Date: 2024-10-28T09:14:00+00:00

Actual source code: qeplin.c
slepc-3.22.1 2024-10-28
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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:    Various types of linearization for quadratic eigenvalue problem
     12: */

     14: #include <slepc/private/pepimpl.h>
     15: #include "linear.h"

     17: /*
     18:     Given the quadratic problem (l^2*M + l*C + K)*x = 0 the linearization is
     19:     A*z = l*B*z for z = [  x  ] and A,B defined as follows:
     20:                         [ l*x ]

     22:             N:
     23:                      A = [-bK      aI    ]     B = [ aI+bC   bM    ]
     24:                          [-aK     -aC+bI ]         [ bI      aM    ]

     26:             S:
     27:                      A = [ bK      aK    ]     B = [ aK-bC  -bM    ]
     28:                          [ aK      aC-bM ]         [-bM     -aM    ]

     30:             H:
     31:                      A = [ aK     -bK    ]     B = [ bM      aK+bC ]
     32:                          [ aC+bM   aK    ]         [-aM      bM    ]
     33:  */

     35: /* - - - N - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     37: PetscErrorCode MatCreateExplicit_Linear_NA(MPI_Comm comm,PEP_LINEAR *ctx,Mat *A)
     38: {
     39:   PetscInt       M,N,m,n;
     40:   Mat            Id,T=NULL;
     41:   PetscReal      a=ctx->alpha,b=ctx->beta;
     42:   PetscScalar    scalt=1.0;

     44:   PetscFunctionBegin;
     45:   PetscCall(MatGetSize(ctx->M,&M,&N));
     46:   PetscCall(MatGetLocalSize(ctx->M,&m,&n));
     47:   PetscCall(MatCreateConstantDiagonal(PetscObjectComm((PetscObject)ctx->M),m,n,M,N,1.0,&Id));
     48:   if (a!=0.0 && b!=0.0) {
     49:     PetscCall(MatDuplicate(ctx->C,MAT_COPY_VALUES,&T));
     50:     PetscCall(MatScale(T,-a*ctx->dsfactor*ctx->sfactor));
     51:     PetscCall(MatShift(T,b));
     52:   } else {
     53:     if (a==0.0) { T = Id; scalt = b; }
     54:     else { T = ctx->C; scalt = -a*ctx->dsfactor*ctx->sfactor; }
     55:   }
     56:   PetscCall(MatCreateTile(-b*ctx->dsfactor,ctx->K,a,Id,-ctx->dsfactor*a,ctx->K,scalt,T,A));
     57:   PetscCall(MatDestroy(&Id));
     58:   if (a!=0.0 && b!=0.0) PetscCall(MatDestroy(&T));
     59:   PetscFunctionReturn(PETSC_SUCCESS);
     60: }

     62: PetscErrorCode MatCreateExplicit_Linear_NB(MPI_Comm comm,PEP_LINEAR *ctx,Mat *B)
     63: {
     64:   PetscInt       M,N,m,n;
     65:   Mat            Id,T=NULL;
     66:   PetscReal      a=ctx->alpha,b=ctx->beta;
     67:   PetscScalar    scalt=1.0;

     69:   PetscFunctionBegin;
     70:   PetscCall(MatGetSize(ctx->M,&M,&N));
     71:   PetscCall(MatGetLocalSize(ctx->M,&m,&n));
     72:   PetscCall(MatCreateConstantDiagonal(PetscObjectComm((PetscObject)ctx->M),m,n,M,N,1.0,&Id));
     73:   if (a!=0.0 && b!=0.0) {
     74:     PetscCall(MatDuplicate(ctx->C,MAT_COPY_VALUES,&T));
     75:     PetscCall(MatScale(T,b*ctx->dsfactor*ctx->sfactor));
     76:     PetscCall(MatShift(T,a));
     77:   } else {
     78:     if (b==0.0) { T = Id; scalt = a; }
     79:     else { T = ctx->C; scalt = b*ctx->dsfactor*ctx->sfactor; }
     80:   }
     81:   PetscCall(MatCreateTile(scalt,T,b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,b,Id,a*ctx->sfactor*ctx->sfactor*ctx->dsfactor,ctx->M,B));
     82:   PetscCall(MatDestroy(&Id));
     83:   if (a!=0.0 && b!=0.0) PetscCall(MatDestroy(&T));
     84:   PetscFunctionReturn(PETSC_SUCCESS);
     85: }

     87: /* - - - S - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     89: PetscErrorCode MatCreateExplicit_Linear_SA(MPI_Comm comm,PEP_LINEAR *ctx,Mat *A)
     90: {
     91:   Mat            T=NULL;
     92:   PetscScalar    scalt=1.0;
     93:   PetscReal      a=ctx->alpha,b=ctx->beta;

