| 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 | Exponential function exp(x) | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/fnimpl.h> /*I "slepcfn.h" I*/ | ||
| 15 | #include <slepcblaslapack.h> | ||
| 16 | |||
| 17 | 28278 | static PetscErrorCode FNEvaluateFunction_Exp(FN fn,PetscScalar x,PetscScalar *y) | |
| 18 | { | ||
| 19 |
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28278 | PetscFunctionBegin; |
| 20 | 28278 | *y = PetscExpScalar(x); | |
| 21 |
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28278 | PetscFunctionReturn(PETSC_SUCCESS); |
| 22 | } | ||
| 23 | |||
| 24 | 8907 | static PetscErrorCode FNEvaluateDerivative_Exp(FN fn,PetscScalar x,PetscScalar *y) | |
| 25 | { | ||
| 26 |
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8907 | PetscFunctionBegin; |
| 27 | 8907 | *y = PetscExpScalar(x); | |
| 28 |
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8907 | PetscFunctionReturn(PETSC_SUCCESS); |
| 29 | } | ||
| 30 | |||
| 31 | #define MAX_PADE 6 | ||
| 32 | |||
| 33 | 160 | static PetscErrorCode FNEvaluateFunctionMat_Exp_Pade(FN fn,Mat A,Mat B) | |
| 34 | { | ||
| 35 | 160 | PetscBLASInt n=0,ld,ld2,*ipiv,inc=1; | |
| 36 | 160 | PetscInt m,j,k,sexp; | |
| 37 | 160 | PetscBool odd; | |
| 38 | 160 | const PetscInt p=MAX_PADE; | |
| 39 | 160 | PetscReal c[MAX_PADE+1],s,*rwork; | |
| 40 | 160 | PetscScalar scale,mone=-1.0,one=1.0,two=2.0,zero=0.0; | |
| 41 | 160 | PetscScalar *Ba,*As,*A2,*Q,*P,*W,*aux; | |
| 42 | 160 | const PetscScalar *Aa; | |
| 43 | |||
| 44 |
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160 | PetscFunctionBegin; |
| 45 |
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160 | PetscCall(MatDenseGetArrayRead(A,&Aa)); |
| 46 |
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160 | PetscCall(MatDenseGetArray(B,&Ba)); |
| 47 |
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160 | PetscCall(MatGetSize(A,&m,NULL)); |
| 48 |
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160 | PetscCall(PetscBLASIntCast(m,&n)); |
| 49 | 160 | ld = n; | |
| 50 | 160 | ld2 = ld*ld; | |
| 51 | 160 | P = Ba; | |
| 52 |
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160 | PetscCall(PetscMalloc6(m*m,&Q,m*m,&W,m*m,&As,m*m,&A2,ld,&rwork,ld,&ipiv)); |
| 53 |
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160 | PetscCall(PetscArraycpy(As,Aa,ld2)); |
| 54 | |||
| 55 | /* Pade' coefficients */ | ||
| 56 | 160 | c[0] = 1.0; | |
| 57 |
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1120 | for (k=1;k<=p;k++) c[k] = c[k-1]*(p+1-k)/(k*(2*p+1-k)); |
| 58 | |||
| 59 | /* Scaling */ | ||
| 60 | 160 | s = LAPACKlange_("I",&n,&n,As,&ld,rwork); | |
| 61 |
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160 | PetscCall(PetscLogFlops(1.0*n*n)); |
| 62 |
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160 | if (s>0.5) { |
| 63 |
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160 | sexp = PetscMax(0,(int)(PetscLogReal(s)/PetscLogReal(2.0))+2); |
| 64 | 160 | scale = PetscPowRealInt(2.0,-sexp); | |
| 65 |
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160 | PetscCallBLAS("BLASscal",BLASscal_(&ld2,&scale,As,&inc)); |
| 66 |
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160 | PetscCall(PetscLogFlops(1.0*n*n)); |
| 67 | } else sexp = 0; | ||
| 68 | |||
| 69 | /* Horner evaluation */ | ||
| 70 |
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160 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,As,&ld,As,&ld,&zero,A2,&ld)); |
| 71 |
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160 | PetscCall(PetscLogFlops(2.0*n*n*n)); |
| 72 |
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160 | PetscCall(PetscArrayzero(Q,ld2)); |
| 73 |
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160 | PetscCall(PetscArrayzero(P,ld2)); |
| 74 |
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6160 | for (j=0;j<n;j++) { |
| 75 | 6000 | Q[j+j*ld] = c[p]; | |
| 76 | 6000 | P[j+j*ld] = c[p-1]; | |
| 77 | } | ||
| 78 | |||
| 79 | odd = PETSC_TRUE; | ||
| 80 |
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960 | for (k=p-1;k>0;k--) { |
| 81 |
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800 | if (odd) { |
| 82 |
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480 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,A2,&ld,&zero,W,&ld)); |
| 83 | 480 | SlepcSwap(Q,W,aux); | |
| 84 |
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18480 | for (j=0;j<n;j++) Q[j+j*ld] += c[k-1]; |
| 85 | odd = PETSC_FALSE; | ||
| 86 | } else { | ||
| 87 |
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320 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,A2,&ld,&zero,W,&ld)); |
| 88 | 320 | SlepcSwap(P,W,aux); | |
| 89 |
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12320 | for (j=0;j<n;j++) P[j+j*ld] += c[k-1]; |
| 90 | odd = PETSC_TRUE; | ||
| 91 | } | ||
| 92 |
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800 | PetscCall(PetscLogFlops(2.0*n*n*n)); |
| 93 | } | ||
| 94 | /*if (odd) { | ||
| 95 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,As,&ld,&zero,W,&ld)); | ||
| 96 | SlepcSwap(Q,W,aux); | ||
| 97 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&ld2,&mone,P,&inc,Q,&inc)); | ||
| 98 | PetscCallLAPACKInfo("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info)); | ||
| 99 | PetscCallBLAS("BLASscal",BLASscal_(&ld2,&two,P,&inc)); | ||
| 100 | for (j=0;j<n;j++) P[j+j*ld] += 1.0; | ||
| 101 | PetscCallBLAS("BLASscal",BLASscal_(&ld2,&mone,P,&inc)); | ||
| 102 | } else {*/ | ||
| 103 |
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160 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,As,&ld,&zero,W,&ld)); |
| 104 | 160 | SlepcSwap(P,W,aux); | |
| 105 |
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160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&ld2,&mone,P,&inc,Q,&inc)); |
| 106 |
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160 | PetscCallLAPACKInfo("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info)); |
| 107 |
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160 | PetscCallBLAS("BLASscal",BLASscal_(&ld2,&two,P,&inc)); |
| 108 |
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6160 | for (j=0;j<n;j++) P[j+j*ld] += 1.0; |
| 109 | /*}*/ | ||
| 110 |
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160 | PetscCall(PetscLogFlops(2.0*n*n*n+2.0*n*n*n/3.0+4.0*n*n)); |
| 111 | |||
| 112 |
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680 | for (k=1;k<=sexp;k++) { |
| 113 |
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520 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,P,&ld,&zero,W,&ld)); |
| 114 |
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520 | PetscCall(PetscArraycpy(P,W,ld2)); |
| 115 | } | ||
| 116 |
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160 | if (P!=Ba) PetscCall(PetscArraycpy(Ba,P,ld2)); |
| 117 |
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160 | PetscCall(PetscLogFlops(2.0*n*n*n*sexp)); |
| 118 | |||
| 119 |
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160 | PetscCall(PetscFree6(Q,W,As,A2,rwork,ipiv)); |
| 120 |
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160 | PetscCall(MatDenseRestoreArrayRead(A,&Aa)); |
| 121 |
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160 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 122 |
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32 | PetscFunctionReturn(PETSC_SUCCESS); |
| 123 | } | ||
| 124 | |||
| 125 | #if defined(PETSC_HAVE_COMPLEX) | ||
| 126 | /* | ||
| 127 | * Set scaling factor (s) and Pade degree (k,m) | ||
| 128 | */ | ||
| 129 | 552 | static PetscErrorCode sexpm_params(PetscReal nrm,PetscInt *s,PetscInt *k,PetscInt *m) | |
| 130 | { | ||
| 131 |
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552 | PetscFunctionBegin; |
| 132 |
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552 | if (nrm>1) { |
| 133 |
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352 | if (nrm<200) {*s = 4; *k = 5; *m = *k-1;} |
| 134 |
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40 | else if (nrm<1e4) {*s = 4; *k = 4; *m = *k+1;} |
| 135 | ✗ | else if (nrm<1e6) {*s = 4; *k = 3; *m = *k+1;} | |
| 136 | ✗ | else if (nrm<1e9) {*s = 3; *k = 3; *m = *k+1;} | |
| 137 | ✗ | else if (nrm<1e11) {*s = 2; *k = 3; *m = *k+1;} | |
| 138 | ✗ | else if (nrm<1e12) {*s = 2; *k = 2; *m = *k+1;} | |
| 139 | ✗ | else if (nrm<1e14) {*s = 2; *k = 1; *m = *k+1;} | |
| 140 | ✗ | else {*s = 1; *k = 1; *m = *k+1;} | |
| 141 | } else { /* nrm<1 */ | ||
| 142 |
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200 | if (nrm>0.5) {*s = 4; *k = 4; *m = *k-1;} |
| 143 |
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160 | else if (nrm>0.3) {*s = 3; *k = 4; *m = *k-1;} |
| 144 |
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120 | else if (nrm>0.15) {*s = 2; *k = 4; *m = *k-1;} |
| 145 |
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120 | else if (nrm>0.07) {*s = 1; *k = 4; *m = *k-1;} |
| 146 |
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120 | else if (nrm>0.01) {*s = 0; *k = 4; *m = *k-1;} |
| 147 |
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120 | else if (nrm>3e-4) {*s = 0; *k = 3; *m = *k-1;} |
| 148 |
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120 | else if (nrm>1e-5) {*s = 0; *k = 3; *m = 0;} |
| 149 |
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120 | else if (nrm>1e-8) {*s = 0; *k = 2; *m = 0;} |
| 150 | 120 | else {*s = 0; *k = 1; *m = 0;} | |
| 151 | } | ||
| 152 |
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552 | PetscFunctionReturn(PETSC_SUCCESS); |
| 153 | } | ||
| 154 | |||
| 155 | /* | ||
| 156 | * Partial fraction form coefficients. | ||
| 157 | * If query, the function returns the size necessary to store the coefficients. | ||
| 158 | */ | ||
| 159 | 432 | static PetscErrorCode getcoeffs(PetscInt k,PetscInt m,PetscComplex *r,PetscComplex *q,PetscComplex *remain,PetscBool query) | |
| 160 | { | ||
| 161 | 432 | PetscInt i; | |
| 162 | 432 | const PetscComplex /* m == k+1 */ | |
| 163 | 432 | p1r4[5] = {-1.582680186458572e+01 - 2.412564578224361e+01*PETSC_i, | |
| 164 | 432 | -1.582680186458572e+01 + 2.412564578224361e+01*PETSC_i, | |
| 165 | 432 | 1.499984465975511e+02 + 6.804227952202417e+01*PETSC_i, | |
| 166 | 432 | 1.499984465975511e+02 - 6.804227952202417e+01*PETSC_i, | |
| 167 | -2.733432894659307e+02 }, | ||
| 168 | 432 | p1q4[5] = { 3.655694325463550e+00 + 6.543736899360086e+00*PETSC_i, | |
| 169 | 432 | 3.655694325463550e+00 - 6.543736899360086e+00*PETSC_i, | |
| 170 | 432 | 5.700953298671832e+00 + 3.210265600308496e+00*PETSC_i, | |
| 171 | 432 | 5.700953298671832e+00 - 3.210265600308496e+00*PETSC_i, | |
| 172 | 6.286704751729261e+00 }, | ||
| 173 | 432 | p1r3[4] = {-1.130153999597152e+01 + 1.247167585025031e+01*PETSC_i, | |
| 174 | 432 | -1.130153999597152e+01 - 1.247167585025031e+01*PETSC_i, | |
| 175 | 432 | 1.330153999597152e+01 - 6.007173273704750e+01*PETSC_i, | |
| 176 | 432 | 1.330153999597152e+01 + 6.007173273704750e+01*PETSC_i}, | |
| 177 | 432 | p1q3[4] = { 3.212806896871536e+00 + 4.773087433276636e+00*PETSC_i, | |
| 178 | 432 | 3.212806896871536e+00 - 4.773087433276636e+00*PETSC_i, | |
| 179 | 432 | 4.787193103128464e+00 + 1.567476416895212e+00*PETSC_i, | |
| 180 | 432 | 4.787193103128464e+00 - 1.567476416895212e+00*PETSC_i}, | |
| 181 | 432 | p1r2[3] = { 7.648749087422928e+00 + 4.171640244747463e+00*PETSC_i, | |
| 182 | 432 | 7.648749087422928e+00 - 4.171640244747463e+00*PETSC_i, | |
| 183 | -1.829749817484586e+01 }, | ||
| 184 | 432 | p1q2[3] = { 2.681082873627756e+00 + 3.050430199247411e+00*PETSC_i, | |
| 185 | 432 | 2.681082873627756e+00 - 3.050430199247411e+00*PETSC_i, | |
| 186 | 3.637834252744491e+00 }, | ||
| 187 | 432 | p1r1[2] = { 1.000000000000000e+00 - 3.535533905932738e+00*PETSC_i, | |
| 188 | 432 | 1.000000000000000e+00 + 3.535533905932738e+00*PETSC_i}, | |
| 189 | 432 | p1q1[2] = { 2.000000000000000e+00 + 1.414213562373095e+00*PETSC_i, | |
| 190 | 432 | 2.000000000000000e+00 - 1.414213562373095e+00*PETSC_i}; | |
| 191 | 432 | const PetscComplex /* m == k-1 */ | |
| 192 | 432 | m1r5[4] = {-1.423367961376821e+02 - 1.385465094833037e+01*PETSC_i, | |
| 193 | 432 | -1.423367961376821e+02 + 1.385465094833037e+01*PETSC_i, | |
| 194 | 432 | 2.647367961376822e+02 - 4.814394493714596e+02*PETSC_i, | |
| 195 | 432 | 2.647367961376822e+02 + 4.814394493714596e+02*PETSC_i}, | |
| 196 | 432 | m1q5[4] = { 5.203941240131764e+00 + 5.805856841805367e+00*PETSC_i, | |
| 197 | 432 | 5.203941240131764e+00 - 5.805856841805367e+00*PETSC_i, | |
| 198 | 432 | 6.796058759868242e+00 + 1.886649260140217e+00*PETSC_i, | |
| 199 | 432 | 6.796058759868242e+00 - 1.886649260140217e+00*PETSC_i}, | |
| 200 | 432 | m1r4[3] = { 2.484269593165883e+01 + 7.460342395992306e+01*PETSC_i, | |
| 201 | 432 | 2.484269593165883e+01 - 7.460342395992306e+01*PETSC_i, | |
| 202 | -1.734353918633177e+02 }, | ||
| 203 | 432 | m1q4[3] = { 4.675757014491557e+00 + 3.913489560603711e+00*PETSC_i, | |
| 204 | 432 | 4.675757014491557e+00 - 3.913489560603711e+00*PETSC_i, | |
| 205 | 5.648485971016893e+00 }, | ||
| 206 | 432 | m1r3[2] = { 2.533333333333333e+01 - 2.733333333333333e+01*PETSC_i, | |
| 207 | 432 | 2.533333333333333e+01 + 2.733333333333333e+01*PETSC_i}, | |
| 208 | 432 | m1q3[2] = { 4.000000000000000e+00 + 2.000000000000000e+00*PETSC_i, | |
| 209 | 432 | 4.000000000000000e+00 - 2.000000000000000e+00*PETSC_i}; | |
| 210 | 432 | const PetscScalar /* m == k-1 */ | |
| 211 | 432 | m1remain5[2] = { 2.000000000000000e-01, 9.800000000000000e+00}, | |
| 212 | 432 | m1remain4[2] = {-2.500000000000000e-01, -7.750000000000000e+00}, | |
| 213 | 432 | m1remain3[2] = { 3.333333333333333e-01, 5.666666666666667e+00}, | |
| 214 | 432 | m1remain2[2] = {-0.5, -3.5}, | |
| 215 | 432 | remain3[4] = {1.0/6.0, 1.0/2.0, 1, 1}, | |
| 216 | 432 | remain2[3] = {1.0/2.0, 1, 1}; | |
| 217 | |||
| 218 |
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432 | PetscFunctionBegin; |
| 219 |
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432 | if (query) { /* query about buffer's size */ |
| 220 |
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216 | if (m==k+1) { |
| 221 | 20 | *remain = 0; | |
| 222 | 20 | *r = *q = k+1; | |
| 223 |
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20 | PetscFunctionReturn(PETSC_SUCCESS); /* quick return */ |
| 224 | } | ||
| 225 |
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196 | if (m==k-1) { |
| 226 | 196 | *remain = 2; | |
| 227 |
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196 | if (k==5) *r = *q = 4; |
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40 | else if (k==4) *r = *q = 3; |
| 229 | ✗ | else if (k==3) *r = *q = 2; | |
| 230 | ✗ | else if (k==2) *r = *q = 1; | |
| 231 | } | ||
| 232 |
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196 | if (m==0) { |
| 233 | ✗ | *r = *q = 0; | |
| 234 | ✗ | *remain = k+1; | |
| 235 | } | ||
| 236 | } else { | ||
| 237 |
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216 | if (m==k+1) { |
| 238 |
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20 | if (k==4) { |
| 239 |
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120 | for (i=0;i<5;i++) { r[i] = p1r4[i]; q[i] = p1q4[i]; } |
| 240 | ✗ | } else if (k==3) { | |
| 241 | ✗ | for (i=0;i<4;i++) { r[i] = p1r3[i]; q[i] = p1q3[i]; } | |
| 242 | ✗ | } else if (k==2) { | |
| 243 | ✗ | for (i=0;i<3;i++) { r[i] = p1r2[i]; q[i] = p1q2[i]; } | |
| 244 | ✗ | } else if (k==1) { | |
| 245 | ✗ | for (i=0;i<2;i++) { r[i] = p1r1[i]; q[i] = p1q1[i]; } | |
| 246 | } | ||
| 247 |
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20 | PetscFunctionReturn(PETSC_SUCCESS); /* quick return */ |
