| 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 | Inverse square root function x^(-1/2) | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/fnimpl.h> /*I "slepcfn.h" I*/ | ||
| 15 | #include <slepcblaslapack.h> | ||
| 16 | |||
| 17 | 492 | static PetscErrorCode FNEvaluateFunction_Invsqrt(FN fn,PetscScalar x,PetscScalar *y) | |
| 18 | { | ||
| 19 |
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492 | PetscFunctionBegin; |
| 20 |
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492 | PetscCheck(x!=0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Function not defined in the requested value"); |
| 21 | #if !defined(PETSC_USE_COMPLEX) | ||
| 22 |
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246 | PetscCheck(x>0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Function not defined in the requested value"); |
| 23 | #endif | ||
| 24 | 492 | *y = 1.0/PetscSqrtScalar(x); | |
| 25 |
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492 | PetscFunctionReturn(PETSC_SUCCESS); |
| 26 | } | ||
| 27 | |||
| 28 | 92 | static PetscErrorCode FNEvaluateDerivative_Invsqrt(FN fn,PetscScalar x,PetscScalar *y) | |
| 29 | { | ||
| 30 |
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92 | PetscFunctionBegin; |
| 31 |
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92 | PetscCheck(x!=0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Derivative not defined in the requested value"); |
| 32 | #if !defined(PETSC_USE_COMPLEX) | ||
| 33 |
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46 | PetscCheck(x>0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Derivative not defined in the requested value"); |
| 34 | #endif | ||
| 35 |
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92 | *y = -1.0/(2.0*PetscPowScalarReal(x,1.5)); |
| 36 |
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92 | PetscFunctionReturn(PETSC_SUCCESS); |
| 37 | } | ||
| 38 | |||
| 39 | 40 | static PetscErrorCode FNEvaluateFunctionMat_Invsqrt_Schur(FN fn,Mat A,Mat B) | |
| 40 | { | ||
| 41 | 40 | PetscBLASInt n=0,ld,*ipiv; | |
| 42 | 40 | PetscScalar *Ba,*Wa; | |
| 43 | 40 | PetscInt m; | |
| 44 | 40 | Mat W; | |
| 45 | |||
| 46 |
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40 | PetscFunctionBegin; |
| 47 |
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40 | PetscCall(FN_AllocateWorkMat(fn,A,&W)); |
| 48 |
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40 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 49 |
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40 | PetscCall(MatDenseGetArray(B,&Ba)); |
| 50 |
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40 | PetscCall(MatDenseGetArray(W,&Wa)); |
| 51 | /* compute B = sqrtm(A) */ | ||
| 52 |
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40 | PetscCall(MatGetSize(A,&m,NULL)); |
| 53 |
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40 | PetscCall(PetscBLASIntCast(m,&n)); |
| 54 | 40 | ld = n; | |
| 55 |
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40 | PetscCall(FNSqrtmSchur(fn,n,Ba,n,PETSC_FALSE)); |
| 56 | /* compute B = A\B */ | ||
| 57 |
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40 | PetscCall(PetscMalloc1(ld,&ipiv)); |
| 58 |
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40 | PetscCallLAPACKInfo("LAPACKgesv",LAPACKgesv_(&n,&n,Wa,&ld,ipiv,Ba,&ld,&info)); |
| 59 |
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40 | PetscCall(PetscLogFlops(2.0*n*n*n/3.0+2.0*n*n*n)); |
| 60 |
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40 | PetscCall(PetscFree(ipiv)); |
| 61 |
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40 | PetscCall(MatDenseRestoreArray(W,&Wa)); |
| 62 |
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40 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 63 |
