallMPI(MPI_Recv(A+n,1,tmat,rank-powtwo,111,PetscObjectComm((PetscObject)bv),MPI_STATUS_IGNORE)); |
| 426 | } | ||
| 427 | } | ||
| 428 | /* Compute QR and build orthogonal matrix */ | ||
| 429 |
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2904 | if (level<nlevels || (level==nlevels && s<size)) { |
| 430 |
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2784 | PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&l,&n,A,&l,tau,work,&lwork,&info)); |
| 431 |
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2784 | SlepcCheckLapackInfo("geqrf",info); |
| 432 |
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2784 | PetscCall(PetscArraycpy(QQ+(level-1)*n*lda,A,n*lda)); |
| 433 |
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2784 | PetscCallBLAS("LAPACKorgqr",LAPACKorgqr_(&l,&n,&n,QQ+(level-1)*n*lda,&l,tau,work,&lwork,&info)); |
| 434 |
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2784 | SlepcCheckLapackInfo("orgqr",info); |
| 435 |
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16320 | for (j=0;j<n;j++) { |
| 436 |
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46208 | for (i=j+1;i<n;i++) A[i+j*lda] = 0.0; |
| 437 | } | ||
| 438 |
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120 | } else if (level==nlevels) { /* only one triangular matrix, set Q=I */ |
| 439 |
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120 | PetscCall(PetscArrayzero(QQ+(level-1)*n*lda,n*lda)); |
| 440 |
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720 | for (j=0;j<n;j++) QQ[j+j*lda+(level-1)*n*lda] = 1.0; |
| 441 | } | ||
| 442 | } | ||
| 443 | |||
| 444 | /* Extract R */ | ||
| 445 |
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1224 | if (R) { |
| 446 |
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6960 | for (j=0;j<n;j++) { |
| 447 |
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24904 | for (i=0;i<=j;i++) R[i+j*ldr] = A[i+j*lda]; |
| 448 |
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19168 | for (i=j+1;i<n;i++) R[i+j*ldr] = 0.0; |
| 449 | } | ||
| 450 | } | ||
| 451 | |||
| 452 | /* Accumulate orthogonal matrices */ | ||
| 453 |
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4128 | for (level=1;level<=nlevels;level++) { |
| 454 | 2904 | plevel = PetscPowInt(2,level); | |
| 455 |
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5808 | PetscCall(PetscMPIIntCast(plevel*PetscFloorReal(rank/(PetscReal)plevel)+(rank+PetscPowInt(2,level-1))%plevel,&s)); |
| 456 |
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2904 | Qhalf = (rank<s)? QQ+(level-1)*n*lda: QQ+(level-1)*n*lda+n; |
| 457 |
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2904 | if (level<nlevels) { |
| 458 |
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1680 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&n,&one,QQ+level*n*lda,&l,Qhalf,&l,&zero,C,&l)); |
| 459 |
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1680 | PetscCall(PetscArraycpy(QQ+level*n*lda,C,n*lda)); |
| 460 | } else { | ||
| 461 |
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1888 | for (i=0;i<m/l;i++) { |
| 462 |
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664 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&n,&one,Q+i*l,&ldq,Qhalf,&l,&zero,C,&l)); |
| 463 |
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3392 | for (j=0;j<n;j++) PetscCall(PetscArraycpy(Q+i*l+j*ldq,C+j*l,l)); |
| 464 | } | ||
| 465 | 1224 | sz = m%l; | |
| 466 |
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1224 | if (sz) { |
| 467 |
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1224 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&sz,&n,&n,&one,Q+(m/l)*l,&ldq,Qhalf,&l,&zero,C,&l)); |
| 468 |
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6960 | for (j=0;j<n;j++) PetscCall(PetscArraycpy(Q+(m/l)*l+j*ldq,C+j*l,sz)); |
| 469 | } | ||
| 470 | } | ||
| 471 | } | ||
| 472 | |||
| 473 |
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1224 | PetscCallMPI(MPI_Type_free(&tmat)); |
| 474 | } | ||
| 475 | |||
| 476 |
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2101 | PetscCall(PetscLogFlops(3.0*m*n*n)); |
| 477 |
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2101 | PetscCall(PetscFPTrapPop()); |
| 478 |
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380 | PetscFunctionReturn(PETSC_SUCCESS); |
| 479 | } | ||
| 480 | |||
| 481 | /* | ||
| 482 | Reduction operation to compute [~,Rout]=qr([Rin1;Rin2]) in the TSQR algorithm; | ||
| 483 | all matrices are upper triangular stored in packed format | ||
| 484 | */ | ||
| 485 | 384 | SLEPC_EXTERN void MPIAPI SlepcGivensPacked(void *in,void *inout,PetscMPIInt *len,MPI_Datatype *datatype) | |
| 486 | { | ||
| 487 | 384 | PetscBLASInt n,i,j,k,one=1; | |
| 488 | 384 | PetscMPIInt tsize; | |
| 489 | 384 | PetscScalar v,s,*R2=(PetscScalar*)in,*R1=(PetscScalar*)inout; | |
| 490 | 384 | PetscReal c; | |
| 491 | |||
| 492 |
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384 | PetscFunctionBegin; |
| 493 |
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384 | PetscCallMPIAbort(PETSC_COMM_SELF,MPI_Type_size(*datatype,&tsize)); /* we assume len=1 */ |
