Date: 2021-02-01T14:41:53+00:00

Actual source code: rginterval.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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:    Interval of the real axis or more generally a (possibly open) rectangle
     12:    of the complex plane
     13: */

     15: #include <slepc/private/rgimpl.h>
     16: #include <petscdraw.h>

     18: typedef struct {
     19:   PetscReal   a,b;     /* interval in the real axis */
     20:   PetscReal   c,d;     /* interval in the imaginary axis */
     21: } RG_INTERVAL;

     23: static PetscErrorCode RGIntervalSetEndpoints_Interval(RG rg,PetscReal a,PetscReal b,PetscReal c,PetscReal d)
     24: {
     25:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

     28:   if (!a && !b && !c && !d) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"At least one argument must be nonzero");
     29:   if (a==b && a) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"Badly defined interval, endpoints must be distinct (or both zero)");
     30:   if (a>b) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"Badly defined interval, must be a<b");
     31:   if (c==d && c) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"Badly defined interval, endpoints must be distinct (or both zero)");
     32:   if (c>d) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"Badly defined interval, must be c<d");
     33: #if !defined(PETSC_USE_COMPLEX)
     34:   if (c!=-d) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"In real scalars the region must be symmetric wrt real axis");
     35: #endif
     36:   ctx->a = a;
     37:   ctx->b = b;
     38:   ctx->c = c;
     39:   ctx->d = d;
     40:   return(0);
     41: }

     43: /*@
     44:    RGIntervalSetEndpoints - Sets the parameters defining the interval region.

     46:    Logically Collective on rg

     48:    Input Parameters:
     49: +  rg  - the region context
     50: .  a,b - endpoints of the interval in the real axis
     51: -  c,d - endpoints of the interval in the imaginary axis

     53:    Options Database Keys:
     54: .  -rg_interval_endpoints - the four endpoints

     56:    Note:
     57:    The region is defined as [a,b]x[c,d]. Particular cases are an interval on
     58:    the real axis (c=d=0), similar for the imaginary axis (a=b=0), the whole
     59:    complex plane (a=-inf,b=inf,c=-inf,d=inf), and so on.

     61:    When PETSc is built with real scalars, the region must be symmetric with
     62:    respect to the real axis.

     64:    Level: advanced

     66: .seealso: RGIntervalGetEndpoints()
     67: @*/
     68: PetscErrorCode RGIntervalSetEndpoints(RG rg,PetscReal a,PetscReal b,PetscReal c,PetscReal d)
     69: {

     78:   PetscTryMethod(rg,"RGIntervalSetEndpoints_C",(RG,PetscReal,PetscReal,PetscReal,PetscReal),(rg,a,b,c,d));
     79:   return(0);
     80: }

     82: static PetscErrorCode RGIntervalGetEndpoints_Interval(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
     83: {
     84:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

     87:   if (a) *a = ctx->a;
     88:   if (b) *b = ctx->b;
     89:   if (c) *c = ctx->c;
     90:   if (d) *d = ctx->d;
     91:   return(0);
     92: }

     94: /*@C
     95:    RGIntervalGetEndpoints - Gets the parameters that define the interval region.

     97:    Not Collective

     99:    Input Parameter:
    100: .  rg - the region context

    102:    Output Parameters:
    103: +  a,b - endpoints of the interval in the real axis
    104: -  c,d - endpoints of the interval in the imaginary axis

    106:    Level: advanced

    108: .seealso: RGIntervalSetEndpoints()
    109: @*/
    110: PetscErrorCode RGIntervalGetEndpoints(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
    111: {

    116:   PetscUseMethod(rg,"RGIntervalGetEndpoints_C",(RG,PetscReal*,PetscReal*,PetscReal*,PetscReal*),(rg,a,b,c,d));
    117:   return(0);
    118: }

    120: PetscErrorCode RGView_Interval(RG rg,PetscViewer viewer)
    121: {
    123:   RG_INTERVAL    *ctx = (RG_INTERVAL*)rg->data;
    124:   PetscBool      isdraw,isascii;
    125:   int            winw,winh;
    126:   PetscDraw      draw;
    127:   PetscDrawAxis  axis;
    128:   PetscReal      a,b,c,d,ab,cd,lx,ly,w,scale=1.2;