| 248 | } | ||
| 249 |
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196 | if (m==k-1) { |
| 250 |
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196 | if (k==5) { |
| 251 |
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780 | for (i=0;i<4;i++) { r[i] = m1r5[i]; q[i] = m1q5[i]; } |
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468 | for (i=0;i<2;i++) remain[i] = m1remain5[i]; |
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40 | } else if (k==4) { |
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160 | for (i=0;i<3;i++) { r[i] = m1r4[i]; q[i] = m1q4[i]; } |
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120 | for (i=0;i<2;i++) remain[i] = m1remain4[i]; |
| 256 | ✗ | } else if (k==3) { | |
| 257 | ✗ | for (i=0;i<2;i++) { r[i] = m1r3[i]; q[i] = m1q3[i]; remain[i] = m1remain3[i]; } | |
| 258 | ✗ | } else if (k==2) { | |
| 259 | ✗ | r[0] = -13.5; q[0] = 3; | |
| 260 | ✗ | for (i=0;i<2;i++) remain[i] = m1remain2[i]; | |
| 261 | } | ||
| 262 | } | ||
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196 | if (m==0) { |
| 264 | ✗ | r = q = NULL; | |
| 265 | ✗ | if (k==3) { | |
| 266 | ✗ | for (i=0;i<4;i++) remain[i] = remain3[i]; | |
| 267 | ✗ | } else if (k==2) { | |
| 268 | ✗ | for (i=0;i<3;i++) remain[i] = remain2[i]; | |
| 269 | } | ||
| 270 | } | ||
| 271 | } | ||
| 272 |
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72 | PetscFunctionReturn(PETSC_SUCCESS); |
| 273 | } | ||
| 274 | |||
| 275 | /* | ||
| 276 | * Product form coefficients. | ||
| 277 | * If query, the function returns the size necessary to store the coefficients. | ||
| 278 | */ | ||
| 279 | 432 | static PetscErrorCode getcoeffsproduct(PetscInt k,PetscInt m,PetscComplex *p,PetscComplex *q,PetscComplex *mult,PetscBool query) | |
| 280 | { | ||
| 281 | 432 | PetscInt i; | |
| 282 | 432 | const PetscComplex /* m == k+1 */ | |
| 283 | 432 | p1p4[4] = {-5.203941240131764e+00 + 5.805856841805367e+00*PETSC_i, | |
| 284 | 432 | -5.203941240131764e+00 - 5.805856841805367e+00*PETSC_i, | |
| 285 | 432 | -6.796058759868242e+00 + 1.886649260140217e+00*PETSC_i, | |
| 286 | 432 | -6.796058759868242e+00 - 1.886649260140217e+00*PETSC_i}, | |
| 287 | 432 | p1q4[5] = { 3.655694325463550e+00 + 6.543736899360086e+00*PETSC_i, | |
| 288 | 432 | 3.655694325463550e+00 - 6.543736899360086e+00*PETSC_i, | |
| 289 | 6.286704751729261e+00 , | ||
| 290 | 432 | 5.700953298671832e+00 + 3.210265600308496e+00*PETSC_i, | |
| 291 | 432 | 5.700953298671832e+00 - 3.210265600308496e+00*PETSC_i}, | |
| 292 | 432 | p1p3[3] = {-4.675757014491557e+00 + 3.913489560603711e+00*PETSC_i, | |
| 293 | 432 | -4.675757014491557e+00 - 3.913489560603711e+00*PETSC_i, | |
| 294 | -5.648485971016893e+00 }, | ||
| 295 | 432 | p1q3[4] = { 3.212806896871536e+00 + 4.773087433276636e+00*PETSC_i, | |
| 296 | 432 | 3.212806896871536e+00 - 4.773087433276636e+00*PETSC_i, | |
| 297 | 432 | 4.787193103128464e+00 + 1.567476416895212e+00*PETSC_i, | |
| 298 | 432 | 4.787193103128464e+00 - 1.567476416895212e+00*PETSC_i}, | |
| 299 | 432 | p1p2[2] = {-4.00000000000000e+00 + 2.000000000000000e+00*PETSC_i, | |
| 300 | 432 | -4.00000000000000e+00 - 2.000000000000000e+00*PETSC_i}, | |
| 301 | 432 | p1q2[3] = { 2.681082873627756e+00 + 3.050430199247411e+00*PETSC_i, | |
| 302 | 432 | 2.681082873627756e+00 - 3.050430199247411e+00*PETSC_i, | |
| 303 | 3.637834252744491e+00 }, | ||
| 304 | 432 | p1q1[2] = { 2.000000000000000e+00 + 1.414213562373095e+00*PETSC_i, | |
| 305 | 432 | 2.000000000000000e+00 - 1.414213562373095e+00*PETSC_i}; | |
| 306 | 432 | const PetscComplex /* m == k-1 */ | |
| 307 | 432 | m1p5[5] = {-3.655694325463550e+00 + 6.543736899360086e+00*PETSC_i, | |
| 308 | 432 | -3.655694325463550e+00 - 6.543736899360086e+00*PETSC_i, | |
| 309 | -6.286704751729261e+00 , | ||
| 310 | 432 | -5.700953298671832e+00 + 3.210265600308496e+00*PETSC_i, | |
| 311 | 432 | -5.700953298671832e+00 - 3.210265600308496e+00*PETSC_i}, | |
| 312 | 432 | m1q5[4] = { 5.203941240131764e+00 + 5.805856841805367e+00*PETSC_i, | |
| 313 | 432 | 5.203941240131764e+00 - 5.805856841805367e+00*PETSC_i, | |
| 314 | 432 | 6.796058759868242e+00 + 1.886649260140217e+00*PETSC_i, | |
| 315 | 432 | 6.796058759868242e+00 - 1.886649260140217e+00*PETSC_i}, | |
| 316 | 432 | m1p4[4] = {-3.212806896871536e+00 + 4.773087433276636e+00*PETSC_i, | |
| 317 | 432 | -3.212806896871536e+00 - 4.773087433276636e+00*PETSC_i, | |
| 318 | 432 | -4.787193103128464e+00 + 1.567476416895212e+00*PETSC_i, | |
| 319 | 432 | -4.787193103128464e+00 - 1.567476416895212e+00*PETSC_i}, | |
| 320 | 432 | m1q4[3] = { 4.675757014491557e+00 + 3.913489560603711e+00*PETSC_i, | |
| 321 | 432 | 4.675757014491557e+00 - 3.913489560603711e+00*PETSC_i, | |
| 322 | 5.648485971016893e+00 }, | ||
| 323 | 432 | m1p3[3] = {-2.681082873627756e+00 + 3.050430199247411e+00*PETSC_i, | |
| 324 | 432 | -2.681082873627756e+00 - 3.050430199247411e+00*PETSC_i, | |
| 325 | -3.637834252744491e+00 }, | ||
| 326 | 432 | m1q3[2] = { 4.000000000000000e+00 + 2.000000000000000e+00*PETSC_i, | |
| 327 | 432 | 4.000000000000000e+00 - 2.000000000000001e+00*PETSC_i}, | |
| 328 | 432 | m1p2[2] = {-2.000000000000000e+00 + 1.414213562373095e+00*PETSC_i, | |
| 329 | 432 | -2.000000000000000e+00 - 1.414213562373095e+00*PETSC_i}; | |
| 330 | |||
| 331 |
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432 | PetscFunctionBegin; |
| 332 |
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432 | if (query) { |
| 333 |
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216 | if (m == k+1) { |
| 334 | 20 | *mult = 1; | |
| 335 | 20 | *p = k; | |
| 336 | 20 | *q = k+1; | |
| 337 |
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20 | PetscFunctionReturn(PETSC_SUCCESS); |
| 338 | } | ||
| 339 |
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196 | if (m==k-1) { |
| 340 | 196 | *mult = 1; | |
| 341 | 196 | *p = k; | |
| 342 | 196 | *q = k-1; | |
| 343 | } | ||
| 344 | } else { | ||
| 345 |
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216 | if (m == k+1) { |
| 346 | 20 | *mult = PetscPowInt(-1,m); | |
| 347 | 20 | *mult *= m; | |
| 348 |
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20 | if (k==4) { |
| 349 |
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100 | for (i=0;i<4;i++) { p[i] = p1p4[i]; q[i] = p1q4[i]; } |
| 350 | 20 | q[4] = p1q4[4]; | |
| 351 | ✗ | } else if (k==3) { | |
| 352 | ✗ | for (i=0;i<3;i++) { p[i] = p1p3[i]; q[i] = p1q3[i]; } | |
| 353 | ✗ | q[3] = p1q3[3]; | |
| 354 | ✗ | } else if (k==2) { | |
| 355 | ✗ | for (i=0;i<2;i++) { p[i] = p1p2[i]; q[i] = p1q2[i]; } | |
| 356 | ✗ | q[2] = p1q2[2]; | |
| 357 | ✗ | } else if (k==1) { | |
| 358 | ✗ | p[0] = -3; | |
| 359 | ✗ | for (i=0;i<2;i++) q[i] = p1q1[i]; | |
| 360 | } | ||
| 361 |
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20 | PetscFunctionReturn(PETSC_SUCCESS); |
| 362 | } | ||
| 363 |
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196 | if (m==k-1) { |
| 364 | 196 | *mult = PetscPowInt(-1,m); | |
| 365 | 196 | *mult /= k; | |
| 366 |
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196 | if (k==5) { |
| 367 |
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780 | for (i=0;i<4;i++) { p[i] = m1p5[i]; q[i] = m1q5[i]; } |
| 368 | 156 | p[4] = m1p5[4]; | |
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40 | } else if (k==4) { |
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160 | for (i=0;i<3;i++) { p[i] = m1p4[i]; q[i] = m1q4[i]; } |
| 371 | 40 | p[3] = m1p4[3]; | |
| 372 | ✗ | } else if (k==3) { | |
| 373 | ✗ | for (i=0;i<2;i++) { p[i] = m1p3[i]; q[i] = m1q3[i]; } | |
| 374 | ✗ | p[2] = m1p3[2]; | |
| 375 | ✗ | } else if (k==2) { | |
| 376 | ✗ | for (i=0;i<2;i++) p[i] = m1p2[i]; | |
| 377 | ✗ | q[0] = 3; | |
| 378 | } | ||
| 379 | } | ||
| 380 | } | ||
| 381 |
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72 | PetscFunctionReturn(PETSC_SUCCESS); |
| 382 | } | ||
| 383 | #endif /* PETSC_HAVE_COMPLEX */ | ||
| 384 | |||
| 385 | #if defined(PETSC_USE_COMPLEX) | ||
| 386 | 100 | static PetscErrorCode getisreal(PetscInt n,PetscComplex *a,PetscBool *result) | |
| 387 | { | ||
| 388 | 100 | PetscInt i; | |
| 389 | |||
| 390 |
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100 | PetscFunctionBegin; |
| 391 | 100 | *result=PETSC_TRUE; | |
| 392 |
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296100 | for (i=0;i<n&&*result;i++) { |
| 393 |
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296000 | if (PetscImaginaryPartComplex(a[i])) *result=PETSC_FALSE; |
| 394 | } | ||
| 395 |
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100 | PetscFunctionReturn(PETSC_SUCCESS); |
| 396 | } | ||
| 397 | #endif | ||
| 398 | |||
| 399 | /* | ||
| 400 | * Matrix exponential implementation based on algorithm and matlab code by Stefan Guettel | ||
| 401 | * and Yuji Nakatsukasa | ||
| 402 | * | ||
| 403 | * Stefan Guettel and Yuji Nakatsukasa, "Scaled and Squared Subdiagonal Pade | ||
| 404 | * Approximation for the Matrix Exponential", | ||
| 405 | * SIAM J. Matrix Anal. Appl. 37(1):145-170, 2016. | ||
| 406 | * https://doi.org/10.1137/15M1027553 | ||
| 407 | */ | ||
| 408 | 520 | static PetscErrorCode FNEvaluateFunctionMat_Exp_GuettelNakatsukasa(FN fn,Mat A,Mat B) | |
| 409 | { | ||
| 410 | #if !defined(PETSC_HAVE_COMPLEX) | ||
| 411 | PetscFunctionBegin; | ||
| 412 | SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This function requires C99 or C++ complex support"); | ||
| 413 | #else | ||
| 414 | 520 | PetscInt i,j,n_,s,k,m,mod; | |
| 415 | 520 | PetscBLASInt n=0,n2=0,irsize=0,rsizediv2,ipsize=0,iremainsize=0,*piv,minlen,lwork=0,one=1; | |
| 416 | 520 | PetscReal nrm,shift=0.0; | |
| 417 | #if defined(PETSC_USE_COMPLEX) | ||
| 418 | 260 | PetscReal *rwork=NULL; | |
| 419 | #endif | ||
| 420 | 520 | PetscComplex *As,*RR,*RR2,*expmA,*expmA2,*Maux,*Maux2,rsize,*r,psize,*p,remainsize,*remainterm,*rootp,*rootq,mult=0.0,scale,cone=1.0,czero=0.0,*aux; | |
| 421 | 520 | PetscScalar *Ba,*Ba2,*sMaux,*wr,*wi,expshift,sone=1.0,szero=0.0,*saux; | |
| 422 | 520 | const PetscScalar *Aa; | |
| 423 | 520 | PetscBool isreal,flg; | |
| 424 | 520 | PetscBLASInt query=-1; | |
| 425 | 520 | PetscScalar work1,*work; | |
| 426 | |||
| 427 |
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520 | PetscFunctionBegin; |
| 428 |
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520 | PetscCall(MatGetSize(A,&n_,NULL)); |
| 429 |
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520 | PetscCall(PetscBLASIntCast(n_,&n)); |
| 430 |
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520 | PetscCall(MatDenseGetArrayRead(A,&Aa)); |
| 431 |
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520 | PetscCall(MatDenseGetArray(B,&Ba)); |
| 432 | 520 | Ba2 = Ba; | |
| 433 |
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520 | PetscCall(PetscBLASIntCast(n*n,&n2)); |
| 434 | |||
| 435 |
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520 | PetscCall(PetscMalloc2(n2,&sMaux,n2,&Maux)); |
| 436 | 520 | Maux2 = Maux; | |
| 437 |
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520 | PetscCall(PetscOptionsGetReal(NULL,NULL,"-fn_expm_estimated_eig",&shift,&flg)); |
| 438 |
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520 | if (!flg) { |
| 439 |
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520 | PetscCall(PetscMalloc2(n,&wr,n,&wi)); |
| 440 |
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520 | PetscCall(PetscArraycpy(sMaux,Aa,n2)); |
| 441 | /* estimate rightmost eigenvalue and shift A with it */ | ||
| 442 | #if !defined(PETSC_USE_COMPLEX) | ||
| 443 |
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260 | PetscCallLAPACKInfo("LAPACKgeev",LAPACKgeev_("N","N",&n,sMaux,&n,wr,wi,NULL,&n,NULL,&n,&work1,&query,&info)); |
| 444 |
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260 | PetscCall(PetscBLASIntCast((PetscInt)work1,&lwork)); |
| 445 |
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260 | PetscCall(PetscMalloc1(lwork,&work)); |
| 446 |
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260 | PetscCallLAPACKInfo("LAPACKgeev",LAPACKgeev_("N","N",&n,sMaux,&n,wr,wi,NULL,&n,NULL,&n,work,&lwork,&info)); |
| 447 |
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260 | PetscCall(PetscFree(work)); |
| 448 | #else | ||
| 449 |
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260 | PetscCall(PetscArraycpy(Maux,Aa,n2)); |
| 450 |
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260 | PetscCallLAPACKInfo("LAPACKgeev",LAPACKgeev_("N","N",&n,Maux,&n,wr,NULL,&n,NULL,&n,&work1,&query,rwork,&info)); |
| 451 |
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260 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(work1),&lwork)); |
| 452 |
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260 | PetscCall(PetscMalloc2(2*n,&rwork,lwork,&work)); |
| 453 |
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260 | PetscCallLAPACKInfo("LAPACKgeev",LAPACKgeev_("N","N",&n,Maux,&n,wr,NULL,&n,NULL,&n,work,&lwork,rwork,&info)); |
| 454 |
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260 | PetscCall(PetscFree2(rwork,work)); |
| 455 | #endif | ||
| 456 |
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520 | PetscCall(PetscLogFlops(25.0*n*n*n+(n*n*n)/3.0+1.0*n*n*n)); |
| 457 | |||
| 458 | 520 | shift = PetscRealPart(wr[0]); | |
| 459 |
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14000 | for (i=1;i<n;i++) { |
| 460 |
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13480 | if (PetscRealPart(wr[i]) > shift) shift = PetscRealPart(wr[i]); |
| 461 | } | ||
| 462 |
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520 | PetscCall(PetscFree2(wr,wi)); |
| 463 | } | ||
| 464 | /* shift so that largest real part is (about) 0 */ | ||
| 465 |
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520 | PetscCall(PetscArraycpy(sMaux,Aa,n2)); |
| 466 |
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520 | if (shift) { |
| 467 |
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14520 | for (i=0;i<n;i++) sMaux[i+i*n] -= shift; |
| 468 |
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520 | PetscCall(PetscLogFlops(1.0*n)); |
| 469 | } | ||
| 470 | #if defined(PETSC_USE_COMPLEX) | ||
| 471 |
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260 | PetscCall(PetscArraycpy(Maux,Aa,n2)); |
| 472 |
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260 | if (shift) { |
| 473 |
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7260 | for (i=0;i<n;i++) Maux[i+i*n] -= shift; |
| 474 |
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260 | PetscCall(PetscLogFlops(1.0*n)); |
| 475 | } | ||
| 476 | #endif | ||
| 477 | |||
| 478 | /* estimate norm(A) and select the scaling factor */ | ||
| 479 | 520 | nrm = LAPACKlange_("O",&n,&n,sMaux,&n,NULL); | |
| 480 |
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520 | PetscCall(PetscLogFlops(1.0*n*n)); |
| 481 |
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520 | PetscCall(sexpm_params(nrm,&s,&k,&m)); |
| 482 |
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520 | if (s==0 && k==1 && m==0) { /* exp(A) = I+A to eps! */ |
| 483 |
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120 | if (shift) expshift = PetscExpReal(shift); |
| 484 |
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1320 | for (i=0;i<n;i++) sMaux[i+i*n] += 1.0; |
| 485 |
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120 | if (shift) { |
| 486 |
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120 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&expshift,sMaux,&one)); |
| 487 |
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120 | PetscCall(PetscLogFlops(1.0*(n+n2))); |
| 488 | ✗ | } else PetscCall(PetscLogFlops(1.0*n)); | |
