Date: 2022-03-31T15:29:04+00:00

Actual source code: rginterval.c
slepc-3.17.0 2022-03-31
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      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:    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;

     32: #if !defined(PETSC_USE_COMPLEX)
     34: #endif
     35:   ctx->a = a;
     36:   ctx->b = b;
     37:   ctx->c = c;
     38:   ctx->d = d;
     39:   PetscFunctionReturn(0);
     40: }

     42: /*@
     43:    RGIntervalSetEndpoints - Sets the parameters defining the interval region.

     45:    Logically Collective on rg

     47:    Input Parameters:
     48: +  rg  - the region context
     49: .  a - left endpoint of the interval in the real axis
     50: .  b - right endpoint of the interval in the real axis
     51: .  c - bottom endpoint of the interval in the imaginary axis
     52: -  d - top endpoint of the interval in the imaginary axis

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

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

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

     65:    Level: advanced

     67: .seealso: RGIntervalGetEndpoints()
     68: @*/
     69: PetscErrorCode RGIntervalSetEndpoints(RG rg,PetscReal a,PetscReal b,PetscReal c,PetscReal d)
     70: {
     76:   PetscTryMethod(rg,"RGIntervalSetEndpoints_C",(RG,PetscReal,PetscReal,PetscReal,PetscReal),(rg,a,b,c,d));
     77:   PetscFunctionReturn(0);
     78: }

     80: static PetscErrorCode RGIntervalGetEndpoints_Interval(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
     81: {
     82:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

     84:   if (a) *a = ctx->a;
     85:   if (b) *b = ctx->b;
     86:   if (c) *c = ctx->c;
     87:   if (d) *d = ctx->d;
     88:   PetscFunctionReturn(0);
     89: }

     91: /*@C
     92:    RGIntervalGetEndpoints - Gets the parameters that define the interval region.

     94:    Not Collective

     96:    Input Parameter:
     97: .  rg - the region context

     99:    Output Parameters:
    100: +  a - left endpoint of the interval in the real axis
    101: .  b - right endpoint of the interval in the real axis
    102: .  c - bottom endpoint of the interval in the imaginary axis
    103: -  d - top endpoint of the interval in the imaginary axis

    105:    Level: advanced

    107: .seealso: RGIntervalSetEndpoints()
    108: @*/
    109: PetscErrorCode RGIntervalGetEndpoints(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
    110: {
    112:   PetscUseMethod(rg,"RGIntervalGetEndpoints_C",(RG,PetscReal*,PetscReal*,PetscReal*,PetscReal*),(rg,a,b,c,d));
    113:   PetscFunctionReturn(0);
    114: }

    116: PetscErrorCode RGView_Interval(RG rg,PetscViewer viewer)
    117: {
    118:   RG_INTERVAL    *ctx = (RG_INTERVAL*)rg->data;
    119:   PetscBool      isdraw,isascii;
    120:   int            winw,winh;
    121:   PetscDraw      draw;
    122:   PetscDrawAxis  axis;
    123:   PetscReal      a,b,c,d,ab,cd,lx,ly,w,scale=1.2;

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

    156: PetscErrorCode RGIsTrivial_Interval(RG rg,PetscBool *trivial)
    157: {
    158:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    160:   if (rg->complement) *trivial = (ctx->a==ctx->b && ctx->c==ctx->d)? PETSC_TRUE: PETSC_FALSE;
    161:   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;
    162:   PetscFunctionReturn(0);
    163: }

    165: PetscErrorCode RGComputeContour_Interval(RG rg,PetscInt n,PetscScalar *cr,PetscScalar *ci)
    166: {
    167:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;
    168:   PetscInt    i,N,Nv,Nh,k1,k0;
    169:   PetscReal   hv,hh,t;

    172:   if (ctx->a==ctx->b || ctx->c==ctx->d) {
    173:     if (ctx->a==ctx->b) {hv = (ctx->d-ctx->c)/(n-1); hh = 0.0;}
    174:     else {hh = (ctx->b-ctx->a)/(n-1); hv = 0.0;}
    175:     for (i=0;i<n;i++) {
    176: #if defined(PETSC_USE_COMPLEX)
    177:       cr[i] = PetscCMPLX(ctx->a+hh*i,ctx->c+hv*i);
    178: #else
    179:       if (cr) cr[i] = ctx->a+hh*i;
    180:       if (ci) ci[i] = ctx->c+hv*i;
    181: #endif
    182:     }
    183:   } else {
    185:     N = n/2;
    186:     t = ((ctx->d-ctx->c)/(ctx->d-ctx->c+ctx->b-ctx->a))*N;
    187:     Nv = t-PetscFloorReal(t)>0.5?PetscCeilReal(t):PetscFloorReal(t);
    188:     if (Nv==0) Nv++;
    189:     else if (Nv==N) Nv--;
    190:     Nh = N-Nv;
    191:     hh = (ctx->b-ctx->a)/Nh;
    192:     hv = (ctx->d-ctx->c)/Nv;
    193:     /* positive imaginary part first */
    194:     k1 = Nv/2+1;
    195:     k0 = Nv-k1;

