Actual source code: vecutil.c

slepc-3.18.0 2022-10-01
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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: */

 11: #include <slepc/private/vecimplslepc.h>

 13: /*@
 14:    VecNormalizeComplex - Normalizes a possibly complex vector by the 2-norm.

 16:    Collective on xr

 18:    Input Parameters:
 19: +  xr - the real part of the vector (overwritten on output)
 20: .  xi - the imaginary part of the vector (not referenced if iscomplex is false)
 21: -  iscomplex - a flag indicating if the vector is complex

 23:    Output Parameter:
 24: .  norm - the vector norm before normalization (can be set to NULL)

 26:    Level: developer

 28: .seealso: BVNormalize()
 29: @*/
 30: PetscErrorCode VecNormalizeComplex(Vec xr,Vec xi,PetscBool iscomplex,PetscReal *norm)
 31: {
 32: #if !defined(PETSC_USE_COMPLEX)
 33:   PetscReal      normr,normi,alpha;
 34: #endif

 37: #if !defined(PETSC_USE_COMPLEX)
 38:   if (iscomplex) {
 40:     VecNormBegin(xr,NORM_2,&normr);
 41:     VecNormBegin(xi,NORM_2,&normi);
 42:     VecNormEnd(xr,NORM_2,&normr);
 43:     VecNormEnd(xi,NORM_2,&normi);
 44:     alpha = SlepcAbsEigenvalue(normr,normi);
 45:     if (norm) *norm = alpha;
 46:     alpha = 1.0 / alpha;
 47:     VecScale(xr,alpha);
 48:     VecScale(xi,alpha);
 49:   } else
 50: #endif
 51:     VecNormalize(xr,norm);
 52:   return 0;
 53: }

 55: static PetscErrorCode VecCheckOrthogonality_Private(Vec V[],PetscInt nv,Vec W[],PetscInt nw,Mat B,PetscViewer viewer,PetscReal *lev,PetscBool norm)
 56: {
 57:   PetscInt       i,j;
 58:   PetscScalar    *vals;
 59:   PetscBool      isascii;
 60:   Vec            w;

 62:   if (!lev) {
 63:     if (!viewer) PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)*V),&viewer);
 66:     PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
 67:     if (!isascii) return 0;
 68:   }

 70:   PetscMalloc1(nv,&vals);
 71:   if (B) VecDuplicate(V[0],&w);
 72:   if (lev) *lev = 0.0;
 73:   for (i=0;i<nw;i++) {
 74:     if (B) {
 75:       if (W) MatMultTranspose(B,W[i],w);
 76:       else MatMultTranspose(B,V[i],w);
 77:     } else {
 78:       if (W) w = W[i];
 79:       else w = V[i];
 80:     }
 81:     VecMDot(w,nv,V,vals);
 82:     for (j=0;j<nv;j++) {
 83:       if (lev) {
 84:         if (i!=j) *lev = PetscMax(*lev,PetscAbsScalar(vals[j]));
 85:         else if (norm) {
 86:           if (PetscRealPart(vals[j])<0.0) *lev = PetscMax(*lev,PetscAbsScalar(vals[j]+PetscRealConstant(1.0)));  /* indefinite case */
 87:           else *lev = PetscMax(*lev,PetscAbsScalar(vals[j]-PetscRealConstant(1.0)));
 88:         }
 89:       } else {
 90: #if !defined(PETSC_USE_COMPLEX)
 91:         PetscViewerASCIIPrintf(viewer," %12g  ",(double)vals[j]);
 92: #else
 93:         PetscViewerASCIIPrintf(viewer," %12g%+12gi ",(double)PetscRealPart(vals[j]),(double)PetscImaginaryPart(vals[j]));
 94: #endif
 95:       }
 96:     }
 97:     if (!lev) PetscViewerASCIIPrintf(viewer,"\n");
 98:   }
 99:   PetscFree(vals);
100:   if (B) VecDestroy(&w);
101:   return 0;
102: }

104: /*@
105:    VecCheckOrthogonality - Checks (or prints) the level of (bi-)orthogonality
106:    of a set of vectors.

108:    Collective on V

110:    Input Parameters:
111: +  V  - a set of vectors
112: .  nv - number of V vectors
113: .  W  - an alternative set of vectors (optional)
114: .  nw - number of W vectors
115: .  B  - matrix defining the inner product (optional)
116: -  viewer - optional visualization context

118:    Output Parameter:
119: .  lev - level of orthogonality (optional)

121:    Notes:
122:    This function computes W'*V and prints the result. It is intended to check
123:    the level of bi-orthogonality of the vectors in the two sets. If W is equal
124:    to NULL then V is used, thus checking the orthogonality of the V vectors.

126:    If matrix B is provided then the check uses the B-inner product, W'*B*V.

128:    If lev is not NULL, it will contain the maximum entry of matrix
129:    W'*V - I (in absolute value) omitting the diagonal. Otherwise, the matrix W'*V
130:    is printed.

132:    Level: developer

134: .seealso: VecCheckOrthonormality()
135: @*/
136: PetscErrorCode VecCheckOrthogonality(Vec V[],PetscInt nv,Vec W[],PetscInt nw,Mat B,PetscViewer viewer,PetscReal *lev)
137: {
142:   if (nv<=0 || nw<=0) return 0;
143:   if (W) {
147:   }
148:   VecCheckOrthogonality_Private(V,nv,W,nw,B,viewer,lev,PETSC_FALSE);
149:   return 0;
150: }

152: /*@
153:    VecCheckOrthonormality - Checks (or prints) the level of (bi-)orthonormality
154:    of a set of vectors.