     95:   PetscFunctionBegin;
     96:   if (a!=0.0 && b!=0.0) {
     97:     PetscCall(MatDuplicate(ctx->C,MAT_COPY_VALUES,&T));
     98:     PetscCall(MatScale(T,a*ctx->dsfactor*ctx->sfactor));
     99:     PetscCall(MatAXPY(T,-b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,UNKNOWN_NONZERO_PATTERN));
    100:   } else {
    101:     if (a==0.0) { T = ctx->M; scalt = -b*ctx->dsfactor*ctx->sfactor*ctx->sfactor; }
    102:     else { T = ctx->C; scalt = a*ctx->dsfactor*ctx->sfactor; }
    103:   }
    104:   PetscCall(MatCreateTile(b*ctx->dsfactor,ctx->K,a*ctx->dsfactor,ctx->K,a*ctx->dsfactor,ctx->K,scalt,T,A));
    105:   if (a!=0.0 && b!=0.0) PetscCall(MatDestroy(&T));
    106:   PetscFunctionReturn(PETSC_SUCCESS);
    107: }

    109: PetscErrorCode MatCreateExplicit_Linear_SB(MPI_Comm comm,PEP_LINEAR *ctx,Mat *B)
    110: {
    111:   Mat            T=NULL;
    112:   PetscScalar    scalt=1.0;
    113:   PetscReal      a=ctx->alpha,b=ctx->beta;

    115:   PetscFunctionBegin;
    116:   if (a!=0.0 && b!=0.0) {
    117:     PetscCall(MatDuplicate(ctx->C,MAT_COPY_VALUES,&T));
    118:     PetscCall(MatScale(T,-b*ctx->dsfactor*ctx->sfactor));
    119:     PetscCall(MatAXPY(T,a*ctx->dsfactor,ctx->K,UNKNOWN_NONZERO_PATTERN));
    120:   } else {
    121:     if (b==0.0) { T = ctx->K; scalt = a*ctx->dsfactor; }
    122:     else { T = ctx->C; scalt = -b*ctx->dsfactor*ctx->sfactor; }
    123:   }
    124:   PetscCall(MatCreateTile(scalt,T,-b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,-b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,-a*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,B));
    125:   if (a!=0.0 && b!=0.0) PetscCall(MatDestroy(&T));
    126:   PetscFunctionReturn(PETSC_SUCCESS);
    127: }

    129: /* - - - H - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    131: PetscErrorCode MatCreateExplicit_Linear_HA(MPI_Comm comm,PEP_LINEAR *ctx,Mat *A)
    132: {
    133:   Mat            T=NULL;
    134:   PetscScalar    scalt=1.0;
    135:   PetscReal      a=ctx->alpha,b=ctx->beta;

    137:   PetscFunctionBegin;
    138:   if (a!=0.0 && b!=0.0) {
    139:     PetscCall(MatDuplicate(ctx->C,MAT_COPY_VALUES,&T));
    140:     PetscCall(MatScale(T,a*ctx->dsfactor*ctx->sfactor));
    141:     PetscCall(MatAXPY(T,b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,UNKNOWN_NONZERO_PATTERN));
    142:   } else {
    143:     if (a==0.0) { T = ctx->M; scalt = b*ctx->dsfactor*ctx->sfactor*ctx->sfactor; }
    144:     else { T = ctx->C; scalt = a*ctx->dsfactor*ctx->sfactor; }
    145:   }
    146:   PetscCall(MatCreateTile(a*ctx->dsfactor,ctx->K,-b*ctx->dsfactor,ctx->K,scalt,T,a*ctx->dsfactor,ctx->K,A));
    147:   if (a!=0.0 && b!=0.0) PetscCall(MatDestroy(&T));
    148:   PetscFunctionReturn(PETSC_SUCCESS);
    149: }

    151: PetscErrorCode MatCreateExplicit_Linear_HB(MPI_Comm comm,PEP_LINEAR *ctx,Mat *B)
    152: {
    153:   Mat            T=NULL;
    154:   PetscScalar    scalt=1.0;
    155:   PetscReal      a=ctx->alpha,b=ctx->beta;

    157:   PetscFunctionBegin;
    158:   if (a!=0.0 && b!=0.0) {
    159:     PetscCall(MatDuplicate(ctx->C,MAT_COPY_VALUES,&T));
    160:     PetscCall(MatScale(T,b*ctx->dsfactor*ctx->sfactor));
    161:     PetscCall(MatAXPY(T,a*ctx->dsfactor,ctx->K,UNKNOWN_NONZERO_PATTERN));
    162:   } else {
    163:     if (b==0.0) { T = ctx->K; scalt = a*ctx->dsfactor; }
    164:     else { T = ctx->C; scalt = b*ctx->dsfactor*ctx->sfactor; }
    165:   }
    166:   PetscCall(MatCreateTile(b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,scalt,T,-a*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,B));
    167:   if (a!=0.0 && b!=0.0) PetscCall(MatDestroy(&T));
    168:   PetscFunctionReturn(PETSC_SUCCESS);
    169: }