| 489 |
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120 | PetscCall(PetscArraycpy(Ba,sMaux,n2)); |
| 490 |
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120 | PetscCall(PetscFree2(sMaux,Maux)); |
| 491 |
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120 | PetscCall(MatDenseRestoreArrayRead(A,&Aa)); |
| 492 |
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120 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 493 |
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24 | PetscFunctionReturn(PETSC_SUCCESS); /* quick return */ |
| 494 | } | ||
| 495 | |||
| 496 |
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400 | PetscCall(PetscMalloc4(n2,&expmA,n2,&As,n2,&RR,n,&piv)); |
| 497 | 400 | expmA2 = expmA; RR2 = RR; | |
| 498 | /* scale matrix */ | ||
| 499 | #if !defined(PETSC_USE_COMPLEX) | ||
| 500 |
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592200 | for (i=0;i<n2;i++) { |
| 501 | 592000 | As[i] = sMaux[i]; | |
| 502 | } | ||
| 503 | #else | ||
| 504 |
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200 | PetscCall(PetscArraycpy(As,sMaux,n2)); |
| 505 | #endif | ||
| 506 | 400 | scale = 1.0/PetscPowRealInt(2.0,s); | |
| 507 |
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400 | PetscCallBLAS("BLASCOMPLEXscal",BLASCOMPLEXscal_(&n2,&scale,As,&one)); |
| 508 |
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400 | PetscCall(SlepcLogFlopsComplex(1.0*n2)); |
| 509 | |||
| 510 | /* evaluate Pade approximant (partial fraction or product form) */ | ||
| 511 |
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400 | if (fn->method==3 || !m) { /* partial fraction */ |
| 512 |
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200 | PetscCall(getcoeffs(k,m,&rsize,&psize,&remainsize,PETSC_TRUE)); |
| 513 |
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200 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(rsize),&irsize)); |
| 514 |
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200 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(psize),&ipsize)); |
| 515 |
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200 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(remainsize),&iremainsize)); |
| 516 |
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200 | PetscCall(PetscMalloc3(irsize,&r,ipsize,&p,iremainsize,&remainterm)); |
| 517 |
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200 | PetscCall(getcoeffs(k,m,r,p,remainterm,PETSC_FALSE)); |
| 518 | |||
| 519 |
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200 | PetscCall(PetscArrayzero(expmA,n2)); |
| 520 | #if !defined(PETSC_USE_COMPLEX) | ||
| 521 | 100 | isreal = PETSC_TRUE; | |
| 522 | #else | ||
| 523 |
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100 | PetscCall(getisreal(n2,Maux,&isreal)); |
| 524 | #endif | ||
| 525 |
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200 | if (isreal) { |
| 526 | 200 | rsizediv2 = irsize/2; | |
| 527 |
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560 | for (i=0;i<rsizediv2;i++) { /* use partial fraction to get R(As) */ |
| 528 |
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360 | PetscCall(PetscArraycpy(Maux,As,n2)); |
| 529 |
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360 | PetscCall(PetscArrayzero(RR,n2)); |
| 530 |
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12760 | for (j=0;j<n;j++) { |
| 531 | 12400 | Maux[j+j*n] -= p[2*i]; | |
| 532 | 12400 | RR[j+j*n] = r[2*i]; | |
| 533 | } | ||
| 534 |
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360 | PetscCallLAPACKInfo("LAPACKCOMPLEXgesv",LAPACKCOMPLEXgesv_(&n,&n,Maux,&n,piv,RR,&n,&info)); |
| 535 |
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|
1180360 | for (j=0;j<n2;j++) { |
| 536 | 1180000 | expmA[j] += RR[j] + PetscConj(RR[j]); | |
| 537 | } | ||
| 538 | /* loop(n) + gesv + loop(n2) */ | ||
| 539 |
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|
360 | PetscCall(SlepcLogFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n)+2.0*n2)); |
| 540 | } | ||
| 541 | |||
| 542 | 200 | mod = ipsize % 2; | |
| 543 |
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200 | if (mod) { |
| 544 |
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60 | PetscCall(PetscArraycpy(Maux,As,n2)); |
| 545 |
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60 | PetscCall(PetscArrayzero(RR,n2)); |
| 546 |
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660 | for (j=0;j<n;j++) { |
| 547 | 600 | Maux[j+j*n] -= p[ipsize-1]; | |
| 548 | 600 | RR[j+j*n] = r[irsize-1]; | |
| 549 | } | ||
| 550 |
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|
60 | PetscCallLAPACKInfo("LAPACKCOMPLEXgesv",LAPACKCOMPLEXgesv_(&n,&n,Maux,&n,piv,RR,&n,&info)); |
| 551 |
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6060 | for (j=0;j<n2;j++) { |
| 552 | 6000 | expmA[j] += RR[j]; | |
| 553 | } | ||
| 554 |
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|
60 | PetscCall(SlepcLogFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n)+1.0*n2)); |
| 555 | } | ||
| 556 | } else { /* complex */ | ||
| 557 | ✗ | for (i=0;i<irsize;i++) { /* use partial fraction to get R(As) */ | |
| 558 | ✗ | PetscCall(PetscArraycpy(Maux,As,n2)); | |
| 559 | ✗ | PetscCall(PetscArrayzero(RR,n2)); | |
| 560 | ✗ | for (j=0;j<n;j++) { | |
| 561 | ✗ | Maux[j+j*n] -= p[i]; | |
| 562 | ✗ | RR[j+j*n] = r[i]; | |
| 563 | } | ||
| 564 | ✗ | PetscCallLAPACKInfo("LAPACKCOMPLEXgesv",LAPACKCOMPLEXgesv_(&n,&n,Maux,&n,piv,RR,&n,&info)); | |
| 565 | ✗ | for (j=0;j<n2;j++) { | |
| 566 | ✗ | expmA[j] += RR[j]; | |
| 567 | } | ||
| 568 | ✗ | PetscCall(SlepcLogFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n)+1.0*n2)); | |
| 569 | } | ||
| 570 | } | ||
| 571 |
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560 | for (i=0;i<iremainsize;i++) { |
| 572 |
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360 | if (!i) { |
| 573 |
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180 | PetscCall(PetscArrayzero(RR,n2)); |
| 574 |
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6380 | for (j=0;j<n;j++) { |
| 575 | 6200 | RR[j+j*n] = remainterm[iremainsize-1]; | |
| 576 | } | ||
| 577 | } else { | ||
| 578 |
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180 | PetscCall(PetscArraycpy(RR,As,n2)); |
| 579 |
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180 | for (j=1;j<i;j++) { |
| 580 | ✗ | PetscCallBLAS("BLASCOMPLEXgemm",BLASCOMPLEXgemm_("N","N",&n,&n,&n,&cone,RR,&n,RR,&n,&czero,Maux,&n)); | |
| 581 | ✗ | SlepcSwap(RR,Maux,aux); | |
| 582 | ✗ | PetscCall(SlepcLogFlopsComplex(2.0*n*n*n)); | |
| 583 | } | ||
| 584 |
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180 | PetscCallBLAS("BLASCOMPLEXscal",BLASCOMPLEXscal_(&n2,&remainterm[iremainsize-1-i],RR,&one)); |
| 585 |
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180 | PetscCall(SlepcLogFlopsComplex(1.0*n2)); |
| 586 | } | ||
| 587 |
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1180360 | for (j=0;j<n2;j++) { |
| 588 | 1180000 | expmA[j] += RR[j]; | |
| 589 | } | ||
| 590 |
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360 | PetscCall(SlepcLogFlopsComplex(1.0*n2)); |
| 591 | } | ||
| 592 |
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200 | PetscCall(PetscFree3(r,p,remainterm)); |
| 593 | } else { /* product form, default */ | ||
| 594 |
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200 | PetscCall(getcoeffsproduct(k,m,&rsize,&psize,&mult,PETSC_TRUE)); |
| 595 |
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200 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(rsize),&irsize)); |
| 596 |
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200 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(psize),&ipsize)); |
| 597 |
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200 | PetscCall(PetscMalloc2(irsize,&rootp,ipsize,&rootq)); |
| 598 |
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200 | PetscCall(getcoeffsproduct(k,m,rootp,rootq,&mult,PETSC_FALSE)); |
| 599 | |||
| 600 |
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200 | PetscCall(PetscArrayzero(expmA,n2)); |
| 601 |
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6600 | for (i=0;i<n;i++) { /* initialize */ |
| 602 | 6400 | expmA[i+i*n] = 1.0; | |
| 603 | } | ||
| 604 | 200 | minlen = PetscMin(irsize,ipsize); | |
| 605 |
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960 | for (i=0;i<minlen;i++) { |
| 606 |
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760 | PetscCall(PetscArraycpy(RR,As,n2)); |
| 607 |
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25960 | for (j=0;j<n;j++) { |
| 608 | 25200 | RR[j+j*n] -= rootp[i]; | |
| 609 | } | ||
| 610 |
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|
760 | PetscCallBLAS("BLASCOMPLEXgemm",BLASCOMPLEXgemm_("N","N",&n,&n,&n,&cone,RR,&n,expmA,&n,&czero,Maux,&n)); |
| 611 | 760 | SlepcSwap(expmA,Maux,aux); | |
| 612 |
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760 | PetscCall(PetscArraycpy(RR,As,n2)); |
| 613 |
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25960 | for (j=0;j<n;j++) { |
| 614 | 25200 | RR[j+j*n] -= rootq[i]; | |
| 615 | } | ||
| 616 |
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|
760 | PetscCallLAPACKInfo("LAPACKCOMPLEXgesv",LAPACKCOMPLEXgesv_(&n,&n,RR,&n,piv,expmA,&n,&info)); |
| 617 | /* loop(n) + gemm + loop(n) + gesv */ | ||
| 618 |
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760 | PetscCall(SlepcLogFlopsComplex(1.0*n+(2.0*n*n*n)+1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n))); |
| 619 | } | ||
| 620 | /* extra numerator */ | ||
| 621 |
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380 | for (i=minlen;i<irsize;i++) { |
| 622 |
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180 | PetscCall(PetscArraycpy(RR,As,n2)); |
| 623 |
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6380 | for (j=0;j<n;j++) { |
| 624 | 6200 | RR[j+j*n] -= rootp[i]; | |
| 625 | } | ||
| 626 |
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|
180 | PetscCallBLAS("BLASCOMPLEXgemm",BLASCOMPLEXgemm_("N","N",&n,&n,&n,&cone,RR,&n,expmA,&n,&czero,Maux,&n)); |
| 627 | 180 | SlepcSwap(expmA,Maux,aux); | |
| 628 |
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180 | PetscCall(SlepcLogFlopsComplex(1.0*n+2.0*n*n*n)); |
| 629 | } | ||
| 630 | /* extra denominator */ | ||
| 631 |
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220 | for (i=minlen;i<ipsize;i++) { |
| 632 |
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20 | PetscCall(PetscArraycpy(RR,As,n2)); |
| 633 |
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220 | for (j=0;j<n;j++) RR[j+j*n] -= rootq[i]; |
| 634 |
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20 | PetscCallLAPACKInfo("LAPACKCOMPLEXgesv",LAPACKCOMPLEXgesv_(&n,&n,RR,&n,piv,expmA,&n,&info)); |
| 635 |
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20 | PetscCall(SlepcLogFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n))); |
| 636 | } | ||
| 637 |
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|
200 | PetscCallBLAS("BLASCOMPLEXscal",BLASCOMPLEXscal_(&n2,&mult,expmA,&one)); |
| 638 |
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200 | PetscCall(SlepcLogFlopsComplex(1.0*n2)); |
| 639 |
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|
200 | PetscCall(PetscFree2(rootp,rootq)); |
| 640 | } | ||
| 641 | |||
| 642 | #if !defined(PETSC_USE_COMPLEX) | ||
| 643 |
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592200 | for (i=0;i<n2;i++) { |
| 644 | 592000 | Ba2[i] = PetscRealPartComplex(expmA[i]); | |
| 645 | } | ||
| 646 | #else | ||
| 647 |
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200 | PetscCall(PetscArraycpy(Ba2,expmA,n2)); |
| 648 | #endif | ||
| 649 | |||
| 650 | /* perform repeated squaring */ | ||
| 651 |
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1960 | for (i=0;i<s;i++) { /* final squaring */ |
| 652 |
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|
1560 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&sone,Ba2,&n,Ba2,&n,&szero,sMaux,&n)); |
| 653 | 1560 | SlepcSwap(Ba2,sMaux,saux); | |
| 654 |
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1560 | PetscCall(PetscLogFlops(2.0*n*n*n)); |
| 655 | } | ||
| 656 |
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400 | if (Ba2!=Ba) { |
| 657 |
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|
40 | PetscCall(PetscArraycpy(Ba,Ba2,n2)); |
| 658 | 40 | sMaux = Ba2; | |
| 659 | } | ||
| 660 |
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400 | if (shift) { |
| 661 | 400 | expshift = PetscExpReal(shift); | |
| 662 |
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|
400 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&expshift,Ba,&one)); |
| 663 |
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|
400 | PetscCall(PetscLogFlops(1.0*n2)); |
| 664 | } | ||
| 665 | |||
| 666 | /* restore pointers */ | ||
| 667 | 400 | Maux = Maux2; expmA = expmA2; RR = RR2; | |
| 668 |
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|
400 | PetscCall(PetscFree2(sMaux,Maux)); |
| 669 |
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|
400 | PetscCall(PetscFree4(expmA,As,RR,piv)); |
| 670 |
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|
400 | PetscCall(MatDenseRestoreArrayRead(A,&Aa)); |
| 671 |
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|
400 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 672 |
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|
80 | PetscFunctionReturn(PETSC_SUCCESS); |
| 673 | #endif | ||
| 674 | } | ||
| 675 | |||
| 676 | #define SMALLN 100 | ||
| 677 | |||
| 678 | /* | ||
| 679 | * Function needed to compute optimal parameters (required workspace is 3*n*n) | ||
| 680 | */ | ||
| 681 | 4600 | static PetscInt ell(PetscBLASInt n,PetscScalar *A,PetscReal coeff,PetscInt m,PetscScalar *work,PetscRandom rand) | |
| 682 | { | ||
| 683 | 4600 | PetscScalar *Ascaled=work; | |
| 684 | 4600 | PetscReal nrm,alpha,beta,rwork[1]; | |
| 685 | 4600 | PetscInt t; | |
| 686 | 4600 | PetscBLASInt i,j; | |
| 687 | |||
| 688 |
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|
4600 | PetscFunctionBegin; |
| 689 | 4600 | beta = PetscPowReal(coeff,1.0/(2*m+1)); | |
| 690 |
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|
116392 | for (i=0;i<n;i++) |
| 691 |
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|
6671592 | for (j=0;j<n;j++) |
| 692 | 6559800 | Ascaled[i+j*n] = beta*PetscAbsScalar(A[i+j*n]); | |
| 693 | 4600 | nrm = LAPACKlange_("O",&n,&n,A,&n,rwork); | |
| 694 |
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|
4600 | PetscCall(PetscLogFlops(2.0*n*n)); |
| 695 |
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|
4600 | PetscCall(SlepcNormAm(n,Ascaled,2*m+1,work+n*n,rand,&alpha)); |
| 696 | 4600 | alpha /= nrm; | |
| 697 |
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|
4600 | t = PetscMax((PetscInt)PetscCeilReal(PetscLogReal(2.0*alpha/PETSC_MACHINE_EPSILON)/PetscLogReal(2.0)/(2*m)),0); |
| 698 |
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|
904 | PetscFunctionReturn(t); |
| 699 | } | ||
| 700 | |||
| 701 | /* | ||
| 702 | * Compute scaling parameter (s) and order of Pade approximant (m) (required workspace is 4*n*n) | ||
| 703 | */ | ||
| 704 | 4598 | static PetscErrorCode expm_params(PetscInt n,PetscScalar **Apowers,PetscInt *s,PetscInt *m,PetscScalar *work) | |
| 705 | { | ||
| 706 | 4598 | PetscScalar sfactor,sone=1.0,szero=0.0,*A=Apowers[0],*Ascaled; | |
| 707 | 4598 | PetscReal d4,d6,d8,d10,eta1,eta3,eta4,eta5,rwork[1]; | |
| 708 | 4598 | PetscBLASInt n_=0,n2,one=1; | |
| 709 | 4598 | PetscRandom rand; | |
| 710 | 4598 | const PetscReal coeff[5] = { 9.92063492063492e-06, 9.94131285136576e-11, /* backward error function */ | |