    197:     for (i=k1;i<Nv;i++) {
    198: #if defined(PETSC_USE_COMPLEX)
    199:       cr[i-k1]   = PetscCMPLX(ctx->b,ctx->c+i*hv);
    200:       cr[i-k1+N] = PetscCMPLX(ctx->a,ctx->d-i*hv);
    201: #else
    202:       if (cr) {cr[i-k1] = ctx->b;      cr[i-k1+N] = ctx->a;}
    203:       if (ci) {ci[i-k1] = ctx->c+i*hv; ci[i-k1+N] = ctx->d-i*hv;}
    204: #endif
    205:     }
    206:     for (i=0;i<Nh;i++) {
    207: #if defined(PETSC_USE_COMPLEX)
    208:       cr[i+k0]   = PetscCMPLX(ctx->b-i*hh,ctx->d);
    209:       cr[i+k0+N] = PetscCMPLX(ctx->a+i*hh,ctx->c);
    210: #else
    211:       if (cr) {cr[i+k0] = ctx->b-i*hh; cr[i+k0+N] = ctx->a+i*hh;}
    212:       if (ci) {ci[i+k0] = ctx->d;      ci[i+k0+N] = ctx->c;}
    213: #endif
    214:     }
    215:     for (i=0;i<k1;i++) {
    216: #if defined(PETSC_USE_COMPLEX)
    217:       cr[i+k0+Nh]   = PetscCMPLX(ctx->a,ctx->d-i*hv);
    218:       cr[i+k0+Nh+N] = PetscCMPLX(ctx->b,ctx->c+i*hv);
    219: #else
    220:       if (cr) {cr[i+k0+Nh] = ctx->a; cr[i+k0+Nh+N] = ctx->b;}
    221:       if (ci) {ci[i+k0+Nh] = ctx->d+i*hv; ci[i+k0+Nh+N] = ctx->c-i*hv;}
    222: #endif
    223:     }
    224:   }
    225:   PetscFunctionReturn(0);
    226: }

    228: PetscErrorCode RGComputeBoundingBox_Interval(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
    229: {
    230:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    232:   if (a) *a = ctx->a;
    233:   if (b) *b = ctx->b;
    234:   if (c) *c = ctx->c;
    235:   if (d) *d = ctx->d;
    236:   PetscFunctionReturn(0);
    237: }

    239: PetscErrorCode RGComputeQuadrature_Interval(RG rg,RGQuadRule quad,PetscInt n,PetscScalar *z,PetscScalar *zn,PetscScalar *w)
    240: {
    241:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;
    242:   PetscReal   theta,max_w=0.0,radius=1.0;
    243:   PetscScalar tmp,tmp2,center=0.0;
    244:   PetscInt    i,j;

    246:   if (quad == RG_QUADRULE_CHEBYSHEV) {
    248:     for (i=0;i<n;i++) {
    249:       theta = PETSC_PI*(i+0.5)/n;
    250:       zn[i] = PetscCosReal(theta);
    251:       w[i]  = PetscCosReal((n-1)*theta)/n;
    252:       if (ctx->c==ctx->d) z[i] = ((ctx->b-ctx->a)*(zn[i]+1.0)/2.0+ctx->a)*rg->sfactor;
    253:       else if (ctx->a==ctx->b) {
    254: #if defined(PETSC_USE_COMPLEX)
    255:         z[i] = ((ctx->d-ctx->c)*(zn[i]+1.0)/2.0+ctx->c)*rg->sfactor*PETSC_i;
    256: #else
    257:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Integration points on a vertical line require complex arithmetic");
    258: #endif
    259:       }
    260:     }
    261:   } else {  /* RG_QUADRULE_TRAPEZOIDAL */
    262: #if defined(PETSC_USE_COMPLEX)
    263:     center = rg->sfactor*PetscCMPLX(ctx->b+ctx->a,ctx->d+ctx->c)/2.0;
    264: #else
    265:     center = rg->sfactor*(ctx->b+ctx->a)/2.0;
    266: #endif
    267:     radius = PetscSqrtReal(PetscPowRealInt(rg->sfactor*(ctx->b-ctx->a)/2.0,2)+PetscPowRealInt(rg->sfactor*(ctx->d-ctx->c)/2.0,2));
    268:     for (i=0;i<n;i++) {
    269:       zn[i] = (z[i]-center)/radius;
    270:       tmp = 1.0; tmp2 = 1.0;
    271:       for (j=0;j<n;j++) {
    272:         tmp *= z[j];
    273:         if (i != j) tmp2 *= z[j]-z[i];
    274:       }
    275:       w[i] = tmp/tmp2;
    276:       max_w = PetscMax(PetscAbsScalar(w[i]),max_w);
    277:     }
    278:     for (i=0;i<n;i++) w[i] /= (PetscScalar)max_w;
    279:   }
    280:   PetscFunctionReturn(0);
    281: }