156:    Collective on V

158:    Input Parameters:
159: +  V  - a set of vectors
160: .  nv - number of V vectors
161: .  W  - an alternative set of vectors (optional)
162: .  nw - number of W vectors
163: .  B  - matrix defining the inner product (optional)
164: -  viewer - optional visualization context

166:    Output Parameter:
167: .  lev - level of orthogonality (optional)

169:    Notes:
170:    This function is equivalent to VecCheckOrthonormality(), but in addition it checks
171:    that the diagonal of W'*V (or W'*B*V) is equal to all ones.

173:    Level: developer

175: .seealso: VecCheckOrthogonality()
176: @*/
177: PetscErrorCode VecCheckOrthonormality(Vec V[],PetscInt nv,Vec W[],PetscInt nw,Mat B,PetscViewer viewer,PetscReal *lev)
178: {
183:   if (nv<=0 || nw<=0) return 0;
184:   if (W) {
188:   }
189:   VecCheckOrthogonality_Private(V,nv,W,nw,B,viewer,lev,PETSC_TRUE);
190:   return 0;
191: }

193: /*@
194:    VecDuplicateEmpty - Creates a new vector of the same type as an existing vector,
195:    but without internal array.

197:    Collective on v

199:    Input Parameters:
200: .  v - a vector to mimic

202:    Output Parameter:
203: .  newv - location to put new vector

205:    Note:
206:    This is similar to VecDuplicate(), but the new vector does not have an internal
207:    array, so the intended usage is with VecPlaceArray().

209:    Level: developer

211: .seealso: MatCreateVecsEmpty()
212: @*/
213: PetscErrorCode VecDuplicateEmpty(Vec v,Vec *newv)
214: {
215:   PetscBool      standard,cuda,mpi;
216:   PetscInt       N,nloc,bs;


222:   PetscObjectTypeCompareAny((PetscObject)v,&standard,VECSEQ,VECMPI,"");
223:   PetscObjectTypeCompareAny((PetscObject)v,&cuda,VECSEQCUDA,VECMPICUDA,"");
224:   if (standard || cuda) {
225:     PetscObjectTypeCompareAny((PetscObject)v,&mpi,VECMPI,VECMPICUDA,"");
226:     VecGetLocalSize(v,&nloc);
227:     VecGetSize(v,&N);
228:     VecGetBlockSize(v,&bs);
229:     if (cuda) {
230: #if defined(PETSC_HAVE_CUDA)
231:       if (mpi) VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)v),bs,nloc,N,NULL,newv);
232:       else VecCreateSeqCUDAWithArray(PetscObjectComm((PetscObject)v),bs,N,NULL,newv);
233: #endif
234:     } else {
235:       if (mpi) VecCreateMPIWithArray(PetscObjectComm((PetscObject)v),bs,nloc,N,NULL,newv);
236:       else VecCreateSeqWithArray(PetscObjectComm((PetscObject)v),bs,N,NULL,newv);
237:     }
238:   } else VecDuplicate(v,newv); /* standard duplicate, with internal array */
239:   return 0;
240: }

242: /*@
243:    VecSetRandomNormal - Sets all components of a vector to normally distributed random values.

245:    Logically Collective on v

247:    Input Parameters:
248: +  v    - the vector to be filled with random values
249: .  rctx - the random number context (can be NULL)
250: .  w1   - first work vector (can be NULL)
251: -  w2   - second work vector (can be NULL)

253:    Output Parameter:
254: .  v    - the vector

256:    Notes:
257:    Fills the two work vectors with uniformly distributed random values (VecSetRandom)
258:    and then applies the Box-Muller transform to get normally distributed values on v.

260:    Level: developer

262: .seealso: VecSetRandom()
263: @*/
264: PetscErrorCode VecSetRandomNormal(Vec v,PetscRandom rctx,Vec w1,Vec w2)
265: {
266:   const PetscScalar *x,*y;
267:   PetscScalar       *z;
268:   PetscInt          n,i;
269:   PetscRandom       rand=NULL;
270:   Vec               v1=NULL,v2=NULL;


278:   if (!rctx) {
279:     PetscRandomCreate(PetscObjectComm((PetscObject)v),&rand);
280:     PetscRandomSetFromOptions(rand);
281:     rctx = rand;
282:   }
283:   if (!w1) {
284:     VecDuplicate(v,&v1);
285:     w1 = v1;
286:   }
287:   if (!w2) {
288:     VecDuplicate(v,&v2);
289:     w2 = v2;
290:   }

294:   VecSetRandom(w1,rctx);
295:   VecSetRandom(w2,rctx);
296:   VecGetLocalSize(v,&n);
297:   VecGetArrayWrite(v,&z);
298:   VecGetArrayRead(w1,&x);
299:   VecGetArrayRead(w2,&y);
300:   for (i=0;i<n;i++) {
301: #if defined(PETSC_USE_COMPLEX)
302:     z[i] = PetscCMPLX(PetscSqrtReal(-2.0*PetscLogReal(PetscRealPart(x[i])))*PetscCosReal(2.0*PETSC_PI*PetscRealPart(y[i])),PetscSqrtReal(-2.0*PetscLogReal(PetscImaginaryPart(x[i])))*PetscCosReal(2.0*PETSC_PI*PetscImaginaryPart(y[i])));
303: #else
304:     z[i] = PetscSqrtReal(-2.0*PetscLogReal(x[i]))*PetscCosReal(2.0*PETSC_PI*y[i]);
305: #endif
306:   }
307:   VecRestoreArrayWrite(v,&z);
308:   VecRestoreArrayRead(w1,&x);
309:   VecRestoreArrayRead(w2,&y);

311:   VecDestroy(&v1);
312:   VecDestroy(&v2);
313:   if (!rctx) PetscRandomDestroy(&rand);
314:   return 0;
315: }