| 711 | 2.22819456055356e-16, 1.69079293431187e-22, 8.82996160201868e-36 }; | ||
| 712 | 4598 | const PetscReal theta[5] = { 1.495585217958292e-002, /* m = 3 */ | |
| 713 | 2.539398330063230e-001, /* m = 5 */ | ||
| 714 | 9.504178996162932e-001, /* m = 7 */ | ||
| 715 | 2.097847961257068e+000, /* m = 9 */ | ||
| 716 | 5.371920351148152e+000 }; /* m = 13 */ | ||
| 717 | |||
| 718 |
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|
4598 | PetscFunctionBegin; |
| 719 | 4598 | *s = 0; | |
| 720 | 4598 | *m = 13; | |
| 721 |
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|
4598 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 722 |
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|
4598 | PetscCall(PetscRandomCreate(PETSC_COMM_SELF,&rand)); |
| 723 | 4598 | d4 = PetscPowReal(LAPACKlange_("O",&n_,&n_,Apowers[2],&n_,rwork),1.0/4.0); | |
| 724 |
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|
4598 | if (d4==0.0) { /* safeguard for the case A = 0 */ |
| 725 | ✗ | *m = 3; | |
| 726 | ✗ | goto done; | |
| 727 | } | ||
| 728 | 4598 | d6 = PetscPowReal(LAPACKlange_("O",&n_,&n_,Apowers[3],&n_,rwork),1.0/6.0); | |
| 729 |
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|
4598 | PetscCall(PetscLogFlops(2.0*n*n)); |
| 730 |
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|
4598 | eta1 = PetscMax(d4,d6); |
| 731 |
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|
4598 | if (eta1<=theta[0] && !ell(n_,A,coeff[0],3,work,rand)) { |
| 732 | 1115 | *m = 3; | |
| 733 | 1115 | goto done; | |
| 734 | } | ||
| 735 |
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|
3483 | if (eta1<=theta[1] && !ell(n_,A,coeff[1],5,work,rand)) { |
| 736 | 1000 | *m = 5; | |
| 737 | 1000 | goto done; | |
| 738 | } | ||
| 739 |
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|
2483 | if (n<SMALLN) { |
| 740 |
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|
2343 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[2],&n_,Apowers[2],&n_,&szero,work,&n_)); |
| 741 | 2343 | d8 = PetscPowReal(LAPACKlange_("O",&n_,&n_,work,&n_,rwork),1.0/8.0); | |
| 742 |
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|
2343 | PetscCall(PetscLogFlops(2.0*n*n*n+1.0*n*n)); |
| 743 | } else { | ||
| 744 |
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|
140 | PetscCall(SlepcNormAm(n_,Apowers[2],2,work,rand,&d8)); |
| 745 | 140 | d8 = PetscPowReal(d8,1.0/8.0); | |
| 746 | } | ||
| 747 |
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|
2483 | eta3 = PetscMax(d6,d8); |
| 748 |
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|
2483 | if (eta3<=theta[2] && !ell(n_,A,coeff[2],7,work,rand)) { |
| 749 | 114 | *m = 7; | |
| 750 | 114 | goto done; | |
| 751 | } | ||
| 752 |
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|
2369 | if (eta3<=theta[3] && !ell(n_,A,coeff[3],9,work,rand)) { |
| 753 | 177 | *m = 9; | |
| 754 | 177 | goto done; | |
| 755 | } | ||
| 756 |
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|
2192 | if (n<SMALLN) { |
| 757 |
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|
2052 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[2],&n_,Apowers[3],&n_,&szero,work,&n_)); |
| 758 | 2052 | d10 = PetscPowReal(LAPACKlange_("O",&n_,&n_,work,&n_,rwork),1.0/10.0); | |
| 759 |
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|
2052 | PetscCall(PetscLogFlops(2.0*n*n*n+1.0*n*n)); |
| 760 | } else { | ||
| 761 |
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|
140 | PetscCall(SlepcNormAm(n_,Apowers[1],5,work,rand,&d10)); |
| 762 | 140 | d10 = PetscPowReal(d10,1.0/10.0); | |
| 763 | } | ||
| 764 |
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|
2192 | eta4 = PetscMax(d8,d10); |
| 765 |
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|
2192 | eta5 = PetscMin(eta3,eta4); |
| 766 |
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|
2192 | *s = PetscMax((PetscInt)PetscCeilReal(PetscLogReal(eta5/theta[4])/PetscLogReal(2.0)),0); |
| 767 |
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|
2192 | if (*s) { |
| 768 | 753 | Ascaled = work+3*n*n; | |
| 769 | 753 | n2 = n_*n_; | |
| 770 |
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|
753 | PetscCallBLAS("BLAScopy",BLAScopy_(&n2,A,&one,Ascaled,&one)); |
| 771 | 753 | sfactor = PetscPowRealInt(2.0,-(*s)); | |
| 772 |
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|
753 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&sfactor,Ascaled,&one)); |
| 773 |
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|
753 | PetscCall(PetscLogFlops(1.0*n*n)); |
| 774 | } else Ascaled = A; | ||
| 775 | 2192 | *s += ell(n_,Ascaled,coeff[4],13,work,rand); | |
| 776 | 4598 | done: | |
| 777 |
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|
4598 | PetscCall(PetscRandomDestroy(&rand)); |
| 778 |
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|
904 | PetscFunctionReturn(PETSC_SUCCESS); |
| 779 | } | ||
| 780 | |||
| 781 | /* | ||
| 782 | * Matrix exponential implementation based on algorithm and matlab code by N. Higham and co-authors | ||
| 783 | * | ||
| 784 | * N. J. Higham, "The scaling and squaring method for the matrix exponential | ||
| 785 | * revisited", SIAM J. Matrix Anal. Appl. 26(4):1179-1193, 2005. | ||
| 786 | */ | ||
| 787 | 4550 | PetscErrorCode FNEvaluateFunctionMat_Exp_Higham(FN fn,Mat A,Mat B) | |
| 788 | { | ||
| 789 | 4550 | PetscBLASInt n_=0,n2,*ipiv,one=1; | |
| 790 | 4550 | PetscInt n,m,j,s; | |
| 791 | 4550 | PetscScalar scale,smone=-1.0,sone=1.0,stwo=2.0,szero=0.0; | |
| 792 | 4550 | PetscScalar *Ba,*Apowers[5],*Q,*P,*W,*work,*aux; | |
| 793 | 4550 | const PetscScalar *Aa,*c; | |
| 794 | 4550 | const PetscScalar c3[4] = { 120, 60, 12, 1 }; | |
| 795 | 4550 | const PetscScalar c5[6] = { 30240, 15120, 3360, 420, 30, 1 }; | |
| 796 | 4550 | const PetscScalar c7[8] = { 17297280, 8648640, 1995840, 277200, 25200, 1512, 56, 1 }; | |
| 797 | 4550 | const PetscScalar c9[10] = { 17643225600.0, 8821612800.0, 2075673600, 302702400, 30270240, | |
| 798 | 2162160, 110880, 3960, 90, 1 }; | ||
| 799 | 4550 | const PetscScalar c13[14] = { 64764752532480000.0, 32382376266240000.0, 7771770303897600.0, | |
| 800 | 1187353796428800.0, 129060195264000.0, 10559470521600.0, | ||
| 801 | 670442572800.0, 33522128640.0, 1323241920.0, | ||
| 802 | 40840800, 960960, 16380, 182, 1 }; | ||
| 803 | |||
| 804 |
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4550 | PetscFunctionBegin; |
| 805 |
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4550 | PetscCall(MatDenseGetArrayRead(A,&Aa)); |
| 806 |
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4550 | PetscCall(MatDenseGetArray(B,&Ba)); |
| 807 |
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4550 | PetscCall(MatGetSize(A,&n,NULL)); |
| 808 |
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|
4550 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 809 | 4550 | n2 = n_*n_; | |
| 810 |
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|
4550 | PetscCall(PetscMalloc2(8*n*n,&work,n,&ipiv)); |
| 811 | |||
| 812 | /* Matrix powers */ | ||
| 813 | 4550 | Apowers[0] = work; /* Apowers[0] = A */ | |
| 814 | 4550 | Apowers[1] = Apowers[0] + n*n; /* Apowers[1] = A^2 */ | |
| 815 | 4550 | Apowers[2] = Apowers[1] + n*n; /* Apowers[2] = A^4 */ | |
| 816 | 4550 | Apowers[3] = Apowers[2] + n*n; /* Apowers[3] = A^6 */ | |
| 817 | 4550 | Apowers[4] = Apowers[3] + n*n; /* Apowers[4] = A^8 */ | |
| 818 | |||
| 819 |
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4550 | PetscCall(PetscArraycpy(Apowers[0],Aa,n2)); |
| 820 |
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|
4550 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[0],&n_,Apowers[0],&n_,&szero,Apowers[1],&n_)); |
| 821 |
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|
4550 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[1],&n_,Apowers[1],&n_,&szero,Apowers[2],&n_)); |
| 822 |
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4550 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[1],&n_,Apowers[2],&n_,&szero,Apowers[3],&n_)); |
| 823 |
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|
4550 | PetscCall(PetscLogFlops(6.0*n*n*n)); |
| 824 | |||
| 825 | /* Compute scaling parameter and order of Pade approximant */ | ||
| 826 |
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4550 | PetscCall(expm_params(n,Apowers,&s,&m,Apowers[4])); |
| 827 | |||
| 828 |
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4550 | if (s) { /* rescale */ |
| 829 |
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3925 | for (j=0;j<4;j++) { |
| 830 |
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3140 | scale = PetscPowRealInt(2.0,-PetscMax(2*j,1)*s); |
| 831 |
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|
3140 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&scale,Apowers[j],&one)); |
| 832 | } | ||
| 833 |
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|
785 | PetscCall(PetscLogFlops(4.0*n*n)); |
| 834 | } | ||
| 835 | |||
| 836 | /* Evaluate the Pade approximant */ | ||
| 837 |
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|
4550 | switch (m) { |
| 838 | case 3: c = c3; break; | ||
| 839 | 1000 | case 5: c = c5; break; | |
| 840 | 98 | case 7: c = c7; break; | |
| 841 | 177 | case 9: c = c9; break; | |
| 842 | 2160 | case 13: c = c13; break; | |
| 843 | ✗ | default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong value of m %" PetscInt_FMT,m); | |
| 844 | } | ||
| 845 | 4550 | P = Ba; | |
| 846 | 4550 | Q = Apowers[4] + n*n; | |
| 847 | 4550 | W = Q + n*n; | |
| 848 |
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4550 | switch (m) { |
| 849 | 2390 | case 3: | |
| 850 | case 5: | ||
| 851 | case 7: | ||
| 852 | case 9: | ||
| 853 |
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2390 | if (m==9) PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[1],&n_,Apowers[3],&n_,&szero,Apowers[4],&n_)); |
| 854 |
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2390 | PetscCall(PetscArrayzero(P,n2)); |
| 855 |
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2390 | PetscCall(PetscArrayzero(Q,n2)); |
| 856 |
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|
25329 | for (j=0;j<n;j++) { |
| 857 | 22939 | P[j+j*n] = c[1]; | |
| 858 | 22939 | Q[j+j*n] = c[0]; | |
| 859 | } | ||
| 860 |
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6507 | for (j=m;j>=3;j-=2) { |
| 861 |
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|
4117 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[j],Apowers[(j+1)/2-1],&one,P,&one)); |
| 862 |
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|
4117 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[j-1],Apowers[(j+1)/2-1],&one,Q,&one)); |
| 863 |
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4117 | PetscCall(PetscLogFlops(4.0*n*n)); |
| 864 | } | ||
| 865 |
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|
2390 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[0],&n_,P,&n_,&szero,W,&n_)); |
| 866 |
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|
2390 | PetscCall(PetscLogFlops(2.0*n*n*n)); |
| 867 | 2822 | SlepcSwap(P,W,aux); | |
| 868 | 1918 | break; | |
| 869 | 2160 | case 13: | |
| 870 | /* P = A*(Apowers[3]*(c[13]*Apowers[3] + c[11]*Apowers[2] + c[9]*Apowers[1]) | ||
| 871 | + c[7]*Apowers[3] + c[5]*Apowers[2] + c[3]*Apowers[1] + c[1]*I) */ | ||
| 872 |
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|
2160 | PetscCallBLAS("BLAScopy",BLAScopy_(&n2,Apowers[3],&one,P,&one)); |
| 873 |
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|
2160 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&c[13],P,&one)); |
| 874 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[11],Apowers[2],&one,P,&one)); |
| 875 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[9],Apowers[1],&one,P,&one)); |
| 876 |
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|
2160 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[3],&n_,P,&n_,&szero,W,&n_)); |
| 877 |
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2160 | PetscCall(PetscLogFlops(5.0*n*n+2.0*n*n*n)); |
| 878 |
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2160 | PetscCall(PetscArrayzero(P,n2)); |
| 879 |
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90473 | for (j=0;j<n;j++) P[j+j*n] = c[1]; |
| 880 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[7],Apowers[3],&one,P,&one)); |
| 881 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[5],Apowers[2],&one,P,&one)); |
| 882 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[3],Apowers[1],&one,P,&one)); |
| 883 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&sone,P,&one,W,&one)); |
| 884 |
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|
2160 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[0],&n_,W,&n_,&szero,P,&n_)); |
| 885 |
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2160 | PetscCall(PetscLogFlops(7.0*n*n+2.0*n*n*n)); |
| 886 | /* Q = Apowers[3]*(c[12]*Apowers[3] + c[10]*Apowers[2] + c[8]*Apowers[1]) | ||
| 887 | + c[6]*Apowers[3] + c[4]*Apowers[2] + c[2]*Apowers[1] + c[0]*I */ | ||
| 888 |
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2160 | PetscCallBLAS("BLAScopy",BLAScopy_(&n2,Apowers[3],&one,Q,&one)); |
| 889 |
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2160 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&c[12],Q,&one)); |
| 890 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[10],Apowers[2],&one,Q,&one)); |
| 891 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[8],Apowers[1],&one,Q,&one)); |
| 892 |
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|
2160 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,Apowers[3],&n_,Q,&n_,&szero,W,&n_)); |
| 893 |
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2160 | PetscCall(PetscLogFlops(5.0*n*n+2.0*n*n*n)); |
| 894 |
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2160 | PetscCall(PetscArrayzero(Q,n2)); |
| 895 |
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90473 | for (j=0;j<n;j++) Q[j+j*n] = c[0]; |
| 896 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[6],Apowers[3],&one,Q,&one)); |
| 897 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[4],Apowers[2],&one,Q,&one)); |
| 898 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&c[2],Apowers[1],&one,Q,&one)); |
| 899 |
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2160 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&sone,W,&one,Q,&one)); |
| 900 |
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2160 | PetscCall(PetscLogFlops(7.0*n*n)); |
| 901 | break; | ||
| 902 | ✗ | default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong value of m %" PetscInt_FMT,m); | |
| 903 | } | ||
| 904 |
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4550 | PetscCallBLAS("BLASaxpy",BLASaxpy_(&n2,&smone,P,&one,Q,&one)); |
| 905 |
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4550 | PetscCallLAPACKInfo("LAPACKgesv",LAPACKgesv_(&n_,&n_,Q,&n_,ipiv,P,&n_,&info)); |
| 906 |
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4550 | PetscCallBLAS("BLASscal",BLASscal_(&n2,&stwo,P,&one)); |
| 907 |
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115802 | for (j=0;j<n;j++) P[j+j*n] += 1.0; |
| 908 |
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4550 | PetscCall(PetscLogFlops(2.0*n*n*n/3.0+4.0*n*n)); |
| 909 | |||
| 910 | /* Squaring */ | ||
| 911 |
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11170 | for (j=1;j<=s;j++) { |
| 912 |
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|
6620 | PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,P,&n_,P,&n_,&szero,W,&n_)); |
| 913 | 6620 | SlepcSwap(P,W,aux); | |