    283: PetscErrorCode RGCheckInside_Interval(RG rg,PetscReal dx,PetscReal dy,PetscInt *inside)
    284: {
    285:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    287:   if (dx>ctx->a && dx<ctx->b) *inside = 1;
    288:   else if (dx==ctx->a || dx==ctx->b) *inside = 0;
    289:   else *inside = -1;
    290:   if (*inside>=0) {
    291:     if (dy>ctx->c && dy<ctx->d) ;
    292:     else if (dy==ctx->c || dy==ctx->d) *inside = 0;
    293:     else *inside = -1;
    294:   }
    295:   PetscFunctionReturn(0);
    296: }

    298: PetscErrorCode RGIsAxisymmetric_Interval(RG rg,PetscBool vertical,PetscBool *symm)
    299: {
    300:   RG_INTERVAL *ctx = (RG_INTERVAL*)rg->data;

    302:   if (vertical) *symm = (ctx->a == -ctx->b)? PETSC_TRUE: PETSC_FALSE;
    303:   else *symm = (ctx->c == -ctx->d)? PETSC_TRUE: PETSC_FALSE;
    304:   PetscFunctionReturn(0);
    305: }

    307: PetscErrorCode RGSetFromOptions_Interval(PetscOptionItems *PetscOptionsObject,RG rg)
    308: {
    309:   PetscBool      flg;
    310:   PetscInt       k;
    311:   PetscReal      array[4]={0,0,0,0};

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

    315:     k = 4;
    316:     PetscOptionsRealArray("-rg_interval_endpoints","Interval endpoints (two or four real values separated with a comma without spaces)","RGIntervalSetEndpoints",array,&k,&flg);
    317:     if (flg) {
    319:       RGIntervalSetEndpoints(rg,array[0],array[1],array[2],array[3]);
    320:     }

    322:   PetscOptionsTail();
    323:   PetscFunctionReturn(0);
    324: }

    326: PetscErrorCode RGDestroy_Interval(RG rg)
    327: {
    328:   PetscFree(rg->data);
    329:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalSetEndpoints_C",NULL);
    330:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalGetEndpoints_C",NULL);
    331:   PetscFunctionReturn(0);
    332: }

    334: SLEPC_EXTERN PetscErrorCode RGCreate_Interval(RG rg)
    335: {
    336:   RG_INTERVAL    *interval;

    338:   PetscNewLog(rg,&interval);
    339:   interval->a = -PETSC_MAX_REAL;
    340:   interval->b = PETSC_MAX_REAL;
    341:   interval->c = -PETSC_MAX_REAL;
    342:   interval->d = PETSC_MAX_REAL;
    343:   rg->data = (void*)interval;

    345:   rg->ops->istrivial         = RGIsTrivial_Interval;
    346:   rg->ops->computecontour    = RGComputeContour_Interval;
    347:   rg->ops->computebbox       = RGComputeBoundingBox_Interval;
    348:   rg->ops->computequadrature = RGComputeQuadrature_Interval;
    349:   rg->ops->checkinside       = RGCheckInside_Interval;
    350:   rg->ops->isaxisymmetric    = RGIsAxisymmetric_Interval;
    351:   rg->ops->setfromoptions    = RGSetFromOptions_Interval;
    352:   rg->ops->view              = RGView_Interval;
    353:   rg->ops->destroy           = RGDestroy_Interval;
    354:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalSetEndpoints_C",RGIntervalSetEndpoints_Interval);
    355:   PetscObjectComposeFunction((PetscObject)rg,"RGIntervalGetEndpoints_C",RGIntervalGetEndpoints_Interval);
    356:   PetscFunctionReturn(0);
    357: }