Actual source code: fnsqrt.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    Square root function  sqrt(x)
     12: */

     14: #include <slepc/private/fnimpl.h>
     15: #include <slepcblaslapack.h>

     17: static PetscErrorCode FNEvaluateFunction_Sqrt(FN fn,PetscScalar x,PetscScalar *y)
     18: {
     19:   PetscFunctionBegin;
     20: #if !defined(PETSC_USE_COMPLEX)
     21:   PetscCheck(x>=0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Function not defined in the requested value");
     22: #endif
     23:   *y = PetscSqrtScalar(x);
     24:   PetscFunctionReturn(PETSC_SUCCESS);
     25: }

     27: static PetscErrorCode FNEvaluateDerivative_Sqrt(FN fn,PetscScalar x,PetscScalar *y)
     28: {
     29:   PetscFunctionBegin;
     30:   PetscCheck(x!=0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Derivative not defined in the requested value");
     31: #if !defined(PETSC_USE_COMPLEX)
     32:   PetscCheck(x>0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Derivative not defined in the requested value");
     33: #endif
     34:   *y = 1.0/(2.0*PetscSqrtScalar(x));
     35:   PetscFunctionReturn(PETSC_SUCCESS);
     36: }

     38: static PetscErrorCode FNEvaluateFunctionMat_Sqrt_Schur(FN fn,Mat A,Mat B)
     39: {
     40:   PetscBLASInt   n=0;
     41:   PetscScalar    *T;
     42:   PetscInt       m;

     44:   PetscFunctionBegin;
     45:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
     46:   PetscCall(MatDenseGetArray(B,&T));
     47:   PetscCall(MatGetSize(A,&m,NULL));
     48:   PetscCall(PetscBLASIntCast(m,&n));
     49:   PetscCall(FNSqrtmSchur(fn,n,T,n,PETSC_FALSE));
     50:   PetscCall(MatDenseRestoreArray(B,&T));
     51:   PetscFunctionReturn(PETSC_SUCCESS);
     52: }

     54: static PetscErrorCode FNEvaluateFunctionMatVec_Sqrt_Schur(FN fn,Mat A,Vec v)
     55: {
     56:   PetscBLASInt   n=0;
     57:   PetscScalar    *T;
     58:   PetscInt       m;
     59:   Mat            B;

     61:   PetscFunctionBegin;
     62:   PetscCall(FN_AllocateWorkMat(fn,A,&B));
     63:   PetscCall(MatDenseGetArray(B,&T));
     64:   PetscCall(MatGetSize(A,&m,NULL));
     65:   PetscCall(PetscBLASIntCast(m,&n));
     66:   PetscCall(FNSqrtmSchur(fn,n,T,n,PETSC_TRUE));
     67:   PetscCall(MatDenseRestoreArray(B,&T));
     68:   PetscCall(MatGetColumnVector(B,v,0));
     69:   PetscCall(FN_FreeWorkMat(fn,&B));
     70:   PetscFunctionReturn(PETSC_SUCCESS);
     71: }

     73: static PetscErrorCode FNEvaluateFunctionMat_Sqrt_DBP(FN fn,Mat A,Mat B)
     74: {
     75:   PetscBLASInt   n=0;
     76:   PetscScalar    *T;
     77:   PetscInt       m;

     79:   PetscFunctionBegin;
     80:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
     81:   PetscCall(MatDenseGetArray(B,&T));
     82:   PetscCall(MatGetSize(A,&m,NULL));
     83:   PetscCall(PetscBLASIntCast(m,&n));
     84:   PetscCall(FNSqrtmDenmanBeavers(fn,n,T,n,PETSC_FALSE));
     85:   PetscCall(MatDenseRestoreArray(B,&T));
     86:   PetscFunctionReturn(PETSC_SUCCESS);
     87: }

     89: static PetscErrorCode FNEvaluateFunctionMat_Sqrt_NS(FN fn,Mat A,Mat B)
     90: {
     91:   PetscBLASInt   n=0;
     92:   PetscScalar    *Ba;
     93:   PetscInt       m;