| 914 | } | ||
| 915 |
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4550 | if (P!=Ba) PetscCall(PetscArraycpy(Ba,P,n2)); |
| 916 |
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4550 | PetscCall(PetscLogFlops(2.0*n*n*n*s)); |
| 917 | |||
| 918 |
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4550 | PetscCall(PetscFree2(work,ipiv)); |
| 919 |
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4550 | PetscCall(MatDenseRestoreArrayRead(A,&Aa)); |
| 920 |
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4550 | PetscCall(MatDenseRestoreArray(B,&Ba)); |
| 921 |
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|
904 | PetscFunctionReturn(PETSC_SUCCESS); |
| 922 | } | ||
| 923 | |||
| 924 | #if defined(PETSC_HAVE_CUDA) | ||
| 925 | #include "../src/sys/classes/fn/impls/cuda/fnutilcuda.h" | ||
| 926 | #include <slepccupmblas.h> | ||
| 927 | |||
| 928 | ✗ | PetscErrorCode FNEvaluateFunctionMat_Exp_Pade_CUDA(FN fn,Mat A,Mat B) | |
| 929 | { | ||
| 930 | ✗ | PetscBLASInt n=0,ld,ld2,*d_ipiv,*d_info,info,one=1; | |
| 931 | ✗ | PetscInt m,k,sexp; | |
| 932 | ✗ | PetscBool odd; | |
| 933 | ✗ | const PetscInt p=MAX_PADE; | |
| 934 | ✗ | PetscReal c[MAX_PADE+1],s; | |
| 935 | ✗ | PetscScalar scale,smone=-1.0,sone=1.0,stwo=2.0,szero=0.0; | |
| 936 | ✗ | const PetscScalar *Aa; | |
| 937 | ✗ | PetscScalar *d_Ba,*d_As,*d_A2,*d_Q,*d_P,*d_W,*aux,**ppP,**d_ppP,**ppQ,**d_ppQ; | |
| 938 | ✗ | cublasHandle_t cublasv2handle; | |
| 939 | |||
| 940 | ✗ | PetscFunctionBegin; | |
| 941 | ✗ | PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* For CUDA event timers */ | |
| 942 | ✗ | PetscCall(PetscCUBLASGetHandle(&cublasv2handle)); | |
| 943 | ✗ | PetscCall(MatGetSize(A,&m,NULL)); | |
| 944 | ✗ | PetscCall(PetscBLASIntCast(m,&n)); | |
| 945 | ✗ | ld = n; | |
| 946 | ✗ | ld2 = ld*ld; | |
| 947 | ✗ | if (A==B) { | |
| 948 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_As,sizeof(PetscScalar)*m*m)); | |
| 949 | ✗ | PetscCall(MatDenseCUDAGetArrayRead(A,&Aa)); | |
| 950 | ✗ | PetscCallCUDA(cudaMemcpy(d_As,Aa,sizeof(PetscScalar)*ld2,cudaMemcpyDeviceToDevice)); | |
| 951 | ✗ | PetscCall(MatDenseCUDARestoreArrayRead(A,&Aa)); | |
| 952 | ✗ | } else PetscCall(MatDenseCUDAGetArrayRead(A,(const PetscScalar**)&d_As)); | |
| 953 | ✗ | PetscCall(MatDenseCUDAGetArrayWrite(B,&d_Ba)); | |
| 954 | |||
| 955 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_Q,sizeof(PetscScalar)*m*m)); | |
| 956 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_W,sizeof(PetscScalar)*m*m)); | |
| 957 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_A2,sizeof(PetscScalar)*m*m)); | |
| 958 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_ipiv,sizeof(PetscBLASInt)*ld)); | |
| 959 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_info,sizeof(PetscBLASInt))); | |
| 960 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_ppP,sizeof(PetscScalar*))); | |
| 961 | ✗ | PetscCallCUDA(cudaMalloc((void **)&d_ppQ,sizeof(PetscScalar*))); | |
| 962 | |||
| 963 | ✗ | PetscCall(PetscMalloc1(1,&ppP)); | |
| 964 | ✗ | PetscCall(PetscMalloc1(1,&ppQ)); | |
| 965 | |||
| 966 | ✗ | d_P = d_Ba; | |
| 967 | ✗ | PetscCall(PetscLogGpuTimeBegin()); | |
| 968 | |||
| 969 | /* Pade' coefficients */ | ||
| 970 | ✗ | c[0] = 1.0; | |
| 971 | ✗ | for (k=1;k<=p;k++) c[k] = c[k-1]*(p+1-k)/(k*(2*p+1-k)); | |
| 972 | |||
| 973 | /* Scaling */ | ||
| 974 | ✗ | PetscCallCUBLAS(cublasXnrm2(cublasv2handle,ld2,d_As,one,&s)); | |
| 975 | ✗ | if (s>0.5) { | |
| 976 | ✗ | sexp = PetscMax(0,(int)(PetscLogReal(s)/PetscLogReal(2.0))+2); | |
| 977 | ✗ | scale = PetscPowRealInt(2.0,-sexp); | |
| 978 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&scale,d_As,one)); | |
| 979 | ✗ | PetscCall(PetscLogGpuFlops(1.0*n*n)); | |
| 980 | } else sexp = 0; | ||
| 981 | |||
| 982 | /* Horner evaluation */ | ||
| 983 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_As,ld,d_As,ld,&szero,d_A2,ld)); | |
| 984 | ✗ | PetscCall(PetscLogGpuFlops(2.0*n*n*n)); | |
| 985 | ✗ | PetscCallCUDA(cudaMemset(d_Q,0,sizeof(PetscScalar)*ld2)); | |
| 986 | ✗ | PetscCallCUDA(cudaMemset(d_P,0,sizeof(PetscScalar)*ld2)); | |
| 987 | ✗ | PetscCall(set_diagonal(n,d_Q,ld,c[p])); | |
| 988 | ✗ | PetscCall(set_diagonal(n,d_P,ld,c[p-1])); | |
| 989 | |||
| 990 | odd = PETSC_TRUE; | ||
| 991 | ✗ | for (k=p-1;k>0;k--) { | |
| 992 | ✗ | if (odd) { | |
| 993 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_Q,ld,d_A2,ld,&szero,d_W,ld)); | |
| 994 | ✗ | SlepcSwap(d_Q,d_W,aux); | |
| 995 | ✗ | PetscCall(shift_diagonal(n,d_Q,ld,c[k-1])); | |
| 996 | odd = PETSC_FALSE; | ||
| 997 | } else { | ||
| 998 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_P,ld,d_A2,ld,&szero,d_W,ld)); | |
| 999 | ✗ | SlepcSwap(d_P,d_W,aux); | |
| 1000 | ✗ | PetscCall(shift_diagonal(n,d_P,ld,c[k-1])); | |
| 1001 | odd = PETSC_TRUE; | ||
| 1002 | } | ||
| 1003 | ✗ | PetscCall(PetscLogGpuFlops(2.0*n*n*n)); | |
| 1004 | } | ||
| 1005 | ✗ | if (odd) { | |
| 1006 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_Q,ld,d_As,ld,&szero,d_W,ld)); | |
| 1007 | ✗ | SlepcSwap(d_Q,d_W,aux); | |
| 1008 | ✗ | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,ld2,&smone,d_P,one,d_Q,one)); | |
| 1009 | |||
| 1010 | ✗ | ppQ[0] = d_Q; | |
| 1011 | ✗ | ppP[0] = d_P; | |
| 1012 | ✗ | PetscCallCUDA(cudaMemcpy(d_ppQ,ppQ,sizeof(PetscScalar*),cudaMemcpyHostToDevice)); | |
| 1013 | ✗ | PetscCallCUDA(cudaMemcpy(d_ppP,ppP,sizeof(PetscScalar*),cudaMemcpyHostToDevice)); | |
| 1014 | |||
| 1015 | ✗ | PetscCallCUBLAS(cublasXgetrfBatched(cublasv2handle,n,d_ppQ,ld,d_ipiv,d_info,one)); | |
| 1016 | ✗ | PetscCallCUDA(cudaMemcpy(&info,d_info,sizeof(PetscBLASInt),cudaMemcpyDeviceToHost)); | |
| 1017 | ✗ | PetscCheck(info>=0,PETSC_COMM_SELF,PETSC_ERR_LIB,"LAPACKgetrf: Illegal value on argument %" PetscBLASInt_FMT,PetscAbsInt(info)); | |
| 1018 | ✗ | PetscCheck(info<=0,PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"LAPACKgetrf: Matrix is singular. U(%" PetscBLASInt_FMT ",%" PetscBLASInt_FMT ") is zero",info,info); | |
| 1019 | ✗ | PetscCallCUBLAS(cublasXgetrsBatched(cublasv2handle,CUBLAS_OP_N,n,n,(const PetscScalar **)d_ppQ,ld,d_ipiv,d_ppP,ld,&info,one)); | |
| 1020 | ✗ | PetscCheck(info>=0,PETSC_COMM_SELF,PETSC_ERR_LIB,"LAPACKgetri: Illegal value on argument %" PetscBLASInt_FMT,PetscAbsInt(info)); | |
| 1021 | ✗ | PetscCheck(info<=0,PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"LAPACKgetri: Matrix is singular. U(%" PetscBLASInt_FMT ",%" PetscBLASInt_FMT ") is zero",info,info); | |
| 1022 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&stwo,d_P,one)); | |
| 1023 | ✗ | PetscCall(shift_diagonal(n,d_P,ld,sone)); | |
| 1024 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&smone,d_P,one)); | |
| 1025 | } else { | ||
| 1026 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_P,ld,d_As,ld,&szero,d_W,ld)); | |
| 1027 | ✗ | SlepcSwap(d_P,d_W,aux); | |
| 1028 | ✗ | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,ld2,&smone,d_P,one,d_Q,one)); | |
| 1029 | |||
| 1030 | ✗ | ppQ[0] = d_Q; | |
| 1031 | ✗ | ppP[0] = d_P; | |
| 1032 | ✗ | PetscCallCUDA(cudaMemcpy(d_ppQ,ppQ,sizeof(PetscScalar*),cudaMemcpyHostToDevice)); | |
| 1033 | ✗ | PetscCallCUDA(cudaMemcpy(d_ppP,ppP,sizeof(PetscScalar*),cudaMemcpyHostToDevice)); | |
| 1034 | |||
| 1035 | ✗ | PetscCallCUBLAS(cublasXgetrfBatched(cublasv2handle,n,d_ppQ,ld,d_ipiv,d_info,one)); | |
| 1036 | ✗ | PetscCallCUDA(cudaMemcpy(&info,d_info,sizeof(PetscBLASInt),cudaMemcpyDeviceToHost)); | |
| 1037 | ✗ | PetscCheck(info>=0,PETSC_COMM_SELF,PETSC_ERR_LIB,"LAPACKgetrf: Illegal value on argument %" PetscBLASInt_FMT,PetscAbsInt(info)); | |
| 1038 | ✗ | PetscCheck(info<=0,PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"LAPACKgetrf: Matrix is singular. U(%" PetscBLASInt_FMT ",%" PetscBLASInt_FMT ") is zero",info,info); | |
| 1039 | ✗ | PetscCallCUBLAS(cublasXgetrsBatched(cublasv2handle,CUBLAS_OP_N,n,n,(const PetscScalar **)d_ppQ,ld,d_ipiv,d_ppP,ld,&info,one)); | |
| 1040 | ✗ | PetscCheck(info>=0,PETSC_COMM_SELF,PETSC_ERR_LIB,"LAPACKgetri: Illegal value on argument %" PetscBLASInt_FMT,PetscAbsInt(info)); | |
| 1041 | ✗ | PetscCheck(info<=0,PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"LAPACKgetri: Matrix is singular. U(%" PetscBLASInt_FMT ",%" PetscBLASInt_FMT ") is zero",info,info); | |
| 1042 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&stwo,d_P,one)); | |
| 1043 | ✗ | PetscCall(shift_diagonal(n,d_P,ld,sone)); | |
| 1044 | } | ||
| 1045 | ✗ | PetscCall(PetscLogGpuFlops(2.0*n*n*n+2.0*n*n*n/3.0+4.0*n*n)); | |
| 1046 | |||
| 1047 | ✗ | for (k=1;k<=sexp;k++) { | |
| 1048 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_P,ld,d_P,ld,&szero,d_W,ld)); | |
| 1049 | ✗ | PetscCallCUDA(cudaMemcpy(d_P,d_W,sizeof(PetscScalar)*ld2,cudaMemcpyDeviceToDevice)); | |
| 1050 | } | ||
| 1051 | ✗ | PetscCall(PetscLogGpuFlops(2.0*n*n*n*sexp)); | |
| 1052 | |||
| 1053 | ✗ | PetscCall(PetscLogGpuTimeEnd()); | |
| 1054 | ✗ | PetscCallCUDA(cudaFree(d_Q)); | |
| 1055 | ✗ | PetscCallCUDA(cudaFree(d_W)); | |
| 1056 | ✗ | PetscCallCUDA(cudaFree(d_A2)); | |
| 1057 | ✗ | PetscCallCUDA(cudaFree(d_ipiv)); | |
| 1058 | ✗ | PetscCallCUDA(cudaFree(d_info)); | |
| 1059 | ✗ | PetscCallCUDA(cudaFree(d_ppP)); | |
| 1060 | ✗ | PetscCallCUDA(cudaFree(d_ppQ)); | |
| 1061 | |||
| 1062 | ✗ | PetscCall(PetscFree(ppP)); | |
| 1063 | ✗ | PetscCall(PetscFree(ppQ)); | |
| 1064 | |||
| 1065 | ✗ | if (d_P!=d_Ba) PetscCallCUDA(cudaMemcpy(d_Ba,d_P,sizeof(PetscScalar)*ld2,cudaMemcpyDeviceToDevice)); | |
| 1066 | ✗ | if (A!=B) { | |
| 1067 | ✗ | if (s>0.5) { /* undo scaling */ | |
| 1068 | ✗ | scale = 1.0/scale; | |
| 1069 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&scale,d_As,one)); | |
| 1070 | } | ||
| 1071 | ✗ | PetscCall(MatDenseCUDARestoreArrayRead(A,(const PetscScalar**)&d_As)); | |
| 1072 | ✗ | } else PetscCallCUDA(cudaFree(d_As)); | |
| 1073 | ✗ | PetscCall(MatDenseCUDARestoreArrayWrite(B,&d_Ba)); | |
| 1074 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 1075 | } | ||
| 1076 | |||
| 1077 | #if defined(PETSC_HAVE_MAGMA) | ||
| 1078 | #include <slepcmagma.h> | ||
| 1079 | |||
| 1080 | 16 | PetscErrorCode FNEvaluateFunctionMat_Exp_Pade_CUDAm(FN fn,Mat A,Mat B) | |
| 1081 | { | ||
| 1082 | 16 | PetscBLASInt n=0,ld,ld2,*piv,one=1; | |
| 1083 | 16 | PetscInt m,k,sexp; | |
| 1084 | 16 | PetscBool odd; | |
| 1085 | 16 | const PetscInt p=MAX_PADE; | |
| 1086 | 16 | PetscReal c[MAX_PADE+1],s; | |
| 1087 | 16 | PetscScalar scale,smone=-1.0,sone=1.0,stwo=2.0,szero=0.0; | |
| 1088 | 16 | const PetscScalar *Aa; | |
| 1089 | 16 | PetscScalar *d_Ba,*d_As,*d_A2,*d_Q,*d_P,*d_W,*aux; | |
| 1090 | 16 | cublasHandle_t cublasv2handle; | |
| 1091 | |||
| 1092 | 16 | PetscFunctionBegin; | |
| 1093 |
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16 | PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* For CUDA event timers */ |
| 1094 |
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16 | PetscCall(PetscCUBLASGetHandle(&cublasv2handle)); |
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16 | PetscCall(SlepcMagmaInit()); |
| 1096 |
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16 | PetscCall(MatGetSize(A,&m,NULL)); |
| 1097 |
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16 | PetscCall(PetscBLASIntCast(m,&n)); |
| 1098 | 16 | ld = n; | |
| 1099 | 16 | ld2 = ld*ld; | |
| 1100 |
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16 | if (A==B) { |
| 1101 |
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4 | PetscCallCUDA(cudaMalloc((void **)&d_As,sizeof(PetscScalar)*m*m)); |
| 1102 |
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4 | PetscCall(MatDenseCUDAGetArrayRead(A,&Aa)); |
| 1103 |
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4 | PetscCallCUDA(cudaMemcpy(d_As,Aa,sizeof(PetscScalar)*ld2,cudaMemcpyDeviceToDevice)); |
| 1104 |
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4 | PetscCall(MatDenseCUDARestoreArrayRead(A,&Aa)); |
| 1105 |
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12 | } else PetscCall(MatDenseCUDAGetArrayRead(A,(const PetscScalar**)&d_As)); |
| 1106 |
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16 | PetscCall(MatDenseCUDAGetArrayWrite(B,&d_Ba)); |
| 1107 | |||
| 1108 |
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16 | PetscCallCUDA(cudaMalloc((void **)&d_Q,sizeof(PetscScalar)*m*m)); |
| 1109 |
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16 | PetscCallCUDA(cudaMalloc((void **)&d_W,sizeof(PetscScalar)*m*m)); |
| 1110 |
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16 | PetscCallCUDA(cudaMalloc((void **)&d_A2,sizeof(PetscScalar)*m*m)); |
| 1111 | |||
| 1112 |
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16 | PetscCall(PetscMalloc1(n,&piv)); |
| 1113 | |||
| 1114 | 16 | d_P = d_Ba; | |
| 1115 |
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16 | PetscCall(PetscLogGpuTimeBegin()); |
| 1116 | |||
| 1117 | /* Pade' coefficients */ | ||
| 1118 | 16 | c[0] = 1.0; | |
| 1119 |
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112 | for (k=1;k<=p;k++) c[k] = c[k-1]*(p+1-k)/(k*(2*p+1-k)); |
| 1120 | |||
| 1121 | /* Scaling */ | ||
| 1122 |
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16 | PetscCallCUBLAS(cublasXnrm2(cublasv2handle,ld2,d_As,one,&s)); |
| 1123 |
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16 | PetscCall(PetscLogGpuFlops(1.0*n*n)); |
| 1124 | |||
| 1125 |
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16 | if (s>0.5) { |
| 1126 |
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16 | sexp = PetscMax(0,(int)(PetscLogReal(s)/PetscLogReal(2.0))+2); |
| 1127 | 16 | scale = PetscPowRealInt(2.0,-sexp); | |
| 1128 |
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16 | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&scale,d_As,one)); |
| 1129 |
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16 | PetscCall(PetscLogGpuFlops(1.0*n*n)); |
| 1130 | } else sexp = 0; | ||
| 1131 | |||
| 1132 | /* Horner evaluation */ | ||
| 1133 |
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16 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_As,ld,d_As,ld,&szero,d_A2,ld)); |
| 1134 |
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16 | PetscCall(PetscLogGpuFlops(2.0*n*n*n)); |
| 1135 |
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16 | PetscCallCUDA(cudaMemset(d_Q,0,sizeof(PetscScalar)*ld2)); |
| 1136 |
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16 | PetscCallCUDA(cudaMemset(d_P,0,sizeof(PetscScalar)*ld2)); |
| 1137 |
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16 | PetscCall(set_diagonal(n,d_Q,ld,c[p])); |
| 1138 |
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16 | PetscCall(set_diagonal(n,d_P,ld,c[p-1])); |
| 1139 | |||
| 1140 | odd = PETSC_TRUE; | ||
| 1141 |
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96 | for (k=p-1;k>0;k--) { |
| 1142 |
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80 | if (odd) { |
| 1143 |
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48 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_Q,ld,d_A2,ld,&szero,d_W,ld)); |
| 1144 | 48 | SlepcSwap(d_Q,d_W,aux); | |
| 1145 |
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48 | PetscCall(shift_diagonal(n,d_Q,ld,c[k-1])); |
| 1146 | odd = PETSC_FALSE; | ||
| 1147 | } else { | ||
| 1148 |
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32 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_P,ld,d_A2,ld,&szero,d_W,ld)); |
| 1149 | 32 | SlepcSwap(d_P,d_W,aux); | |
| 1150 |
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32 | PetscCall(shift_diagonal(n,d_P,ld,c[k-1])); |
| 1151 | odd = PETSC_TRUE; | ||
| 1152 | } | ||
| 1153 |
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80 | PetscCall(PetscLogGpuFlops(2.0*n*n*n)); |