    131:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);
    132:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    133:   if (isascii) {
    134:     PetscViewerASCIIPrintf(viewer,"  region: [%g,%g]x[%g,%g]\n",RGShowReal(ctx->a),RGShowReal(ctx->b),RGShowReal(ctx->c),RGShowReal(ctx->d));
    135:   } else if (isdraw) {
    136:     PetscViewerDrawGetDraw(viewer,0,&draw);
    137:     PetscDrawCheckResizedWindow(draw);
    138:     PetscDrawGetWindowSize(draw,&winw,&winh);
    139:     winw = PetscMax(winw,1); winh = PetscMax(winh,1);
    140:     PetscDrawClear(draw);
    141:     PetscDrawSetTitle(draw,"Interval region");
    142:     PetscDrawAxisCreate(draw,&axis);
    143:     a  = ctx->a*rg->sfactor;
    144:     b  = ctx->b*rg->sfactor;
    145:     c  = ctx->c*rg->sfactor;
    146:     d  = ctx->d*rg->sfactor;
    147:     lx = b-a;
    148:     ly = d-c;
    149:     ab = (a+b)/2;
    150:     cd = (c+d)/2;
    151:     w  = scale*PetscMax(lx/winw,ly/winh)/2;
    152:     PetscDrawAxisSetLimits(axis,ab-w*winw,ab+w*winw,cd-w*winh,cd+w*winh);
    153:     PetscDrawAxisDraw(axis);
    154:     PetscDrawAxisDestroy(&axis);
    155:     PetscDrawRectangle(draw,a,c,b,d,PETSC_DRAW_BLUE,PETSC_DRAW_BLUE,PETSC_DRAW_BLUE,PETSC_DRAW_BLUE);
    156:     PetscDrawFlush(draw);
    157:     PetscDrawSave(draw);
    158:     PetscDrawPause(draw);
    159:   }
    160:   return(0);
    161: }

    163: PetscErrorCode RGIsTrivial_Interval(RG rg,PetscBool *trivial)
    164: {
    165:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    168:   if (rg->complement) *trivial = (ctx->a==ctx->b && ctx->c==ctx->d)? PETSC_TRUE: PETSC_FALSE;
    169:   else *trivial = (ctx->a<=-PETSC_MAX_REAL && ctx->b>=PETSC_MAX_REAL && ctx->c<=-PETSC_MAX_REAL && ctx->d>=PETSC_MAX_REAL)? PETSC_TRUE: PETSC_FALSE;
    170:   return(0);
    171: }

    173: PetscErrorCode RGComputeContour_Interval(RG rg,PetscInt n,PetscScalar *cr,PetscScalar *ci)
    174: {
    175:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;
    176:   PetscInt    i,pt,idx,j;
    177:   PetscReal   hr[4],hi[4],h,off,d[4],vr[4],vi[4];

    180:   if (!(ctx->a>-PETSC_MAX_REAL && ctx->b<PETSC_MAX_REAL && ctx->c>-PETSC_MAX_REAL && ctx->d<PETSC_MAX_REAL)) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_SUP,"Contour not defined in unbounded regions");
    181:   if (ctx->a==ctx->b || ctx->c==ctx->d) {
    182:     if (ctx->a==ctx->b) {hi[0] = (ctx->d-ctx->c)/(n-1); hr[0] = 0.0;}
    183:     else {hr[0] = (ctx->b-ctx->a)/(n-1); hi[0] = 0.0;}
    184:     for (i=0;i<n;i++) {
    185: #if defined(PETSC_USE_COMPLEX)
    186:       cr[i] = PetscCMPLX(ctx->a+hr[0]*i,ctx->c+hi[0]*i);
    187: #else
    188:       cr[i] = ctx->a+hr[0]*i; ci[i] = ctx->c+hi[0]*i;
    189: #endif
    190:     }
    191:   } else {
    192:     d[1] = d[3] = ctx->d-ctx->c; d[0] = d[2] = ctx->b-ctx->a;
    193:     h = 2.0*(d[0]+d[1])/n;
    194:     vr[0] = ctx->a; vr[1] = ctx->b; vr[2] = ctx->b; vr[3] = ctx->a;
    195:     vi[0] = ctx->c; vi[1] = ctx->c; vi[2] = ctx->d; vi[3] = ctx->d;
    196:     hr[0] = h;   hr[1] = 0.0; hr[2] = -h;  hr[3] = 0.0;
    197:     hi[0] = 0.0; hi[1] = h;   hi[2] = 0.0; hi[3] = -h;
    198:     off = 0.0; idx = 0;
    199:     for (i=0;i<4;i++) {
    200: #if defined(PETSC_USE_COMPLEX)
    201:       cr[idx] = PetscCMPLX(vr[i]+off*(hr[i]/h),vi[i]+off*(hi[i]/h));
    202: #else
    203:       cr[idx] = vr[i]+off*(hr[i]/h); ci[idx] = vi[i]+off*(hi[i]/h);
    204: #endif
    205:       idx++;
    206:       pt = (PetscInt)((d[i]-off)/h)+1;
    207:       for (j=1;j<pt && idx<n;j++) {
    208: #if defined(PETSC_USE_COMPLEX)
    209:         cr[idx] = cr[idx-1]+PetscCMPLX(hr[i],hi[i]);
    210: #else
    211:         cr[idx] = cr[idx-1]+hr[i]; ci[idx] = ci[idx-1]+hi[i];
    212: #endif
    213:         idx++;
    214:       }
    215:       off += pt*h-d[i];
    216:       if (off>=d[i+1]) {off -= d[i+1]; i++;}
    217:     }
    218:   }
    219:   return(0);
    220: }