     95:   PetscFunctionBegin;
     96:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
     97:   PetscCall(MatDenseGetArray(B,&Ba));
     98:   PetscCall(MatGetSize(A,&m,NULL));
     99:   PetscCall(PetscBLASIntCast(m,&n));
    100:   PetscCall(FNSqrtmNewtonSchulz(fn,n,Ba,n,PETSC_FALSE));
    101:   PetscCall(MatDenseRestoreArray(B,&Ba));
    102:   PetscFunctionReturn(PETSC_SUCCESS);
    103: }

    105: #define MAXIT 50

    107: /*
    108:    Computes the principal square root of the matrix A using the
    109:    Sadeghi iteration. A is overwritten with sqrtm(A).
    110:  */
    111: PetscErrorCode FNSqrtmSadeghi(FN fn,PetscBLASInt n,PetscScalar *A,PetscBLASInt ld)
    112: {
    113:   PetscScalar    *M,*M2,*G,*X=A,*work,work1,sqrtnrm;
    114:   PetscScalar    szero=0.0,sone=1.0,smfive=-5.0,s1d16=1.0/16.0;
    115:   PetscReal      tol,Mres=0.0,nrm,rwork[1],done=1.0;
    116:   PetscInt       i,it;
    117:   PetscBLASInt   N,*piv=NULL,info,lwork=0,query=-1,one=1,zero=0;
    118:   PetscBool      converged=PETSC_FALSE;
    119:   unsigned int   ftz;

    121:   PetscFunctionBegin;
    122:   N = n*n;
    123:   tol = PetscSqrtReal((PetscReal)n)*PETSC_MACHINE_EPSILON/2;
    124:   PetscCall(SlepcSetFlushToZero(&ftz));

    126:   /* query work size */
    127:   PetscCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,piv,&work1,&query,&info));
    128:   PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(work1),&lwork));

    130:   PetscCall(PetscMalloc5(N,&M,N,&M2,N,&G,lwork,&work,n,&piv));
    131:   PetscCall(PetscArraycpy(M,A,N));

    133:   /* scale M */
    134:   nrm = LAPACKlange_("fro",&n,&n,M,&n,rwork);
    135:   if (nrm>1.0) {
    136:     sqrtnrm = PetscSqrtReal(nrm);
    137:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&nrm,&done,&N,&one,M,&N,&info));
    138:     SlepcCheckLapackInfo("lascl",info);
    139:     tol *= nrm;
    140:   }
    141:   PetscCall(PetscInfo(fn,"||A||_F = %g, new tol: %g\n",(double)nrm,(double)tol));

    143:   /* X = I */
    144:   PetscCall(PetscArrayzero(X,N));
    145:   for (i=0;i<n;i++) X[i+i*ld] = 1.0;

    147:   for (it=0;it<MAXIT && !converged;it++) {

    149:     /* G = (5/16)*I + (1/16)*M*(15*I-5*M+M*M) */
    150:     PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&sone,M,&ld,M,&ld,&szero,M2,&ld));
    151:     PetscCallBLAS("BLASaxpy",BLASaxpy_(&N,&smfive,M,&one,M2,&one));
    152:     for (i=0;i<n;i++) M2[i+i*ld] += 15.0;
    153:     PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&s1d16,M,&ld,M2,&ld,&szero,G,&ld));
    154:     for (i=0;i<n;i++) G[i+i*ld] += 5.0/16.0;

    156:     /* X = X*G */
    157:     PetscCall(PetscArraycpy(M2,X,N));
    158:     PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&sone,M2,&ld,G,&ld,&szero,X,&ld));

    160:     /* M = M*inv(G*G) */
    161:     PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&sone,G,&ld,G,&ld,&szero,M2,&ld));
    162:     PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,M2,&ld,piv,&info));
    163:     SlepcCheckLapackInfo("getrf",info);
    164:     PetscCallBLAS("LAPACKgetri",LAPACKgetri_(&n,M2,&ld,piv,work,&lwork,&info));
    165:     SlepcCheckLapackInfo("getri",info);

