Date: 2022-03-31T15:29:25+00:00

Actual source code: qeplin.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:    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:   MatGetSize(ctx->M,&M,&N);
     45:   MatGetLocalSize(ctx->M,&m,&n);
     46:   MatCreateConstantDiagonal(PetscObjectComm((PetscObject)ctx->M),m,n,M,N,1.0,&Id);
     47:   if (a!=0.0 && b!=0.0) {
     48:     MatDuplicate(ctx->C,MAT_COPY_VALUES,&T);
     49:     MatScale(T,-a*ctx->dsfactor*ctx->sfactor);
     50:     MatShift(T,b);
     51:   } else {
     52:     if (a==0.0) { T = Id; scalt = b; }
     53:     else { T = ctx->C; scalt = -a*ctx->dsfactor*ctx->sfactor; }
     54:   }
     55:   MatCreateTile(-b*ctx->dsfactor,ctx->K,a,Id,-ctx->dsfactor*a,ctx->K,scalt,T,A);
     56:   MatDestroy(&Id);
     57:   if (a!=0.0 && b!=0.0) MatDestroy(&T);
     58:   PetscFunctionReturn(0);
     59: }

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

     68:   MatGetSize(ctx->M,&M,&N);
     69:   MatGetLocalSize(ctx->M,&m,&n);
     70:   MatCreateConstantDiagonal(PetscObjectComm((PetscObject)ctx->M),m,n,M,N,1.0,&Id);
     71:   if (a!=0.0 && b!=0.0) {
     72:     MatDuplicate(ctx->C,MAT_COPY_VALUES,&T);
     73:     MatScale(T,b*ctx->dsfactor*ctx->sfactor);
     74:     MatShift(T,a);
     75:   } else {
     76:     if (b==0.0) { T = Id; scalt = a; }
     77:     else { T = ctx->C; scalt = b*ctx->dsfactor*ctx->sfactor; }
     78:   }
     79:   MatCreateTile(scalt,T,b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,b,Id,a*ctx->sfactor*ctx->sfactor*ctx->dsfactor,ctx->M,B);
     80:   MatDestroy(&Id);
     81:   if (a!=0.0 && b!=0.0) MatDestroy(&T);
     82:   PetscFunctionReturn(0);
     83: }

     85: /* - - - S - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     87: PetscErrorCode MatCreateExplicit_Linear_SA(MPI_Comm comm,PEP_LINEAR *ctx,Mat *A)
     88: {
     89:   Mat            T=NULL;
     90:   PetscScalar    scalt=1.0;
     91:   PetscReal      a=ctx->alpha,b=ctx->beta;

     93:   if (a!=0.0 && b!=0.0) {
     94:     MatDuplicate(ctx->C,MAT_COPY_VALUES,&T);
     95:     MatScale(T,a*ctx->dsfactor*ctx->sfactor);
     96:     MatAXPY(T,-b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,UNKNOWN_NONZERO_PATTERN);
     97:   } else {
     98:     if (a==0.0) { T = ctx->M; scalt = -b*ctx->dsfactor*ctx->sfactor*ctx->sfactor; }
     99:     else { T = ctx->C; scalt = a*ctx->dsfactor*ctx->sfactor; }
    100:   }
    101:   MatCreateTile(b*ctx->dsfactor,ctx->K,a*ctx->dsfactor,ctx->K,a*ctx->dsfactor,ctx->K,scalt,T,A);
    102:   if (a!=0.0 && b!=0.0) MatDestroy(&T);
    103:   PetscFunctionReturn(0);
    104: }

    106: PetscErrorCode MatCreateExplicit_Linear_SB(MPI_Comm comm,PEP_LINEAR *ctx,Mat *B)
    107: {
    108:   Mat            T=NULL;
    109:   PetscScalar    scalt=1.0;
    110:   PetscReal      a=ctx->alpha,b=ctx->beta;

    112:   if (a!=0.0 && b!=0.0) {
    113:     MatDuplicate(ctx->C,MAT_COPY_VALUES,&T);
    114:     MatScale(T,-b*ctx->dsfactor*ctx->sfactor);
    115:     MatAXPY(T,a*ctx->dsfactor,ctx->K,UNKNOWN_NONZERO_PATTERN);
    116:   } else {
    117:     if (b==0.0) { T = ctx->K; scalt = a*ctx->dsfactor; }
    118:     else { T = ctx->C; scalt = -b*ctx->dsfactor*ctx->sfactor; }
    119:   }
    120:   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);
    121:   if (a!=0.0 && b!=0.0) MatDestroy(&T);
    122:   PetscFunctionReturn(0);
    123: }

    125: /* - - - H - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    127: PetscErrorCode MatCreateExplicit_Linear_HA(MPI_Comm comm,PEP_LINEAR *ctx,Mat *A)
    128: {
    129:   Mat            T=NULL;
    130:   PetscScalar    scalt=1.0;
    131:   PetscReal      a=ctx->alpha,b=ctx->beta;

    133:   if (a!=0.0 && b!=0.0) {
    134:     MatDuplicate(ctx->C,MAT_COPY_VALUES,&T);
    135:     MatScale(T,a*ctx->dsfactor*ctx->sfactor);
    136:     MatAXPY(T,b*ctx->dsfactor*ctx->sfactor*ctx->sfactor,ctx->M,UNKNOWN_NONZERO_PATTERN);
    137:   } else {
    138:     if (a==0.0) { T = ctx->M; scalt = b*ctx->dsfactor*ctx->sfactor*ctx->sfactor; }
    139:     else { T = ctx->C; scalt = a*ctx->dsfactor*ctx->sfactor; }
    140:   }
    141:   MatCreateTile(a*ctx->dsfactor,ctx->K,-b*ctx->dsfactor,ctx->K,scalt,T,a*ctx->dsfactor,ctx->K,A);
    142:   if (a!=0.0 && b!=0.0) MatDestroy(&T);
    143:   PetscFunctionReturn(0);
    144: }

    146: PetscErrorCode MatCreateExplicit_Linear_HB(MPI_Comm comm,PEP_LINEAR *ctx,Mat *B)
    147: {
    148:   Mat            T=NULL;
    149:   PetscScalar    scalt=1.0;
    150:   PetscReal      a=ctx->alpha,b=ctx->beta;

    152:   if (a!=0.0 && b!=0.0) {
    153:     MatDuplicate(ctx->C,MAT_COPY_VALUES,&T);
    154:     MatScale(T,b*ctx->dsfactor*ctx->sfactor);
    155:     MatAXPY(T,a*ctx->dsfactor,ctx->K,UNKNOWN_NONZERO_PATTERN);
    156:   } else {
    157:     if (b==0.0) { T = ctx->K; scalt = a*ctx->dsfactor; }
    158:     else { T = ctx->C; scalt = b*ctx->dsfactor*ctx->sfactor; }
    159:   }
    160:   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);
    161:   if (a!=0.0 && b!=0.0) MatDestroy(&T);
    162:   PetscFunctionReturn(0);
    163: }