| 494 | 384 | tsize /= sizeof(PetscScalar); | |
| 495 | 384 | n = (-1+(PetscBLASInt)PetscSqrtReal(1+8*tsize))/2; | |
| 496 |
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1920 | for (j=0;j<n;j++) { |
| 497 |
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6144 | for (i=0;i<=j;i++) { |
| 498 | 4608 | LAPACKlartg_(R1+(2*n-j-1)*j/2+j,R2+(2*n-i-1)*i/2+j,&c,&s,&v); | |
| 499 | 4608 | R1[(2*n-j-1)*j/2+j] = v; | |
| 500 | 4608 | k = n-j-1; | |
| 501 |
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4608 | if (k) BLASrot_(&k,R1+(2*n-j-1)*j/2+j+1,&one,R2+(2*n-i-1)*i/2+j+1,&one,&c,&s); |
| 502 | } | ||
| 503 | } | ||
| 504 |
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384 | PetscFunctionReturnVoid(); |
| 505 | } | ||
| 506 | |||
| 507 | /* | ||
| 508 | Computes the R factor of the QR factorization of an mxn matrix via parallel TSQR | ||
| 509 | */ | ||
| 510 | 794 | PetscErrorCode BVOrthogonalize_LAPACK_TSQR_OnlyR(BV bv,PetscInt m_,PetscInt n_,PetscScalar *Q,PetscInt ldq_,PetscScalar *R,PetscInt ldr) | |
| 511 | { | ||
| 512 | 794 | PetscInt worklen; | |
| 513 | 794 | PetscBLASInt m,n,ldq,i,j,s,nb,lwork,info; | |
| 514 | 794 | PetscScalar *tau,*work,*A=NULL,*R1=NULL,*R2=NULL; | |
| 515 | 794 | PetscMPIInt size,count; | |
| 516 | 794 | MPI_Datatype tmat; | |
| 517 | |||
| 518 |
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794 | PetscFunctionBegin; |
| 519 |
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794 | PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); |
| 520 |
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794 | PetscCall(PetscBLASIntCast(m_,&m)); |
| 521 |
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794 | PetscCall(PetscBLASIntCast(n_,&n)); |
| 522 |
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794 | PetscCall(PetscBLASIntCast(ldq_,&ldq)); |
| 523 | 794 | nb = 16; | |
| 524 | 794 | s = n+n*(n-1)/2; /* length of packed triangular matrix */ | |
| 525 |
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794 | PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)bv),&size)); |
| 526 | 794 | worklen = n+n*nb+2*s+ldq*n; | |
| 527 |
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794 | PetscCall(BVAllocateWork_Private(bv,worklen)); |
| 528 | 794 | tau = bv->work; | |
| 529 | 794 | work = bv->work+n; | |
| 530 | 794 | R1 = bv->work+n+n*nb; | |
| 531 | 794 | R2 = bv->work+n+n*nb+s; | |
| 532 | 794 | A = bv->work+n+n*nb+2*s; | |
| 533 |
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794 | PetscCall(PetscBLASIntCast(n*nb,&lwork)); |
| 534 |
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794 | PetscCall(PetscArraycpy(A,Q,ldq*n)); |
| 535 | |||
| 536 | /* Compute QR */ | ||
| 537 |
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794 | PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&m,&n,A,&ldq,tau,work,&lwork,&info)); |
| 538 |
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794 | SlepcCheckLapackInfo("geqrf",info); |
| 539 | |||
| 540 |
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794 | if (size==1) { |
| 541 | /* Extract R */ | ||
| 542 |
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6970 | for (j=0;j<n;j++) { |
| 543 |
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62320 | for (i=0;i<=PetscMin(j,m-1);i++) R[i+j*ldr] = A[i+j*ldq]; |
| 544 |
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55760 | for (i=PetscMin(j,m-1)+1;i<n;i++) R[i+j*ldr] = 0.0; |
| 545 | } | ||
| 546 | } else { | ||
| 547 | /* Use MPI reduction operation to obtain global R */ | ||
| 548 |
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384 | PetscCall(PetscMPIIntCast(s,&count)); |
| 549 |
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384 | PetscCallMPI(MPI_Type_contiguous(count,MPIU_SCALAR,&tmat)); |
| 550 |
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384 | PetscCallMPI(MPI_Type_commit(&tmat)); |
| 551 |
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1920 | for (i=0;i<n;i++) { |
| 552 |
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6144 | for (j=i;j<n;j++) R1[(2*n-i-1)*i/2+j] = (i<m)?A[i+j*ldq]:0.0; |
| 553 | } | ||
| 554 |
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384 | PetscCallMPI(MPIU_Allreduce(R1,R2,1,tmat,MPIU_TSQR,PetscObjectComm((PetscObject)bv))); |
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1920 | for (i=0;i<n;i++) { |
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4608 | for (j=0;j<i;j++) R[i+j*ldr] = 0.0; |
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6144 | for (j=i;j<n;j++) R[i+j*ldr] = R2[(2*n-i-1)*i/2+j]; |
| 558 | } | ||
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384 | PetscCallMPI(MPI_Type_free(&tmat)); |
| 560 | } | ||
| 561 | |||
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794 | PetscCall(PetscLogFlops(3.0*m*n*n)); |
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794 | PetscCall(PetscFPTrapPop()); |
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146 | PetscFunctionReturn(PETSC_SUCCESS); |
| 565 | } | ||
| 566 |