    167:     PetscCall(PetscArraycpy(G,M,N));
    168:     PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&sone,G,&ld,M2,&ld,&szero,M,&ld));

    170:     /* check ||I-M|| */
    171:     PetscCall(PetscArraycpy(M2,M,N));
    172:     for (i=0;i<n;i++) M2[i+i*ld] -= 1.0;
    173:     Mres = LAPACKlange_("fro",&n,&n,M2,&n,rwork);
    174:     PetscCheck(!PetscIsNanReal(Mres),PETSC_COMM_SELF,PETSC_ERR_FP,"The computed norm is not-a-number");
    175:     if (Mres<=tol) converged = PETSC_TRUE;
    176:     PetscCall(PetscInfo(fn,"it: %" PetscInt_FMT " res: %g\n",it,(double)Mres));
    177:     PetscCall(PetscLogFlops(8.0*n*n*n+2.0*n*n+2.0*n*n*n/3.0+4.0*n*n*n/3.0+2.0*n*n*n+2.0*n*n));
    178:   }

    180:   PetscCheck(Mres<=tol,PETSC_COMM_SELF,PETSC_ERR_LIB,"SQRTM not converged after %d iterations",MAXIT);

    182:   /* undo scaling */
    183:   if (nrm>1.0) PetscCallBLAS("BLASscal",BLASscal_(&N,&sqrtnrm,A,&one));

    185:   PetscCall(PetscFree5(M,M2,G,work,piv));
    186:   PetscCall(SlepcResetFlushToZero(&ftz));
    187:   PetscFunctionReturn(PETSC_SUCCESS);
    188: }

    190: #if defined(PETSC_HAVE_CUDA)
    191: #include "../src/sys/classes/fn/impls/cuda/fnutilcuda.h"
    192: #include <slepccupmblas.h>

    194: #if defined(PETSC_HAVE_MAGMA)
    195: #include <slepcmagma.h>

    197: /*
    198:  * Matrix square root by Sadeghi iteration. CUDA version.
    199:  * Computes the principal square root of the matrix A using the
    200:  * Sadeghi iteration. A is overwritten with sqrtm(A).
    201:  */
    202: PetscErrorCode FNSqrtmSadeghi_CUDAm(FN fn,PetscBLASInt n,PetscScalar *d_A,PetscBLASInt ld)
    203: {
    204:   PetscScalar        *d_M,*d_M2,*d_G,*d_work,alpha;
    205:   const PetscScalar  szero=0.0,sone=1.0,smfive=-5.0,s15=15.0,s1d16=1.0/16.0;
    206:   PetscReal          tol,Mres=0.0,nrm,sqrtnrm=1.0;
    207:   PetscInt           it,nb,lwork;
    208:   PetscBLASInt       *piv,N;
    209:   const PetscBLASInt one=1;
    210:   PetscBool          converged=PETSC_FALSE;
    211:   cublasHandle_t     cublasv2handle;

    213:   PetscFunctionBegin;
    214:   PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* For CUDA event timers */
    215:   PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
    216:   PetscCall(SlepcMagmaInit());
    217:   N = n*n;
    218:   tol = PetscSqrtReal((PetscReal)n)*PETSC_MACHINE_EPSILON/2;

    220:   PetscCall(PetscMalloc1(n,&piv));
    221:   PetscCallCUDA(cudaMalloc((void **)&d_M,sizeof(PetscScalar)*N));
    222:   PetscCallCUDA(cudaMalloc((void **)&d_M2,sizeof(PetscScalar)*N));
    223:   PetscCallCUDA(cudaMalloc((void **)&d_G,sizeof(PetscScalar)*N));

    225:   nb = magma_get_xgetri_nb(n);
    226:   lwork = nb*n;
    227:   PetscCallCUDA(cudaMalloc((void **)&d_work,sizeof(PetscScalar)*lwork));
    228:   PetscCall(PetscLogGpuTimeBegin());