| 1154 | } | ||
| 1155 |
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16 | if (odd) { |
| 1156 | ✗ | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_Q,ld,d_As,ld,&szero,d_W,ld)); | |
| 1157 | ✗ | SlepcSwap(d_Q,d_W,aux); | |
| 1158 | ✗ | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,ld2,&smone,d_P,one,d_Q,one)); | |
| 1159 | ✗ | PetscCallMAGMA(magma_xgesv_gpu,n,n,d_Q,ld,piv,d_P,ld); | |
| 1160 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&stwo,d_P,one)); | |
| 1161 | ✗ | PetscCall(shift_diagonal(n,d_P,ld,sone)); | |
| 1162 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&smone,d_P,one)); | |
| 1163 | } else { | ||
| 1164 |
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16 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_P,ld,d_As,ld,&szero,d_W,ld)); |
| 1165 | 16 | SlepcSwap(d_P,d_W,aux); | |
| 1166 |
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16 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,ld2,&smone,d_P,one,d_Q,one)); |
| 1167 |
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16 | PetscCallMAGMA(magma_xgesv_gpu,n,n,d_Q,ld,piv,d_P,ld); |
| 1168 |
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16 | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&stwo,d_P,one)); |
| 1169 |
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16 | PetscCall(shift_diagonal(n,d_P,ld,sone)); |
| 1170 | } | ||
| 1171 |
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16 | PetscCall(PetscLogGpuFlops(2.0*n*n*n+2.0*n*n*n/3.0+4.0*n*n)); |
| 1172 | |||
| 1173 |
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96 | for (k=1;k<=sexp;k++) { |
| 1174 |
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80 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_P,ld,d_P,ld,&szero,d_W,ld)); |
| 1175 |
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80 | PetscCallCUDA(cudaMemcpy(d_P,d_W,sizeof(PetscScalar)*ld2,cudaMemcpyDeviceToDevice)); |
| 1176 | } | ||
| 1177 |
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16 | PetscCall(PetscLogGpuFlops(2.0*n*n*n*sexp)); |
| 1178 | |||
| 1179 |
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16 | PetscCall(PetscLogGpuTimeEnd()); |
| 1180 |
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16 | PetscCallCUDA(cudaFree(d_Q)); |
| 1181 |
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16 | PetscCallCUDA(cudaFree(d_W)); |
| 1182 |
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16 | PetscCallCUDA(cudaFree(d_A2)); |
| 1183 |
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16 | PetscCall(PetscFree(piv)); |
| 1184 | |||
| 1185 |
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16 | if (d_P!=d_Ba) PetscCallCUDA(cudaMemcpy(d_Ba,d_P,sizeof(PetscScalar)*ld2,cudaMemcpyDeviceToDevice)); |
| 1186 |
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16 | if (A!=B) { |
| 1187 |
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12 | if (s>0.5) { /* undo scaling */ |
| 1188 | 12 | scale = 1.0/scale; | |
| 1189 |
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12 | PetscCallCUBLAS(cublasXscal(cublasv2handle,ld2,&scale,d_As,one)); |
| 1190 | } | ||
| 1191 |
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12 | PetscCall(MatDenseCUDARestoreArrayRead(A,(const PetscScalar**)&d_As)); |
| 1192 |
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4 | } else PetscCallCUDA(cudaFree(d_As)); |
| 1193 |
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16 | PetscCall(MatDenseCUDARestoreArrayWrite(B,&d_Ba)); |
| 1194 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 1195 | } | ||
| 1196 | |||
| 1197 | /* | ||
| 1198 | * Matrix exponential implementation based on algorithm and matlab code by N. Higham and co-authors | ||
| 1199 | * | ||
| 1200 | * N. J. Higham, "The scaling and squaring method for the matrix exponential | ||
| 1201 | * revisited", SIAM J. Matrix Anal. Appl. 26(4):1179-1193, 2005. | ||
| 1202 | */ | ||
| 1203 | 48 | PetscErrorCode FNEvaluateFunctionMat_Exp_Higham_CUDAm(FN fn,Mat A,Mat B) | |
| 1204 | { | ||
| 1205 | 48 | PetscBLASInt n_=0,n2,*ipiv,one=1; | |
| 1206 | 48 | PetscInt n,m,j,s; | |
| 1207 | 48 | PetscScalar scale,smone=-1.0,sone=1.0,stwo=2.0,szero=0.0; | |
| 1208 | 48 | PetscScalar *d_Ba,*Apowers[5],*d_Apowers[5],*d_Q,*d_P,*d_W,*work,*d_work,*aux; | |
| 1209 | 48 | const PetscScalar *Aa,*c; | |
| 1210 | 48 | const PetscScalar c3[4] = { 120, 60, 12, 1 }; | |
| 1211 | 48 | const PetscScalar c5[6] = { 30240, 15120, 3360, 420, 30, 1 }; | |
| 1212 | 48 | const PetscScalar c7[8] = { 17297280, 8648640, 1995840, 277200, 25200, 1512, 56, 1 }; | |
| 1213 | 48 | const PetscScalar c9[10] = { 17643225600, 8821612800, 2075673600, 302702400, 30270240, | |
| 1214 | 2162160, 110880, 3960, 90, 1 }; | ||
| 1215 | 48 | const PetscScalar c13[14] = { 64764752532480000, 32382376266240000, 7771770303897600, | |
| 1216 | 1187353796428800, 129060195264000, 10559470521600, | ||
| 1217 | 670442572800, 33522128640, 1323241920, | ||
| 1218 | 40840800, 960960, 16380, 182, 1 }; | ||
| 1219 | 48 | cublasHandle_t cublasv2handle; | |
| 1220 | |||
| 1221 | 48 | PetscFunctionBegin; | |
| 1222 |
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48 | PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* For CUDA event timers */ |
| 1223 |
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48 | PetscCall(PetscCUBLASGetHandle(&cublasv2handle)); |
| 1224 |
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48 | PetscCall(SlepcMagmaInit()); |
| 1225 |
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48 | PetscCall(MatGetSize(A,&n,NULL)); |
| 1226 |
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48 | PetscCall(PetscBLASIntCast(n,&n_)); |
| 1227 | 48 | n2 = n_*n_; | |
| 1228 |
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48 | PetscCall(PetscMalloc2(8*n*n,&work,n,&ipiv)); |
| 1229 | /* Matrix powers */ | ||
| 1230 | 48 | Apowers[0] = work; /* Apowers[0] = A */ | |
| 1231 | 48 | Apowers[1] = Apowers[0] + n*n; /* Apowers[1] = A^2 */ | |
| 1232 | 48 | Apowers[2] = Apowers[1] + n*n; /* Apowers[2] = A^4 */ | |
| 1233 | 48 | Apowers[3] = Apowers[2] + n*n; /* Apowers[3] = A^6 */ | |
| 1234 | 48 | Apowers[4] = Apowers[3] + n*n; /* Apowers[4] = A^8 */ | |
| 1235 |
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48 | if (A==B) { |
| 1236 |
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4 | PetscCallCUDA(cudaMalloc((void**)&d_work,7*n*n*sizeof(PetscScalar))); |
| 1237 | 4 | d_Apowers[0] = d_work; /* d_Apowers[0] = A */ | |
| 1238 | 4 | d_Apowers[1] = d_Apowers[0] + n*n; /* d_Apowers[1] = A^2 */ | |
| 1239 |
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4 | PetscCall(MatDenseCUDAGetArrayRead(A,&Aa)); |
| 1240 |
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4 | PetscCallCUDA(cudaMemcpy(d_Apowers[0],Aa,n2*sizeof(PetscScalar),cudaMemcpyDeviceToDevice)); |
| 1241 |
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4 | PetscCall(MatDenseCUDARestoreArrayRead(A,&Aa)); |
| 1242 | } else { | ||
| 1243 |
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44 | PetscCallCUDA(cudaMalloc((void**)&d_work,6*n*n*sizeof(PetscScalar))); |
| 1244 |
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44 | PetscCall(MatDenseCUDAGetArrayRead(A,(const PetscScalar**)&d_Apowers[0])); |
| 1245 | 44 | d_Apowers[1] = d_work; /* d_Apowers[1] = A^2 */ | |
| 1246 | } | ||
| 1247 |
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48 | PetscCall(MatDenseCUDAGetArrayWrite(B,&d_Ba)); |
| 1248 | 48 | d_Apowers[2] = d_Apowers[1] + n*n; /* d_Apowers[2] = A^4 */ | |
| 1249 | 48 | d_Apowers[3] = d_Apowers[2] + n*n; /* d_Apowers[3] = A^6 */ | |
| 1250 | 48 | d_Apowers[4] = d_Apowers[3] + n*n; /* d_Apowers[4] = A^8 */ | |
| 1251 | 48 | d_Q = d_Apowers[4] + n*n; | |
| 1252 | 48 | d_W = d_Q + n*n; | |
| 1253 | |||
| 1254 |
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48 | PetscCall(PetscLogGpuTimeBegin()); |
| 1255 | |||
| 1256 |
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48 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[0],n_,d_Apowers[0],n_,&szero,d_Apowers[1],n_)); |
| 1257 |
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48 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[1],n_,d_Apowers[1],n_,&szero,d_Apowers[2],n_)); |
| 1258 |
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|
48 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[1],n_,d_Apowers[2],n_,&szero,d_Apowers[3],n_)); |
| 1259 |
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48 | PetscCall(PetscLogGpuFlops(6.0*n*n*n)); |
| 1260 | |||
| 1261 |
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48 | PetscCallCUDA(cudaMemcpy(Apowers[0],d_Apowers[0],n2*sizeof(PetscScalar),cudaMemcpyDeviceToHost)); |
| 1262 |
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48 | PetscCallCUDA(cudaMemcpy(Apowers[1],d_Apowers[1],3*n2*sizeof(PetscScalar),cudaMemcpyDeviceToHost)); |
| 1263 |
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|
48 | PetscCall(PetscLogGpuToCpu(4*n2*sizeof(PetscScalar))); |
| 1264 | /* Compute scaling parameter and order of Pade approximant */ | ||
| 1265 |
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48 | PetscCall(expm_params(n,Apowers,&s,&m,Apowers[4])); |
| 1266 | |||
| 1267 |
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|
48 | if (s) { /* rescale */ |
| 1268 |
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|
80 | for (j=0;j<4;j++) { |
| 1269 |
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|
64 | scale = PetscPowRealInt(2.0,-PetscMax(2*j,1)*s); |
| 1270 |
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|
64 | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&scale,d_Apowers[j],one)); |
| 1271 | } | ||
| 1272 |
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|
16 | PetscCall(PetscLogGpuFlops(4.0*n*n)); |
| 1273 | } | ||
| 1274 | |||
| 1275 | /* Evaluate the Pade approximant */ | ||
| 1276 |
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|
48 | switch (m) { |
| 1277 | case 3: c = c3; break; | ||
| 1278 | ✗ | case 5: c = c5; break; | |
| 1279 | 16 | case 7: c = c7; break; | |
| 1280 | ✗ | case 9: c = c9; break; | |
| 1281 | 32 | case 13: c = c13; break; | |
| 1282 | ✗ | default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong value of m %" PetscInt_FMT,m); | |
| 1283 | } | ||
| 1284 | 48 | d_P = d_Ba; | |
| 1285 |
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48 | switch (m) { |
| 1286 | 16 | case 3: | |
| 1287 | case 5: | ||
| 1288 | case 7: | ||
| 1289 | case 9: | ||
| 1290 |
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|
16 | if (m==9) PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[1],n_,d_Apowers[3],n_,&szero,d_Apowers[4],n_)); |
| 1291 |
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16 | PetscCallCUDA(cudaMemset(d_P,0,sizeof(PetscScalar)*n2)); |
| 1292 |
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16 | PetscCallCUDA(cudaMemset(d_Q,0,sizeof(PetscScalar)*n2)); |
| 1293 |
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16 | PetscCall(set_diagonal(n,d_P,n,c[1])); |
| 1294 |
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16 | PetscCall(set_diagonal(n,d_Q,n,c[0])); |
| 1295 |
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64 | for (j=m;j>=3;j-=2) { |
| 1296 |
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|
48 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[j],d_Apowers[(j+1)/2-1],one,d_P,one)); |
| 1297 |
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|
48 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[j-1],d_Apowers[(j+1)/2-1],one,d_Q,one)); |
| 1298 |
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48 | PetscCall(PetscLogGpuFlops(4.0*n*n)); |
| 1299 | } | ||
| 1300 |
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|
16 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[0],n_,d_P,n_,&szero,d_W,n_)); |
| 1301 |
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|
16 | PetscCall(PetscLogGpuFlops(2.0*n*n*n)); |
| 1302 | 48 | SlepcSwap(d_P,d_W,aux); | |
| 1303 | break; | ||
| 1304 | 32 | case 13: | |
| 1305 | /* P = A*(Apowers[3]*(c[13]*Apowers[3] + c[11]*Apowers[2] + c[9]*Apowers[1]) | ||
| 1306 | + c[7]*Apowers[3] + c[5]*Apowers[2] + c[3]*Apowers[1] + c[1]*I) */ | ||
| 1307 |
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32 | PetscCallCUDA(cudaMemcpy(d_P,d_Apowers[3],n2*sizeof(PetscScalar),cudaMemcpyDeviceToDevice)); |
| 1308 |
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32 | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&c[13],d_P,one)); |
| 1309 |
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|
32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[11],d_Apowers[2],one,d_P,one)); |
| 1310 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[9],d_Apowers[1],one,d_P,one)); |
| 1311 |
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|
32 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[3],n_,d_P,n_,&szero,d_W,n_)); |
| 1312 |
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32 | PetscCall(PetscLogGpuFlops(5.0*n*n+2.0*n*n*n)); |
| 1313 | |||
| 1314 |
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32 | PetscCallCUDA(cudaMemset(d_P,0,sizeof(PetscScalar)*n2)); |
| 1315 |
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32 | PetscCall(set_diagonal(n,d_P,n,c[1])); |
| 1316 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[7],d_Apowers[3],one,d_P,one)); |
| 1317 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[5],d_Apowers[2],one,d_P,one)); |
| 1318 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[3],d_Apowers[1],one,d_P,one)); |
| 1319 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&sone,d_P,one,d_W,one)); |
| 1320 |
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32 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[0],n_,d_W,n_,&szero,d_P,n_)); |
| 1321 |
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32 | PetscCall(PetscLogGpuFlops(7.0*n*n+2.0*n*n*n)); |
| 1322 | /* Q = Apowers[3]*(c[12]*Apowers[3] + c[10]*Apowers[2] + c[8]*Apowers[1]) | ||
| 1323 | + c[6]*Apowers[3] + c[4]*Apowers[2] + c[2]*Apowers[1] + c[0]*I */ | ||
| 1324 |
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32 | PetscCallCUDA(cudaMemcpy(d_Q,d_Apowers[3],n2*sizeof(PetscScalar),cudaMemcpyDeviceToDevice)); |
| 1325 |
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32 | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&c[12],d_Q,one)); |
| 1326 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[10],d_Apowers[2],one,d_Q,one)); |
| 1327 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[8],d_Apowers[1],one,d_Q,one)); |
| 1328 |
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32 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_Apowers[3],n_,d_Q,n_,&szero,d_W,n_)); |
| 1329 |
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32 | PetscCall(PetscLogGpuFlops(5.0*n*n+2.0*n*n*n)); |
| 1330 |
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32 | PetscCallCUDA(cudaMemset(d_Q,0,sizeof(PetscScalar)*n2)); |
| 1331 |
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32 | PetscCall(set_diagonal(n,d_Q,n,c[0])); |
| 1332 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[6],d_Apowers[3],one,d_Q,one)); |
| 1333 |
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|
32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[4],d_Apowers[2],one,d_Q,one)); |
| 1334 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&c[2],d_Apowers[1],one,d_Q,one)); |
| 1335 |
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32 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&sone,d_W,one,d_Q,one)); |
| 1336 |
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32 | PetscCall(PetscLogGpuFlops(7.0*n*n)); |