    222: PetscErrorCode RGComputeBoundingBox_Interval(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
    223: {
    224:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    227:   if (a) *a = ctx->a;
    228:   if (b) *b = ctx->b;
    229:   if (c) *c = ctx->c;
    230:   if (d) *d = ctx->d;
    231:   return(0);
    232: }

    234: PetscErrorCode RGCheckInside_Interval(RG rg,PetscReal dx,PetscReal dy,PetscInt *inside)
    235: {
    236:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    239:   if (dx>ctx->a && dx<ctx->b) *inside = 1;
    240:   else if (dx==ctx->a || dx==ctx->b) *inside = 0;
    241:   else *inside = -1;
    242:   if (*inside>=0) {
    243:     if (dy>ctx->c && dy<ctx->d) ;
    244:     else if (dy==ctx->c || dy==ctx->d) *inside = 0;
    245:     else *inside = -1;
    246:   }
    247:   return(0);
    248: }

    250: PetscErrorCode RGSetFromOptions_Interval(PetscOptionItems *PetscOptionsObject,RG rg)
    251: {
    253:   PetscBool      flg;
    254:   PetscInt       k;
    255:   PetscReal      array[4]={0,0,0,0};

    258:   PetscOptionsHead(PetscOptionsObject,"RG Interval Options");

    260:     k = 4;
    261:     PetscOptionsRealArray("-rg_interval_endpoints","Interval endpoints (two or four real values separated with a comma without spaces)","RGIntervalSetEndpoints",array,&k,&flg);
    262:     if (flg) {
    263:       if (k<2) SETERRQ(PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_SIZ,"Must pass at least two values in -rg_interval_endpoints (comma-separated without spaces)");
    264:       RGIntervalSetEndpoints(rg,array[0],array[1],array[2],array[3]);
    265:     }

    267:   PetscOptionsTail();
    268:   return(0);
    269: }

    271: PetscErrorCode RGDestroy_Interval(RG rg)
    272: {

    276:   PetscFree(rg->data);
    277:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalSetEndpoints_C",NULL);
    278:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalGetEndpoints_C",NULL);
    279:   return(0);
    280: }

    282: SLEPC_EXTERN PetscErrorCode RGCreate_Interval(RG rg)
    283: {
    284:   RG_INTERVAL    *interval;

    288:   PetscNewLog(rg,&interval);
    289:   interval->a = -PETSC_MAX_REAL;
    290:   interval->b = PETSC_MAX_REAL;
    291:   interval->c = -PETSC_MAX_REAL;
    292:   interval->d = PETSC_MAX_REAL;
    293:   rg->data = (void*)interval;

    295:   rg->ops->istrivial      = RGIsTrivial_Interval;
    296:   rg->ops->computecontour = RGComputeContour_Interval;
    297:   rg->ops->computebbox    = RGComputeBoundingBox_Interval;
    298:   rg->ops->checkinside    = RGCheckInside_Interval;
    299:   rg->ops->setfromoptions = RGSetFromOptions_Interval;
    300:   rg->ops->view           = RGView_Interval;
    301:   rg->ops->destroy        = RGDestroy_Interval;
    302:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalSetEndpoints_C",RGIntervalSetEndpoints_Interval);
    303:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalGetEndpoints_C",RGIntervalGetEndpoints_Interval);
    304:   return(0);
    305: }