    230:   /* M = A */
    231:   PetscCallCUDA(cudaMemcpy(d_M,d_A,sizeof(PetscScalar)*N,cudaMemcpyDeviceToDevice));

    233:   /* scale M */
    234:   PetscCallCUBLAS(cublasXnrm2(cublasv2handle,N,d_M,one,&nrm));
    235:   if (nrm>1.0) {
    236:     sqrtnrm = PetscSqrtReal(nrm);
    237:     alpha = 1.0/nrm;
    238:     PetscCallCUBLAS(cublasXscal(cublasv2handle,N,&alpha,d_M,one));
    239:     tol *= nrm;
    240:   }
    241:   PetscCall(PetscInfo(fn,"||A||_F = %g, new tol: %g\n",(double)nrm,(double)tol));

    243:   /* X = I */
    244:   PetscCallCUDA(cudaMemset(d_A,0,sizeof(PetscScalar)*N));
    245:   PetscCall(set_diagonal(n,d_A,ld,sone));

    247:   for (it=0;it<MAXIT && !converged;it++) {

    249:     /* G = (5/16)*I + (1/16)*M*(15*I-5*M+M*M) */
    250:     PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_M,ld,d_M,ld,&szero,d_M2,ld));
    251:     PetscCallCUBLAS(cublasXaxpy(cublasv2handle,N,&smfive,d_M,one,d_M2,one));
    252:     PetscCall(shift_diagonal(n,d_M2,ld,s15));
    253:     PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&s1d16,d_M,ld,d_M2,ld,&szero,d_G,ld));
    254:     PetscCall(shift_diagonal(n,d_G,ld,5.0/16.0));

    256:     /* X = X*G */
    257:     PetscCallCUDA(cudaMemcpy(d_M2,d_A,sizeof(PetscScalar)*N,cudaMemcpyDeviceToDevice));
    258:     PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_M2,ld,d_G,ld,&szero,d_A,ld));

    260:     /* M = M*inv(G*G) */
    261:     PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_G,ld,d_G,ld,&szero,d_M2,ld));
    262:     /* magma */
    263:     PetscCallMAGMA(magma_xgetrf_gpu,n,n,d_M2,ld,piv);
    264:     PetscCallMAGMA(magma_xgetri_gpu,n,d_M2,ld,piv,d_work,lwork);
    265:     /* magma */
    266:     PetscCallCUDA(cudaMemcpy(d_G,d_M,sizeof(PetscScalar)*N,cudaMemcpyDeviceToDevice));
    267:     PetscCallCUBLAS(cublasXgemm(cublasv2handle,CUBLAS_OP_N,CUBLAS_OP_N,n,n,n,&sone,d_G,ld,d_M2,ld,&szero,d_M,ld));

    269:     /* check ||I-M|| */
    270:     PetscCallCUDA(cudaMemcpy(d_M2,d_M,sizeof(PetscScalar)*N,cudaMemcpyDeviceToDevice));
    271:     PetscCall(shift_diagonal(n,d_M2,ld,-1.0));
    272:     PetscCallCUBLAS(cublasXnrm2(cublasv2handle,N,d_M2,one,&Mres));
    273:     PetscCheck(!PetscIsNanReal(Mres),PETSC_COMM_SELF,PETSC_ERR_FP,"The computed norm is not-a-number");
    274:     if (Mres<=tol) converged = PETSC_TRUE;
    275:     PetscCall(PetscInfo(fn,"it: %" PetscInt_FMT " res: %g\n",it,(double)Mres));
    276:     PetscCall(PetscLogGpuFlops(8.0*n*n*n+2.0*n*n+2.0*n*n*n/3.0+4.0*n*n*n/3.0+2.0*n*n*n+2.0*n*n));
    277:   }

    279:   PetscCheck(Mres<=tol,PETSC_COMM_SELF,PETSC_ERR_LIB,"SQRTM not converged after %d iterations", MAXIT);

    281:   if (nrm>1.0) {
    282:     alpha = sqrtnrm;
    283:     PetscCallCUBLAS(cublasXscal(cublasv2handle,N,&alpha,d_A,one));
    284:   }
    285:   PetscCall(PetscLogGpuTimeEnd());

