Date: 2015-09-03T15:03:49+00:00

Actual source code: fnexp.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    Exponential function  exp(x)

      4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      6:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      8:    This file is part of SLEPc.

     10:    SLEPc is free software: you can redistribute it and/or modify it under  the
     11:    terms of version 3 of the GNU Lesser General Public License as published by
     12:    the Free Software Foundation.

     14:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     15:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     16:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     17:    more details.

     19:    You  should have received a copy of the GNU Lesser General  Public  License
     20:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     21:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     22: */

     24: #include <slepc/private/fnimpl.h>      /*I "slepcfn.h" I*/
     25: #include <slepcblaslapack.h>

     29: PetscErrorCode FNEvaluateFunction_Exp(FN fn,PetscScalar x,PetscScalar *y)
     30: {
     32:   *y = PetscExpScalar(x);
     33:   return(0);
     34: }

     38: PetscErrorCode FNEvaluateDerivative_Exp(FN fn,PetscScalar x,PetscScalar *y)
     39: {
     41:   *y = PetscExpScalar(x);
     42:   return(0);
     43: }

     45: #define MAX_PADE 6
     46: #define SWAP(a,b,t) {t=a;a=b;b=t;}

     50: PetscErrorCode FNEvaluateFunctionMat_Exp(FN fn,Mat A,Mat B)
     51: {
     52: #if defined(PETSC_MISSING_LAPACK_GESV) || defined(SLEPC_MISSING_LAPACK_LANGE)
     54:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESV/LANGE - Lapack routines are unavailable");
     55: #else
     57:   PetscBLASInt   n,ld,ld2,*ipiv,info,inc=1;
     58:   PetscInt       m,j,k,sexp;
     59:   PetscBool      odd;
     60:   const PetscInt p=MAX_PADE;
     61:   PetscReal      c[MAX_PADE+1],s,*rwork;
     62:   PetscScalar    scale,mone=-1.0,one=1.0,two=2.0,zero=0.0;
     63:   PetscScalar    *Aa,*Ba,*As,*A2,*Q,*P,*W,*aux;

     66:   MatDenseGetArray(A,&Aa);
     67:   MatDenseGetArray(B,&Ba);
     68:   MatGetSize(A,&m,NULL);
     69:   PetscBLASIntCast(m,&n);
     70:   ld  = n;
     71:   ld2 = ld*ld;
     72:   P   = Ba;
     73:   PetscMalloc6(m*m,&Q,m*m,&W,m*m,&As,m*m,&A2,ld,&rwork,ld,&ipiv);
     74:   PetscMemcpy(As,Aa,ld2*sizeof(PetscScalar));

     76:   /* Pade' coefficients */
     77:   c[0] = 1.0;
     78:   for (k=1;k<=p;k++) c[k] = c[k-1]*(p+1-k)/(k*(2*p+1-k));

     80:   /* Scaling */
     81:   s = LAPACKlange_("I",&n,&n,As,&ld,rwork);
     82:   if (s>0.5) {
     83:     sexp = PetscMax(0,(int)(PetscLogReal(s)/PetscLogReal(2.0))+2);
     84:     scale = PetscPowRealInt(2.0,-sexp);
     85:     PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&scale,As,&inc));
     86:   } else sexp = 0;

     88:   /* Horner evaluation */
     89:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,As,&ld,As,&ld,&zero,A2,&ld));
     90:   PetscMemzero(Q,ld2*sizeof(PetscScalar));
     91:   PetscMemzero(P,ld2*sizeof(PetscScalar));
     92:   for (j=0;j<n;j++) {
     93:     Q[j+j*ld] = c[p];
     94:     P[j+j*ld] = c[p-1];
     95:   }

     97:   odd = PETSC_TRUE;
     98:   for (k=p-1;k>0;k--) {
     99:     if (odd) {
    100:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,A2,&ld,&zero,W,&ld));
    101:       SWAP(Q,W,aux);
    102:       for (j=0;j<n;j++) Q[j+j*ld] += c[k-1];
    103:       odd = PETSC_FALSE;
    104:     } else {
    105:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,A2,&ld,&zero,W,&ld));
    106:       SWAP(P,W,aux);
    107:       for (j=0;j<n;j++) P[j+j*ld] += c[k-1];
    108:       odd = PETSC_TRUE;
    109:     }
    110:   }
    111:   if (odd) {
    112:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,As,&ld,&zero,W,&ld));
    113:     SWAP(Q,W,aux);
    114:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&ld2,&mone,P,&inc,Q,&inc));
    115:     PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info));
    116:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESV %d",info);
    117:     PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&two,P,&inc));
    118:     for (j=0;j<n;j++) P[j+j*ld] += 1.0;
    119:     PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&mone,P,&inc));
    120:   } else {
    121:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,As,&ld,&zero,W,&ld));
    122:     SWAP(P,W,aux);
    123:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&ld2,&mone,P,&inc,Q,&inc));
    124:     PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info));
    125:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESV %d",info);
    126:     PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&two,P,&inc));
    127:     for (j=0;j<n;j++) P[j+j*ld] += 1.0;
    128:   }

    130:   for (k=1;k<=sexp;k++) {
    131:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,P,&ld,&zero,W,&ld));
    132:     PetscMemcpy(P,W,ld2*sizeof(PetscScalar));
    133:   }
    134:   if (P!=Ba) { PetscMemcpy(Ba,P,ld2*sizeof(PetscScalar)); }

    136:   PetscFree6(Q,W,As,A2,rwork,ipiv);
    137:   MatDenseRestoreArray(A,&Aa);
    138:   MatDenseRestoreArray(B,&Ba);
    139:   return(0);
    140: #endif
    141: }

    145: PetscErrorCode FNView_Exp(FN fn,PetscViewer viewer)
    146: {
    148:   PetscBool      isascii;
    149:   char           str[50];

    152:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    153:   if (isascii) {
    154:     if (fn->beta==(PetscScalar)1.0) {
    155:       if (fn->alpha==(PetscScalar)1.0) {
    156:         PetscViewerASCIIPrintf(viewer,"  Exponential: exp(x)\n");
    157:       } else {
    158:         SlepcSNPrintfScalar(str,50,fn->alpha,PETSC_TRUE);
    159:         PetscViewerASCIIPrintf(viewer,"  Exponential: exp(%s*x)\n",str);
    160:       }
    161:     } else {
    162:       SlepcSNPrintfScalar(str,50,fn->beta,PETSC_TRUE);
    163:       if (fn->alpha==(PetscScalar)1.0) {
    164:         PetscViewerASCIIPrintf(viewer,"  Exponential: %s*exp(x)\n",str);
    165:       } else {
    166:         PetscViewerASCIIPrintf(viewer,"  Exponential: %s",str);
    167:         SlepcSNPrintfScalar(str,50,fn->alpha,PETSC_TRUE);
    168:         PetscViewerASCIIPrintf(viewer,"*exp(%s*x)\n",str);
    169:       }
    170:     }
    171:   }
    172:   return(0);
    173: }

    177: PETSC_EXTERN PetscErrorCode FNCreate_Exp(FN fn)
    178: {
    180:   fn->ops->evaluatefunction    = FNEvaluateFunction_Exp;
    181:   fn->ops->evaluatederivative  = FNEvaluateDerivative_Exp;
    182:   fn->ops->evaluatefunctionmat = FNEvaluateFunctionMat_Exp;
    183:   fn->ops->view                = FNView_Exp;
    184:   return(0);
    185: }