| 1337 | break; | ||
| 1338 | ✗ | default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong value of m %" PetscInt_FMT,m); | |
| 1339 | } | ||
| 1340 |
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48 | PetscCallCUBLAS(cublasXaxpy(cublasv2handle,n2,&smone,d_P,one,d_Q,one)); |
| 1341 | |||
| 1342 |
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48 | PetscCallMAGMA(magma_xgesv_gpu,n_,n_,d_Q,n_,ipiv,d_P,n_); |
| 1343 | |||
| 1344 |
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48 | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&stwo,d_P,one)); |
| 1345 |
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48 | PetscCall(shift_diagonal(n,d_P,n,sone)); |
| 1346 |
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|
48 | PetscCall(PetscLogGpuFlops(2.0*n*n*n/3.0+4.0*n*n)); |
| 1347 | |||
| 1348 | /* Squaring */ | ||
| 1349 |
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64 | for (j=1;j<=s;j++) { |
| 1350 |
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|
16 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n_,n_,n_,&sone,d_P,n_,d_P,n_,&szero,d_W,n_)); |
| 1351 | 16 | SlepcSwap(d_P,d_W,aux); | |
| 1352 | } | ||
| 1353 |
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48 | PetscCall(PetscLogGpuFlops(2.0*n*n*n*s)); |
| 1354 |
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48 | PetscCall(PetscLogGpuTimeEnd()); |
| 1355 | |||
| 1356 |
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48 | PetscCall(PetscFree2(work,ipiv)); |
| 1357 |
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|
48 | if (d_P!=d_Ba) PetscCallCUDA(cudaMemcpy(d_Ba,d_P,n2*sizeof(PetscScalar),cudaMemcpyDeviceToDevice)); |
| 1358 |
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48 | if (A!=B) { |
| 1359 |
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|
44 | if (s>0.5) { /* undo scaling */ |
| 1360 | 12 | scale = 1.0/PetscPowRealInt(2.0,-s); | |
| 1361 |
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12 | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&scale,d_Apowers[0],one)); |
| 1362 | } | ||
| 1363 |
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44 | PetscCall(MatDenseCUDARestoreArrayRead(A,(const PetscScalar**)&d_Apowers[0])); |
| 1364 | } | ||
| 1365 |
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48 | PetscCall(MatDenseCUDARestoreArrayWrite(B,&d_Ba)); |
| 1366 |
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48 | PetscCallCUDA(cudaFree(d_work)); |
| 1367 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 1368 | } | ||
| 1369 | |||
| 1370 | /* | ||
| 1371 | * Matrix exponential implementation based on algorithm and matlab code by Stefan Guettel | ||
| 1372 | * and Yuji Nakatsukasa | ||
| 1373 | * | ||
| 1374 | * Stefan Guettel and Yuji Nakatsukasa, "Scaled and Squared Subdiagonal Pade' | ||
| 1375 | * Approximation for the Matrix Exponential", | ||
| 1376 | * SIAM J. Matrix Anal. Appl. 37(1):145-170, 2016. | ||
| 1377 | * https://doi.org/10.1137/15M1027553 | ||
| 1378 | */ | ||
| 1379 | 32 | PetscErrorCode FNEvaluateFunctionMat_Exp_GuettelNakatsukasa_CUDAm(FN fn,Mat A,Mat B) | |
| 1380 | { | ||
| 1381 | 32 | PetscInt i,j,n_,s,k,m,mod; | |
| 1382 | 32 | PetscBLASInt n=0,n2=0,irsize=0,rsizediv2,ipsize=0,iremainsize=0,query=-1,*piv,minlen,lwork=0,one=1; | |
| 1383 | 32 | PetscReal nrm,shift=0.0,rone=1.0,rzero=0.0; | |
| 1384 | #if defined(PETSC_USE_COMPLEX) | ||
| 1385 | 16 | PetscReal *rwork=NULL; | |
| 1386 | #endif | ||
| 1387 | 32 | PetscComplex *d_As,*d_RR,*d_RR2,*d_expmA,*d_expmA2,*d_Maux,*d_Maux2,rsize,*r,psize,*p,remainsize,*remainterm,*rootp,*rootq,mult=0.0,scale,cone=1.0,czero=0.0,*aux; | |
| 1388 | 32 | PetscScalar *d_Aa,*d_Ba,*d_Ba2,*Maux,*d_sMaux,*wr,*wi,expshift,sone=1.0,szero=0.0,*work,work1,*saux; | |
| 1389 | 32 | const PetscScalar *Aa; | |
| 1390 | 32 | PetscBool isreal,*d_isreal,flg; | |
| 1391 | 32 | cublasHandle_t cublasv2handle; | |
| 1392 | |||
| 1393 | 32 | PetscFunctionBegin; | |
| 1394 |
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32 | PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* For CUDA event timers */ |
| 1395 |
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|
32 | PetscCall(PetscCUBLASGetHandle(&cublasv2handle)); |
| 1396 |
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|
32 | PetscCall(SlepcMagmaInit()); |
| 1397 |
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|
32 | PetscCall(MatGetSize(A,&n_,NULL)); |
| 1398 |
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|
32 | PetscCall(PetscBLASIntCast(n_,&n)); |
| 1399 |
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|
32 | PetscCall(PetscBLASIntCast(n*n,&n2)); |
| 1400 | |||
| 1401 |
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|
32 | if (A==B) { |
| 1402 |
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|
8 | PetscCallCUDA(cudaMalloc((void **)&d_Aa,sizeof(PetscScalar)*n2)); |
| 1403 |
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|
8 | PetscCall(MatDenseCUDAGetArrayRead(A,&Aa)); |
| 1404 |
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8 | PetscCallCUDA(cudaMemcpy(d_Aa,Aa,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); |
| 1405 |
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|
8 | PetscCall(MatDenseCUDARestoreArrayRead(A,&Aa)); |
| 1406 |
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|
24 | } else PetscCall(MatDenseCUDAGetArrayRead(A,(const PetscScalar**)&d_Aa)); |
| 1407 |
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|
32 | PetscCall(MatDenseCUDAGetArrayWrite(B,&d_Ba)); |
| 1408 | 32 | d_Ba2 = d_Ba; | |
| 1409 | |||
| 1410 |
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|
32 | PetscCallCUDA(cudaMalloc((void **)&d_isreal,sizeof(PetscBool))); |
| 1411 |
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|
32 | PetscCallCUDA(cudaMalloc((void **)&d_sMaux,sizeof(PetscScalar)*n2)); |
| 1412 |
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|
32 | PetscCallCUDA(cudaMalloc((void **)&d_Maux,sizeof(PetscComplex)*n2)); |
| 1413 | |||
| 1414 |
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|
32 | PetscCall(PetscLogGpuTimeBegin()); |
| 1415 | 32 | d_Maux2 = d_Maux; | |
| 1416 |
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|
32 | PetscCall(PetscOptionsGetReal(NULL,NULL,"-fn_expm_estimated_eig",&shift,&flg)); |
| 1417 |
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|
32 | if (!flg) { |
| 1418 |
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|
32 | PetscCall(PetscMalloc2(n,&wr,n,&wi)); |
| 1419 | /* estimate rightmost eigenvalue and shift A with it */ | ||
| 1420 |
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|
32 | PetscCall(PetscMalloc1(n2,&Maux)); |
| 1421 |
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|
32 | PetscCall(MatDenseGetArrayRead(A,&Aa)); |
| 1422 |
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|
32 | PetscCall(PetscArraycpy(Maux,Aa,n2)); |
| 1423 |
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|
32 | PetscCall(MatDenseRestoreArrayRead(A,&Aa)); |
| 1424 | #if !defined(PETSC_USE_COMPLEX) | ||
| 1425 |
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|
16 | PetscCallMAGMA(magma_xgeev,MagmaNoVec,MagmaNoVec,n,Maux,n,wr,wi,NULL,n,NULL,n,&work1,query); |
| 1426 |
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|
16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(work1),&lwork)); |
| 1427 |
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|
16 | PetscCall(PetscMalloc1(lwork,&work)); |
| 1428 |
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|
16 | PetscCallMAGMA(magma_xgeev,MagmaNoVec,MagmaNoVec,n,Maux,n,wr,wi,NULL,n,NULL,n,work,lwork); |
| 1429 |
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|
16 | PetscCall(PetscFree(work)); |
| 1430 | #else | ||
| 1431 |
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|
16 | PetscCallMAGMA(magma_xgeev,MagmaNoVec,MagmaNoVec,n,Maux,n,wr,NULL,n,NULL,n,&work1,query,rwork); |
| 1432 |
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16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(work1),&lwork)); |
| 1433 |
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|
16 | PetscCall(PetscMalloc2(2*n,&rwork,lwork,&work)); |
| 1434 |
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|
16 | PetscCallMAGMA(magma_xgeev,MagmaNoVec,MagmaNoVec,n,Maux,n,wr,NULL,n,NULL,n,work,lwork,rwork); |
| 1435 |
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16 | PetscCall(PetscFree2(rwork,work)); |
| 1436 | #endif | ||
| 1437 |
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|
32 | PetscCall(PetscFree(Maux)); |
| 1438 |
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32 | PetscCall(PetscLogGpuFlops(25.0*n*n*n+(n*n*n)/3.0+1.0*n*n*n)); |
| 1439 | |||
| 1440 | 32 | shift = PetscRealPart(wr[0]); | |
| 1441 |
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320 | for (i=1;i<n;i++) { |
| 1442 |
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|
288 | if (PetscRealPart(wr[i]) > shift) shift = PetscRealPart(wr[i]); |
| 1443 | } | ||
| 1444 |
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|
32 | PetscCall(PetscFree2(wr,wi)); |
| 1445 | } | ||
| 1446 | /* shift so that largest real part is (about) 0 */ | ||
| 1447 |
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32 | PetscCallCUDA(cudaMemcpy(d_sMaux,d_Aa,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); |
| 1448 |
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32 | if (shift) { |
| 1449 |
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32 | PetscCall(shift_diagonal(n,d_sMaux,n,-shift)); |
| 1450 |
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32 | PetscCall(PetscLogGpuFlops(1.0*n)); |
| 1451 | } | ||
| 1452 | #if defined(PETSC_USE_COMPLEX) | ||
| 1453 |
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16 | PetscCallCUDA(cudaMemcpy(d_Maux,d_Aa,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); |
| 1454 |
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16 | if (shift) { |
| 1455 |
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16 | PetscCall(shift_diagonal(n,d_Maux,n,-shift)); |
| 1456 |
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16 | PetscCall(PetscLogGpuFlops(1.0*n)); |
| 1457 | } | ||
| 1458 | #endif | ||
| 1459 |
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32 | if (A!=B) PetscCall(MatDenseCUDARestoreArrayRead(A,(const PetscScalar**)&d_Aa)); |
| 1460 |
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|
8 | else PetscCallCUDA(cudaFree(d_Aa)); |
| 1461 | |||
| 1462 | /* estimate norm(A) and select the scaling factor */ | ||
| 1463 |
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32 | PetscCallCUBLAS(cublasXnrm2(cublasv2handle,n2,d_sMaux,one,&nrm)); |
| 1464 |
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32 | PetscCall(PetscLogGpuFlops(2.0*n*n)); |
| 1465 |
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32 | PetscCall(sexpm_params(nrm,&s,&k,&m)); |
| 1466 |
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32 | if (s==0 && k==1 && m==0) { /* exp(A) = I+A to eps! */ |
| 1467 | ✗ | if (shift) expshift = PetscExpReal(shift); | |
| 1468 | ✗ | PetscCall(shift_Cdiagonal(n,d_Maux,n,rone,rzero)); | |
| 1469 | ✗ | if (shift) { | |
| 1470 | ✗ | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&expshift,d_sMaux,one)); | |
| 1471 | ✗ | PetscCall(PetscLogGpuFlops(1.0*(n+n2))); | |
| 1472 | ✗ | } else PetscCall(PetscLogGpuFlops(1.0*n)); | |
| 1473 | ✗ | PetscCallCUDA(cudaMemcpy(d_Ba,d_sMaux,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); | |
| 1474 | ✗ | PetscCallCUDA(cudaFree(d_isreal)); | |
| 1475 | ✗ | PetscCallCUDA(cudaFree(d_sMaux)); | |
| 1476 | ✗ | PetscCallCUDA(cudaFree(d_Maux)); | |
| 1477 | ✗ | PetscCall(MatDenseCUDARestoreArrayWrite(B,&d_Ba)); | |
| 1478 | PetscFunctionReturn(PETSC_SUCCESS); /* quick return */ | ||
| 1479 | } | ||
| 1480 | |||
| 1481 |
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32 | PetscCallCUDA(cudaMalloc((void **)&d_expmA,sizeof(PetscComplex)*n2)); |
| 1482 |
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32 | PetscCallCUDA(cudaMalloc((void **)&d_As,sizeof(PetscComplex)*n2)); |
| 1483 |
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32 | PetscCallCUDA(cudaMalloc((void **)&d_RR,sizeof(PetscComplex)*n2)); |
| 1484 | 32 | d_expmA2 = d_expmA; d_RR2 = d_RR; | |
| 1485 |
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|
32 | PetscCall(PetscMalloc1(n,&piv)); |
| 1486 | /* scale matrix */ | ||
| 1487 | #if !defined(PETSC_USE_COMPLEX) | ||
| 1488 |
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|
16 | PetscCall(copy_array2D_S2C(n,n,d_As,n,d_sMaux,n)); |
| 1489 | #else | ||
| 1490 |
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16 | PetscCallCUDA(cudaMemcpy(d_As,d_sMaux,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); |
| 1491 | #endif | ||
| 1492 | 32 | scale = 1.0/PetscPowRealInt(2.0,s); | |
| 1493 |
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32 | PetscCallCUBLAS(cublasXCscal(cublasv2handle,n2,(const cuComplex *)&scale,(cuComplex *)d_As,one)); |
| 1494 |
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|
32 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n2)); |
| 1495 | |||
| 1496 | /* evaluate Pade approximant (partial fraction or product form) */ | ||
| 1497 |
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32 | if (fn->method==3 || !m) { /* partial fraction */ |
| 1498 |
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|
16 | PetscCall(getcoeffs(k,m,&rsize,&psize,&remainsize,PETSC_TRUE)); |
| 1499 |
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|
16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(rsize),&irsize)); |
| 1500 |
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|
16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(psize),&ipsize)); |
| 1501 |
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16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(remainsize),&iremainsize)); |
| 1502 |
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|
16 | PetscCall(PetscMalloc3(irsize,&r,ipsize,&p,iremainsize,&remainterm)); |
| 1503 |
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|
16 | PetscCall(getcoeffs(k,m,r,p,remainterm,PETSC_FALSE)); |
| 1504 | |||
| 1505 |
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16 | PetscCallCUDA(cudaMemset(d_expmA,0,sizeof(PetscComplex)*n2)); |
| 1506 | #if !defined(PETSC_USE_COMPLEX) | ||
| 1507 | 8 | isreal = PETSC_TRUE; | |
| 1508 | #else | ||
| 1509 |
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|
8 | PetscCall(getisreal_array2D(n,n,d_Maux,n,d_isreal)); |
| 1510 |
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8 | PetscCallCUDA(cudaMemcpy(&isreal,d_isreal,sizeof(PetscBool),cudaMemcpyDeviceToHost)); |
| 1511 | #endif | ||
| 1512 |
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16 | if (isreal) { |
| 1513 | 16 | rsizediv2 = irsize/2; | |
| 1514 |
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48 | for (i=0;i<rsizediv2;i++) { /* use partial fraction to get R(As) */ |
| 1515 |
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32 | PetscCallCUDA(cudaMemcpy(d_Maux,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); |
| 1516 |
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32 | PetscCallCUDA(cudaMemset(d_RR,0,sizeof(PetscComplex)*n2)); |
| 1517 |
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32 | PetscCall(shift_Cdiagonal(n,d_Maux,n,-PetscRealPartComplex(p[2*i]),-PetscImaginaryPartComplex(p[2*i]))); |
| 1518 |
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32 | PetscCall(set_Cdiagonal(n,d_RR,n,PetscRealPartComplex(r[2*i]),PetscImaginaryPartComplex(r[2*i]))); |
| 1519 |
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32 | PetscCallMAGMA(magma_Cgesv_gpu,n,n,d_Maux,n,piv,d_RR,n); |