    287:   PetscCallCUDA(cudaFree(d_M));
    288:   PetscCallCUDA(cudaFree(d_M2));
    289:   PetscCallCUDA(cudaFree(d_G));
    290:   PetscCallCUDA(cudaFree(d_work));
    291:   PetscCall(PetscFree(piv));
    292:   PetscFunctionReturn(PETSC_SUCCESS);
    293: }
    294: #endif /* PETSC_HAVE_MAGMA */
    295: #endif /* PETSC_HAVE_CUDA */

    297: static PetscErrorCode FNEvaluateFunctionMat_Sqrt_Sadeghi(FN fn,Mat A,Mat B)
    298: {
    299:   PetscBLASInt   n=0;
    300:   PetscScalar    *Ba;
    301:   PetscInt       m;

    303:   PetscFunctionBegin;
    304:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
    305:   PetscCall(MatDenseGetArray(B,&Ba));
    306:   PetscCall(MatGetSize(A,&m,NULL));
    307:   PetscCall(PetscBLASIntCast(m,&n));
    308:   PetscCall(FNSqrtmSadeghi(fn,n,Ba,n));
    309:   PetscCall(MatDenseRestoreArray(B,&Ba));
    310:   PetscFunctionReturn(PETSC_SUCCESS);
    311: }

    313: #if defined(PETSC_HAVE_CUDA)
    314: PetscErrorCode FNEvaluateFunctionMat_Sqrt_NS_CUDA(FN fn,Mat A,Mat B)
    315: {
    316:   PetscBLASInt   n=0;
    317:   PetscScalar    *Ba;
    318:   PetscInt       m;

    320:   PetscFunctionBegin;
    321:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
    322:   PetscCall(MatDenseCUDAGetArray(B,&Ba));
    323:   PetscCall(MatGetSize(A,&m,NULL));
    324:   PetscCall(PetscBLASIntCast(m,&n));
    325:   PetscCall(FNSqrtmNewtonSchulz_CUDA(fn,n,Ba,n,PETSC_FALSE));
    326:   PetscCall(MatDenseCUDARestoreArray(B,&Ba));
    327:   PetscFunctionReturn(PETSC_SUCCESS);
    328: }

    330: #if defined(PETSC_HAVE_MAGMA)
    331: PetscErrorCode FNEvaluateFunctionMat_Sqrt_DBP_CUDAm(FN fn,Mat A,Mat B)
    332: {
    333:   PetscBLASInt   n=0;
    334:   PetscScalar    *T;
    335:   PetscInt       m;

    337:   PetscFunctionBegin;
    338:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
    339:   PetscCall(MatDenseCUDAGetArray(B,&T));
    340:   PetscCall(MatGetSize(A,&m,NULL));
    341:   PetscCall(PetscBLASIntCast(m,&n));
    342:   PetscCall(FNSqrtmDenmanBeavers_CUDAm(fn,n,T,n,PETSC_FALSE));
    343:   PetscCall(MatDenseCUDARestoreArray(B,&T));
    344:   PetscFunctionReturn(PETSC_SUCCESS);
    345: }

    347: PetscErrorCode FNEvaluateFunctionMat_Sqrt_Sadeghi_CUDAm(FN fn,Mat A,Mat B)
    348: {
    349:   PetscBLASInt   n=0;
    350:   PetscScalar    *Ba;
    351:   PetscInt       m;

    353:   PetscFunctionBegin;
    354:   if (A!=B) PetscCall(MatCopy(A,B,SAME_NONZERO_PATTERN));
    355:   PetscCall(MatDenseCUDAGetArray(B,&Ba));
    356:   PetscCall(MatGetSize(A,&m,NULL));
    357:   PetscCall(PetscBLASIntCast(m,&n));
    358:   PetscCall(FNSqrtmSadeghi_CUDAm(fn,n,Ba,n));
    359:   PetscCall(MatDenseCUDARestoreArray(B,&Ba));
    360:   PetscFunctionReturn(PETSC_SUCCESS);
    361: }
    362: #endif /* PETSC_HAVE_MAGMA */
    363: #endif /* PETSC_HAVE_CUDA */