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40 | PetscCall(FN_FreeWorkMat(fn,&W)); |
| 64 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 65 | } | ||
| 66 | |||
| 67 | 40 | static PetscErrorCode FNEvaluateFunctionMatVec_Invsqrt_Schur(FN fn,Mat A,Vec v) | |
| 68 | { | ||
| 69 | 40 | PetscBLASInt n=0,ld,*ipiv,one=1; | |
| 70 | 40 | PetscScalar *Ba,*Wa; | |
| 71 | 40 | PetscInt m; | |
| 72 | 40 | Mat B,W; | |
| 73 | |||
| 74 |
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40 | PetscFunctionBegin; |
| 75 |
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40 | PetscCall(FN_AllocateWorkMat(fn,A,&B)); |
| 76 |
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40 | PetscCall(FN_AllocateWorkMat(fn,A,&W)); |
| 77 |
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40 | PetscCall(MatDenseGetArray(B,&Ba)); |
| 78 |
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40 | PetscCall(MatDenseGetArray(W,&Wa)); |
| 79 | /* compute B_1 = sqrtm(A)*e_1 */ | ||
| 80 |
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40 | PetscCall(MatGetSize(A,&m,NULL)); |
| 81 |
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40 | PetscCall(PetscBLASIntCast(m,&n)); |
| 82 | 40 | ld = n; | |
| 83 |
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40 | PetscCall(FNSqrtmSchur(fn,n,Ba,n,PETSC_TRUE)); |
| 84 | /* compute B_1 = A\B_1 */ | ||
| 85 |
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40 | PetscCall(PetscMalloc1(ld,&ipiv)); |
| 86 |
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40 | PetscCallLAPACKInfo("LAPACKgesv",LAPACKgesv_(&n,&one,Wa,&ld,ipiv,Ba,&ld,&info)); |
| 87 |
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40 | PetscCall(PetscFree(ipiv)); |
| 88 |
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40 | PetscCall(MatDenseRestoreArray(W,&Wa)); |
| 89 |
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40 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 90 |
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40 | PetscCall(MatGetColumnVector(B,v,0)); |
| 91 |
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40 | PetscCall(FN_FreeWorkMat(fn,&W)); |
| 92 |
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40 | PetscCall(FN_FreeWorkMat(fn,&B)); |
| 93 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 94 | } | ||
| 95 | |||
| 96 | 120 | static PetscErrorCode FNEvaluateFunctionMat_Invsqrt_DBP(FN fn,Mat A,Mat B) | |
| 97 | { | ||
| 98 | 120 | PetscBLASInt n=0; | |
| 99 | 120 | PetscScalar *T; | |
| 100 | 120 | PetscInt m; | |
| 101 | |||
| 102 |
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120 | PetscFunctionBegin; |
| 103 |
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120 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 104 |
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120 | PetscCall(MatDenseGetArray(B,&T)); |
| 105 |
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120 | PetscCall(MatGetSize(A,&m,NULL)); |
| 106 |
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120 | PetscCall(PetscBLASIntCast(m,&n)); |
| 107 |
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120 | PetscCall(FNSqrtmDenmanBeavers(fn,n,T,n,PETSC_TRUE)); |
| 108 |
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120 | PetscCall(MatDenseRestoreArray(B,&T)); |
| 109 |
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24 | PetscFunctionReturn(PETSC_SUCCESS); |
| 110 | } | ||
| 111 | |||
| 112 | 120 | static PetscErrorCode FNEvaluateFunctionMat_Invsqrt_NS(FN fn,Mat A,Mat B) | |
| 113 | { | ||
| 114 | 120 | PetscBLASInt n=0; | |
| 115 | 120 | PetscScalar *T; | |
| 116 | 120 | PetscInt m; | |
| 117 | |||
| 118 |
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120 | PetscFunctionBegin; |
| 119 |
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120 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 120 |