| 1520 |
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32 | PetscCall(add_array2D_Conj(n,n,d_RR,n)); |
| 1521 |
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|
32 | PetscCallCUBLAS(cublasXCaxpy(cublasv2handle,n2,&cone,d_RR,one,d_expmA,one)); |
| 1522 | /* shift(n) + gesv + axpy(n2) */ | ||
| 1523 |
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|
32 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n)+2.0*n2)); |
| 1524 | } | ||
| 1525 | |||
| 1526 | 16 | mod = ipsize % 2; | |
| 1527 |
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|
16 | if (mod) { |
| 1528 | ✗ | PetscCallCUDA(cudaMemcpy(d_Maux,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); | |
| 1529 | ✗ | PetscCallCUDA(cudaMemset(d_RR,0,sizeof(PetscComplex)*n2)); | |
| 1530 | ✗ | PetscCall(shift_Cdiagonal(n,d_Maux,n,-PetscRealPartComplex(p[ipsize-1]),-PetscImaginaryPartComplex(p[ipsize-1]))); | |
| 1531 | ✗ | PetscCall(set_Cdiagonal(n,d_RR,n,PetscRealPartComplex(r[irsize-1]),PetscImaginaryPartComplex(r[irsize-1]))); | |
| 1532 | ✗ | PetscCallMAGMA(magma_Cgesv_gpu,n,n,d_Maux,n,piv,d_RR,n); | |
| 1533 | ✗ | PetscCallCUBLAS(cublasXCaxpy(cublasv2handle,n2,&cone,d_RR,one,d_expmA,one)); | |
| 1534 | ✗ | PetscCall(SlepcLogGpuFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n)+1.0*n2)); | |
| 1535 | } | ||
| 1536 | } else { /* complex */ | ||
| 1537 | ✗ | for (i=0;i<irsize;i++) { /* use partial fraction to get R(As) */ | |
| 1538 | ✗ | PetscCallCUDA(cudaMemcpy(d_Maux,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); | |
| 1539 | ✗ | PetscCallCUDA(cudaMemset(d_RR,0,sizeof(PetscComplex)*n2)); | |
| 1540 | ✗ | PetscCall(shift_Cdiagonal(n,d_Maux,n,-PetscRealPartComplex(p[i]),-PetscImaginaryPartComplex(p[i]))); | |
| 1541 | ✗ | PetscCall(set_Cdiagonal(n,d_RR,n,PetscRealPartComplex(r[i]),PetscImaginaryPartComplex(r[i]))); | |
| 1542 | ✗ | PetscCallMAGMA(magma_Cgesv_gpu,n,n,d_Maux,n,piv,d_RR,n); | |
| 1543 | ✗ | PetscCallCUBLAS(cublasXCaxpy(cublasv2handle,n2,&cone,d_RR,one,d_expmA,one)); | |
| 1544 | ✗ | PetscCall(SlepcLogGpuFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n)+1.0*n2)); | |
| 1545 | } | ||
| 1546 | } | ||
| 1547 |
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48 | for (i=0;i<iremainsize;i++) { |
| 1548 |
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32 | if (!i) { |
| 1549 |
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16 | PetscCallCUDA(cudaMemset(d_RR,0,sizeof(PetscComplex)*n2)); |
| 1550 |
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16 | PetscCall(set_Cdiagonal(n,d_RR,n,PetscRealPartComplex(remainterm[iremainsize-1]),PetscImaginaryPartComplex(remainterm[iremainsize-1]))); |
| 1551 | } else { | ||
| 1552 |
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16 | PetscCallCUDA(cudaMemcpy(d_RR,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); |
| 1553 |
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16 | for (j=1;j<i;j++) { |
| 1554 | ✗ | PetscCallCUBLAS(cublasXCgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&cone,d_RR,n,d_RR,n,&czero,d_Maux,n)); | |
| 1555 | ✗ | SlepcSwap(d_RR,d_Maux,aux); | |
| 1556 | ✗ | PetscCall(SlepcLogGpuFlopsComplex(2.0*n*n*n)); | |
| 1557 | } | ||
| 1558 |
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16 | PetscCallCUBLAS(cublasXCscal(cublasv2handle,n2,&remainterm[iremainsize-1-i],d_RR,one)); |
| 1559 |
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16 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n2)); |
| 1560 | } | ||
| 1561 |
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32 | PetscCallCUBLAS(cublasXCaxpy(cublasv2handle,n2,&cone,d_RR,one,d_expmA,one)); |
| 1562 |
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32 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n2)); |
| 1563 | } | ||
| 1564 |
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|
16 | PetscCall(PetscFree3(r,p,remainterm)); |
| 1565 | } else { /* product form, default */ | ||
| 1566 |
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|
16 | PetscCall(getcoeffsproduct(k,m,&rsize,&psize,&mult,PETSC_TRUE)); |
| 1567 |
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|
16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(rsize),&irsize)); |
| 1568 |
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16 | PetscCall(PetscBLASIntCast((PetscInt)PetscRealPartComplex(psize),&ipsize)); |
| 1569 |
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16 | PetscCall(PetscMalloc2(irsize,&rootp,ipsize,&rootq)); |
| 1570 |
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|
16 | PetscCall(getcoeffsproduct(k,m,rootp,rootq,&mult,PETSC_FALSE)); |
| 1571 | |||
| 1572 |
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16 | PetscCallCUDA(cudaMemset(d_expmA,0,sizeof(PetscComplex)*n2)); |
| 1573 |
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16 | PetscCall(set_Cdiagonal(n,d_expmA,n,rone,rzero)); /* initialize */ |
| 1574 | 16 | minlen = PetscMin(irsize,ipsize); | |
| 1575 |
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80 | for (i=0;i<minlen;i++) { |
| 1576 |
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64 | PetscCallCUDA(cudaMemcpy(d_RR,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); |
| 1577 |
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|
64 | PetscCall(shift_Cdiagonal(n,d_RR,n,-PetscRealPartComplex(rootp[i]),-PetscImaginaryPartComplex(rootp[i]))); |
| 1578 |
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|
64 | PetscCallCUBLAS(cublasXCgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&cone,d_RR,n,d_expmA,n,&czero,d_Maux,n)); |
| 1579 | 64 | SlepcSwap(d_expmA,d_Maux,aux); | |
| 1580 |
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64 | PetscCallCUDA(cudaMemcpy(d_RR,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); |
| 1581 |
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64 | PetscCall(shift_Cdiagonal(n,d_RR,n,-PetscRealPartComplex(rootq[i]),-PetscImaginaryPartComplex(rootq[i]))); |
| 1582 |
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|
64 | PetscCallMAGMA(magma_Cgesv_gpu,n,n,d_RR,n,piv,d_expmA,n); |
| 1583 | /* shift(n) + gemm + shift(n) + gesv */ | ||
| 1584 |
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|
64 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n+(2.0*n*n*n)+1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n))); |
| 1585 | } | ||
| 1586 | /* extra enumerator */ | ||
| 1587 |
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32 | for (i=minlen;i<irsize;i++) { |
| 1588 |
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16 | PetscCallCUDA(cudaMemcpy(d_RR,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); |
| 1589 |
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16 | PetscCall(shift_Cdiagonal(n,d_RR,n,-PetscRealPartComplex(rootp[i]),-PetscImaginaryPartComplex(rootp[i]))); |
| 1590 |
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|
16 | PetscCallCUBLAS(cublasXCgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&cone,d_RR,n,d_expmA,n,&czero,d_Maux,n)); |
| 1591 | 16 | SlepcSwap(d_expmA,d_Maux,aux); | |
| 1592 |
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16 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n+2.0*n*n*n)); |
| 1593 | } | ||
| 1594 | /* extra denominator */ | ||
| 1595 |
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|
16 | for (i=minlen;i<ipsize;i++) { |
| 1596 | ✗ | PetscCallCUDA(cudaMemcpy(d_RR,d_As,sizeof(PetscComplex)*n2,cudaMemcpyDeviceToDevice)); | |
| 1597 | ✗ | PetscCall(shift_Cdiagonal(n,d_RR,n,-PetscRealPartComplex(rootq[i]),-PetscImaginaryPartComplex(rootq[i]))); | |
| 1598 | ✗ | PetscCallMAGMA(magma_Cgesv_gpu,n,n,d_RR,n,piv,d_expmA,n); | |
| 1599 | ✗ | PetscCall(SlepcLogGpuFlopsComplex(1.0*n+(2.0*n*n*n/3.0+2.0*n*n*n))); | |
| 1600 | } | ||
| 1601 |
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16 | PetscCallCUBLAS(cublasXCscal(cublasv2handle,n2,&mult,d_expmA,one)); |
| 1602 |
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16 | PetscCall(SlepcLogGpuFlopsComplex(1.0*n2)); |
| 1603 |
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|
16 | PetscCall(PetscFree2(rootp,rootq)); |
| 1604 | } | ||
| 1605 | |||
| 1606 | #if !defined(PETSC_USE_COMPLEX) | ||
| 1607 |
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|
16 | PetscCall(copy_array2D_C2S(n,n,d_Ba2,n,d_expmA,n)); |
| 1608 | #else | ||
| 1609 |
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|
16 | PetscCallCUDA(cudaMemcpy(d_Ba2,d_expmA,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); |
| 1610 | #endif | ||
| 1611 | |||
| 1612 | /* perform repeated squaring */ | ||
| 1613 |
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160 | for (i=0;i<s;i++) { /* final squaring */ |
| 1614 |
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|
128 | PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_Ba2,n,d_Ba2,n,&szero,d_sMaux,n)); |
| 1615 | 128 | SlepcSwap(d_Ba2,d_sMaux,saux); | |
| 1616 |
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128 | PetscCall(PetscLogGpuFlops(2.0*n*n*n)); |
| 1617 | } | ||
| 1618 |
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|
32 | if (d_Ba2!=d_Ba) { |
| 1619 | ✗ | PetscCallCUDA(cudaMemcpy(d_Ba,d_Ba2,sizeof(PetscScalar)*n2,cudaMemcpyDeviceToDevice)); | |
| 1620 | ✗ | d_sMaux = d_Ba2; | |
| 1621 | } | ||
| 1622 |
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32 | if (shift) { |
| 1623 | 32 | expshift = PetscExpReal(shift); | |
| 1624 |
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32 | PetscCallCUBLAS(cublasXscal(cublasv2handle,n2,&expshift,d_Ba,one)); |
| 1625 |
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32 | PetscCall(PetscLogGpuFlops(1.0*n2)); |
| 1626 | } | ||
| 1627 | |||
| 1628 |
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|
32 | PetscCall(PetscLogGpuTimeEnd()); |
| 1629 | |||
| 1630 | /* restore pointers */ | ||
| 1631 | 32 | d_Maux = d_Maux2; d_expmA = d_expmA2; d_RR = d_RR2; | |
| 1632 |
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32 | PetscCall(MatDenseCUDARestoreArrayWrite(B,&d_Ba)); |
| 1633 |
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32 | PetscCallCUDA(cudaFree(d_isreal)); |
| 1634 |
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32 | PetscCallCUDA(cudaFree(d_sMaux)); |
| 1635 |
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32 | PetscCallCUDA(cudaFree(d_Maux)); |
| 1636 |
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32 | PetscCallCUDA(cudaFree(d_expmA)); |
| 1637 |
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32 | PetscCallCUDA(cudaFree(d_As)); |
| 1638 |
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32 | PetscCallCUDA(cudaFree(d_RR)); |
| 1639 |
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|
32 | PetscCall(PetscFree(piv)); |
| 1640 | PetscFunctionReturn(PETSC_SUCCESS); | ||
| 1641 | } | ||
| 1642 | #endif /* PETSC_HAVE_MAGMA */ | ||
| 1643 | #endif /* PETSC_HAVE_CUDA */ | ||
| 1644 | |||
| 1645 | 319 | static PetscErrorCode FNView_Exp(FN fn,PetscViewer viewer) | |
| 1646 | { | ||
| 1647 | 319 | PetscBool isascii; | |
| 1648 | 319 | char str[50]; | |
| 1649 | 319 | const char *methodname[] = { | |
| 1650 | "scaling & squaring, [m/m] Pade approximant (Higham)", | ||
| 1651 | "scaling & squaring, [6/6] Pade approximant", | ||
| 1652 | "scaling & squaring, subdiagonal Pade approximant (product form)", | ||
| 1653 | "scaling & squaring, subdiagonal Pade approximant (partial fraction)" | ||
| 1654 | }; | ||
| 1655 | 319 | const int nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname); | |
| 1656 | |||
| 1657 |
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319 | PetscFunctionBegin; |
| 1658 |
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319 | PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii)); |
| 1659 |
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319 | if (isascii) { |
| 1660 |
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319 | if (fn->beta==(PetscScalar)1.0) { |
| 1661 |
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|
269 | if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscViewerASCIIPrintf(viewer," exponential: exp(x)\n")); |
| 1662 | else { | ||
| 1663 |
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105 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE)); |
| 1664 |
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105 | PetscCall(PetscViewerASCIIPrintf(viewer," exponential: exp(%s*x)\n",str)); |
| 1665 | } | ||
| 1666 | } else { | ||
| 1667 |
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50 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE)); |
| 1668 |
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50 | if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscViewerASCIIPrintf(viewer," exponential: %s*exp(x)\n",str)); |
| 1669 | else { | ||
| 1670 |
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50 | PetscCall(PetscViewerASCIIPrintf(viewer," exponential: %s",str)); |
| 1671 |
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50 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE)); |
| 1672 |
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50 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE)); |
| 1673 |
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50 | PetscCall(PetscViewerASCIIPrintf(viewer,"*exp(%s*x)\n",str)); |
| 1674 |
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50 | PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE)); |
| 1675 | } | ||
| 1676 | } | ||
| 1677 |
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|
319 | if (fn->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer," computing matrix functions with: %s\n",methodname[fn->method])); |
| 1678 | } | ||
| 1679 |
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|
59 | PetscFunctionReturn(PETSC_SUCCESS); |
| 1680 | } | ||
| 1681 | |||
| 1682 | /*MC | ||
| 1683 | FNEXP - FNEXP = "exp" - The exponential function $f(x)=e^x$. | ||
| 1684 | |||
| 1685 | Level: beginner | ||
| 1686 | |||
| 1687 | .seealso: [](sec:fn), `FN`, `FNType`, `FNSetType()` | ||
| 1688 | M*/ | ||
| 1689 | |||
| 1690 | 1160 | SLEPC_EXTERN PetscErrorCode FNCreate_Exp(FN fn) | |
| 1691 | { | ||
| 1692 |
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|
1160 | PetscFunctionBegin; |
| 1693 | 1160 | fn->ops->evaluatefunction = FNEvaluateFunction_Exp; | |
| 1694 | 1160 | fn->ops->evaluatederivative = FNEvaluateDerivative_Exp; | |
| 1695 | 1160 | fn->ops->evaluatefunctionmat[0] = FNEvaluateFunctionMat_Exp_Higham; | |
| 1696 | 1160 | fn->ops->evaluatefunctionmat[1] = FNEvaluateFunctionMat_Exp_Pade; | |
| 1697 | 1160 | fn->ops->evaluatefunctionmat[2] = FNEvaluateFunctionMat_Exp_GuettelNakatsukasa; /* product form */ | |
| 1698 | 1160 | fn->ops->evaluatefunctionmat[3] = FNEvaluateFunctionMat_Exp_GuettelNakatsukasa; /* partial fraction */ | |
| 1699 | #if defined(PETSC_HAVE_CUDA) | ||
| 1700 | 255 | fn->ops->evaluatefunctionmatcuda[1] = FNEvaluateFunctionMat_Exp_Pade_CUDA; | |
| 1701 | #if defined(PETSC_HAVE_MAGMA) | ||
| 1702 | 255 | fn->ops->evaluatefunctionmatcuda[0] = FNEvaluateFunctionMat_Exp_Higham_CUDAm; | |
| 1703 | 255 | fn->ops->evaluatefunctionmatcuda[1] = FNEvaluateFunctionMat_Exp_Pade_CUDAm; | |
| 1704 | 255 | fn->ops->evaluatefunctionmatcuda[2] = FNEvaluateFunctionMat_Exp_GuettelNakatsukasa_CUDAm; /* product form */ | |
| 1705 | 255 | fn->ops->evaluatefunctionmatcuda[3] = FNEvaluateFunctionMat_Exp_GuettelNakatsukasa_CUDAm; /* partial fraction */ | |
| 1706 | #endif | ||
| 1707 | #endif | ||
| 1708 | 1160 | fn->ops->view = FNView_Exp; | |
| 1709 |
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1160 | PetscFunctionReturn(PETSC_SUCCESS); |
| 1710 | } | ||
| 1711 |