    365: static PetscErrorCode FNView_Sqrt(FN fn,PetscViewer viewer)
    366: {
    367:   PetscBool      isascii;
    368:   char           str[50];
    369:   const char     *methodname[] = {
    370:                   "Schur method for the square root",
    371:                   "Denman-Beavers (product form)",
    372:                   "Newton-Schulz iteration",
    373:                   "Sadeghi iteration"
    374:   };
    375:   const int      nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);

    377:   PetscFunctionBegin;
    378:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    379:   if (isascii) {
    380:     if (fn->beta==(PetscScalar)1.0) {
    381:       if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscViewerASCIIPrintf(viewer,"  square root: sqrt(x)\n"));
    382:       else {
    383:         PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE));
    384:         PetscCall(PetscViewerASCIIPrintf(viewer,"  square root: sqrt(%s*x)\n",str));
    385:       }
    386:     } else {
    387:       PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->beta,PETSC_TRUE));
    388:       if (fn->alpha==(PetscScalar)1.0) PetscCall(PetscViewerASCIIPrintf(viewer,"  square root: %s*sqrt(x)\n",str));
    389:       else {
    390:         PetscCall(PetscViewerASCIIPrintf(viewer,"  square root: %s",str));
    391:         PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    392:         PetscCall(SlepcSNPrintfScalar(str,sizeof(str),fn->alpha,PETSC_TRUE));
    393:         PetscCall(PetscViewerASCIIPrintf(viewer,"*sqrt(%s*x)\n",str));
    394:         PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
    395:       }
    396:     }
    397:     if (fn->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"  computing matrix functions with: %s\n",methodname[fn->method]));
    398:   }
    399:   PetscFunctionReturn(PETSC_SUCCESS);
    400: }

    402: /*MC
    403:    FNSQRT - FNSQRT = "sqrt" - The square root function $f(x)=\sqrt{x}$.

    405:    Level: beginner

    407: .seealso: [](sec:fn), `FN`, `FNType`, `FNSetType()`
    408: M*/

    410: SLEPC_EXTERN PetscErrorCode FNCreate_Sqrt(FN fn)
    411: {
    412:   PetscFunctionBegin;
    413:   fn->ops->evaluatefunction          = FNEvaluateFunction_Sqrt;
    414:   fn->ops->evaluatederivative        = FNEvaluateDerivative_Sqrt;
    415:   fn->ops->evaluatefunctionmat[0]    = FNEvaluateFunctionMat_Sqrt_Schur;
    416:   fn->ops->evaluatefunctionmat[1]    = FNEvaluateFunctionMat_Sqrt_DBP;
    417:   fn->ops->evaluatefunctionmat[2]    = FNEvaluateFunctionMat_Sqrt_NS;
    418:   fn->ops->evaluatefunctionmat[3]    = FNEvaluateFunctionMat_Sqrt_Sadeghi;
    419: #if defined(PETSC_HAVE_CUDA)
    420:   fn->ops->evaluatefunctionmatcuda[2] = FNEvaluateFunctionMat_Sqrt_NS_CUDA;
    421: #if defined(PETSC_HAVE_MAGMA)
    422:   fn->ops->evaluatefunctionmatcuda[1] = FNEvaluateFunctionMat_Sqrt_DBP_CUDAm;
    423:   fn->ops->evaluatefunctionmatcuda[3] = FNEvaluateFunctionMat_Sqrt_Sadeghi_CUDAm;
    424: #endif /* PETSC_HAVE_MAGMA */
    425: #endif /* PETSC_HAVE_CUDA */
    426:   fn->ops->evaluatefunctionmatvec[0] = FNEvaluateFunctionMatVec_Sqrt_Schur;
    427:   fn->ops->view                      = FNView_Sqrt;
    428:   PetscFunctionReturn(PETSC_SUCCESS);
    429: }