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120 | PetscCall(MatDenseGetArray(B,&T)); |
| 121 |
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120 | PetscCall(MatGetSize(A,&m,NULL)); |
| 122 |
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120 | PetscCall(PetscBLASIntCast(m,&n)); |
| 123 |
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120 | PetscCall(FNSqrtmNewtonSchulz(fn,n,T,n,PETSC_TRUE)); |
| 124 |
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120 | PetscCall(MatDenseRestoreArray(B,&T)); |
| 125 |
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24 | PetscFunctionReturn(PETSC_SUCCESS); |
| 126 | } | ||
| 127 | |||
| 128 | 120 | static PetscErrorCode FNEvaluateFunctionMat_Invsqrt_Sadeghi(FN fn,Mat A,Mat B) | |
| 129 | { | ||
| 130 | 120 | PetscBLASInt n=0,ld,*ipiv; | |
| 131 | 120 | PetscScalar *Ba,*Wa; | |
| 132 | 120 | PetscInt m; | |
| 133 | 120 | Mat W; | |
| 134 | |||
| 135 |
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120 | PetscFunctionBegin; |
| 136 |
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120 | PetscCall(FN_AllocateWorkMat(fn,A,&W)); |
| 137 |
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120 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 138 |
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120 | PetscCall(MatDenseGetArray(B,&Ba)); |
| 139 |
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120 | PetscCall(MatDenseGetArray(W,&Wa)); |
| 140 | /* compute B = sqrtm(A) */ | ||
| 141 |
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120 | PetscCall(MatGetSize(A,&m,NULL)); |
| 142 |
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120 | PetscCall(PetscBLASIntCast(m,&n)); |
| 143 | 120 | ld = n; | |
| 144 |
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120 | PetscCall(FNSqrtmSadeghi(fn,n,Ba,n)); |
| 145 | /* compute B = A\B */ | ||
| 146 |
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120 | PetscCall(PetscMalloc1(ld,&ipiv)); |
| 147 |
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120 | PetscCallLAPACKInfo("LAPACKgesv",LAPACKgesv_(&n,&n,Wa,&ld,ipiv,Ba,&ld,&info)); |
| 148 |
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120 | PetscCall(PetscLogFlops(2.0*n*n*n/3.0+2.0*n*n*n)); |
| 149 |
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120 | PetscCall(PetscFree(ipiv)); |
| 150 |
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120 | PetscCall(MatDenseRestoreArray(W,&Wa)); |
| 151 |
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120 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 152 |
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120 | PetscCall(FN_FreeWorkMat(fn,&W)); |
| 153 |
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24 | PetscFunctionReturn(PETSC_SUCCESS); |
| 154 | } | ||
| 155 | |||
| 156 | #if defined(PETSC_HAVE_CUDA) | ||
| 157 | 24 | PetscErrorCode FNEvaluateFunctionMat_Invsqrt_NS_CUDA(FN fn,Mat A,Mat B) | |
| 158 | { | ||
| 159 | 24 | PetscBLASInt n=0; | |
| 160 | 24 | PetscScalar *Ba; | |
| 161 | 24 | PetscInt m; | |
| 162 | |||
| 163 | 24 | PetscFunctionBegin; | |
| 164 |
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24 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 165 |
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24 | PetscCall(MatDenseCUDAGetArray(B,&Ba)); |
| 166 |
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24 | PetscCall(MatGetSize(A,&m,NULL)); |
| 167 |
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24 | PetscCall(PetscBLASIntCast(m,&n)); |
| 168 |
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24 | PetscCall(FNSqrtmNewtonSchulz_CUDA(fn,n,Ba,n,PETSC_TRUE)); |
| 169 |
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24 | PetscCall(MatDenseCUDARestoreArray(B,&Ba)); |
| 170 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 171 | } | ||
| 172 | |||
| 173 | #if defined(PETSC_HAVE_MAGMA) | ||
| 174 | #include <slepcmagma.h> | ||
| 175 | |||
| 176 | 24 | PetscErrorCode FNEvaluateFunctionMat_Invsqrt_DBP_CUDAm(FN fn,Mat A,Mat B) | |
| 177 | { | ||
| 178 | 24 | PetscBLASInt n=0; | |
| 179 | 24 | PetscScalar *T; | |
| 180 | 24 | PetscInt m; | |
| 181 | |||
| 182 | 24 | PetscFunctionBegin; | |
| 183 |
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24 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 184 |
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24 | PetscCall(MatDenseCUDAGetArray(B,&T)); |
| 185 |
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24 | PetscCall(MatGetSize(A,&m,NULL)); |
| 186 |
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24 | PetscCall(PetscBLASIntCast(m,&n)); |
| 187 |
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24 | PetscCall(FNSqrtmDenmanBeavers_CUDAm(fn,n,T,n,PETSC_TRUE)); |
| 188 |
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24 | PetscCall(MatDenseCUDARestoreArray(B,&T)); |
| 189 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 190 | } | ||
| 191 | |||
| 192 | 24 | PetscErrorCode FNEvaluateFunctionMat_Invsqrt_Sadeghi_CUDAm(FN fn,Mat A,Mat B) | |
| 193 | { | ||
| 194 | 24 | PetscBLASInt n=0,ld,*ipiv; | |
| 195 | 24 | PetscScalar *Ba,*Wa; | |
| 196 | 24 | PetscInt m; | |
| 197 | 24 | Mat W; | |
| 198 | |||
| 199 | 24 | PetscFunctionBegin; | |
| 200 |
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24 | PetscCall(FN_AllocateWorkMat(fn,A,&W)); |
| 201 |
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24 | if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN)); |
| 202 |
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24 | PetscCall(MatDenseCUDAGetArray(B,&Ba)); |
| 203 |
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24 | PetscCall(MatDenseCUDAGetArray(W,&Wa)); |
| 204 | /* compute B = sqrtm(A) */ | ||
| 205 |
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24 | PetscCall(MatGetSize(A,&m,NULL)); |
| 206 |
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24 | PetscCall(PetscBLASIntCast(m,&n)); |
| 207 | 24 | ld = n; | |
| 208 |
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24 | PetscCall(FNSqrtmSadeghi_CUDAm(fn,n,Ba,n)); |
| 209 | /* compute B = A\B */ | ||
| 210 |
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24 | PetscCall(SlepcMagmaInit()); |
| 211 |
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24 | PetscCall(PetscMalloc1(ld,&ipiv)); |
| 212 |
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24 | PetscCallMAGMA(magma_xgesv_gpu,n,n,Wa,ld,ipiv,Ba,ld); |
| 213 | 24 | PetscCall(PetscLogFlops(2.0*n*n*n/3.0+2.0*n*n*n)); | |
| 214 |
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24 | PetscCall(PetscFree(ipiv)); |
| 215 |
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24 | PetscCall(MatDenseCUDARestoreArray(W,&Wa)); |
| 216 |
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24 | PetscCall(MatDenseCUDARestoreArray(B,&Ba)); |
| 217 |
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24 | PetscCall(FN_FreeWorkMat(fn,&W)); |
| 218 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 219 | } | ||
| 220 | #endif /* PETSC_HAVE_MAGMA */ | ||
| 221 | #endif /* PETSC_HAVE_CUDA */ | ||
| 222 | |||
| 223 | 92 | static PetscErrorCode FNView_Invsqrt(FN fn,PetscViewer viewer) | |
| 224 | { | ||
| 225 | 92 | PetscBool isascii; | |
| 226 | 92 | char str[50]; | |
| 227 | 92 | const char *methodname[] = { | |
| 228 | "Schur method for inv(A)*sqrtm(A)", | ||
| 229 | "Denman-Beavers (product form)", | ||
| 230 | "Newton-Schulz iteration", | ||
| 231 | "Sadeghi iteration" | ||
| 232 | }; | ||
| 233 | 92 | const int nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname); | |
| 234 | |||
| 235 |
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92 | PetscFunctionBegin; |
| 236 |
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92 | PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii)); |
| 237 |
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92 | if (isascii) { |
| 238 |
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92 | if (fn->beta==(PetscScalar)1.0) { |
| 239 | ✗ | if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscViewerASCIIPrintf(viewer," inverse square root: x^(-1/2)\n")); | |
| 240 | else { | ||
| 241 | ✗ | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE)); | |
| 242 | ✗ | PetscCall(PetscViewerASCIIPrintf(viewer," inverse square root: (%s*x)^(-1/2)\n",str)); | |
| 243 | } | ||
| 244 | } else { | ||
| 245 |
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92 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE)); |
| 246 |
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92 | if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscViewerASCIIPrintf(viewer," inverse square root: %s*x^(-1/2)\n",str)); |
| 247 | else { | ||
| 248 |
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92 | PetscCall(PetscViewerASCIIPrintf(viewer," inverse square root: %s",str)); |
| 249 |
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92 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 250 |
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92 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE)); |
| 251 |
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92 | PetscCall(PetscViewerASCIIPrintf(viewer,"*(%s*x)^(-1/2)\n",str)); |
| 252 |
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92 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 253 | } | ||
| 254 | } | ||
| 255 |
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92 | if (fn->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer," computing matrix functions with: %s\n",methodname[fn->method])); |
| 256 | } | ||
| 257 |
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16 | PetscFunctionReturn(PETSC_SUCCESS); |
| 258 | } | ||
| 259 | |||
| 260 | /*MC | ||
| 261 | FNINVSQRT - FNINVSQRT = "invsqrt" - The inverse square root function $f(x)=x^{-\frac{1}{2}}$. | ||
| 262 | |||
| 263 | Level: beginner | ||
| 264 | |||
| 265 | .seealso: [](sec:fn), `FN`, `FNType`, `FNSetType()` | ||
| 266 | M*/ | ||
| 267 | |||
| 268 | 92 | SLEPC_EXTERN PetscErrorCode FNCreate_Invsqrt(FN fn) | |
| 269 | { | ||
| 270 |
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92 | PetscFunctionBegin; |
| 271 | 92 | fn->ops->evaluatefunction = FNEvaluateFunction_Invsqrt; | |
| 272 | 92 | fn->ops->evaluatederivative = FNEvaluateDerivative_Invsqrt; | |
| 273 | 92 | fn->ops->evaluatefunctionmat[0] = FNEvaluateFunctionMat_Invsqrt_Schur; | |
| 274 | 92 | fn->ops->evaluatefunctionmat[1] = FNEvaluateFunctionMat_Invsqrt_DBP; | |
| 275 | 92 | fn->ops->evaluatefunctionmat[2] = FNEvaluateFunctionMat_Invsqrt_NS; | |
| 276 | 92 | fn->ops->evaluatefunctionmat[3] = FNEvaluateFunctionMat_Invsqrt_Sadeghi; | |
| 277 | #if defined(PETSC_HAVE_CUDA) | ||
| 278 | 28 | fn->ops->evaluatefunctionmatcuda[2] = FNEvaluateFunctionMat_Invsqrt_NS_CUDA; | |
| 279 | #if defined(PETSC_HAVE_MAGMA) | ||
| 280 | 28 | fn->ops->evaluatefunctionmatcuda[1] = FNEvaluateFunctionMat_Invsqrt_DBP_CUDAm; | |
| 281 | 28 | fn->ops->evaluatefunctionmatcuda[3] = FNEvaluateFunctionMat_Invsqrt_Sadeghi_CUDAm; | |
| 282 | #endif /* PETSC_HAVE_MAGMA */ | ||
| 283 | #endif /* PETSC_HAVE_CUDA */ | ||
| 284 | 92 | fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Invsqrt_Schur; | |
| 285 | 92 | fn->ops->view = FNView_Invsqrt; | |
| 286 |
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92 | PetscFunctionReturn(PETSC_SUCCESS); |
| 287 | } | ||
| 288 |