1: /*
  2:     This file implements CGLS, the Conjugate Gradient method for Least-Squares problems.
  3: */
  4:  #include <petsc/private/kspimpl.h>

  6: typedef struct {
  7:   PetscInt  nwork_n,nwork_m;
  8:   Vec       *vwork_m;   /* work vectors of length m, where the system is size m x n */
  9:   Vec       *vwork_n;   /* work vectors of length n */
 10: } KSP_CGLS;

 12: static PetscErrorCode KSPSetUp_CGLS(KSP ksp)
 13: {
 15:   KSP_CGLS       *cgls = (KSP_CGLS*)ksp->data;

 18:   cgls->nwork_m = 2;
 19:   if (cgls->vwork_m) {
 20:     VecDestroyVecs(cgls->nwork_m,&cgls->vwork_m);
 21:   }
 22: 
 23:   cgls->nwork_n = 2;
 24:   if (cgls->vwork_n) {
 25:     VecDestroyVecs(cgls->nwork_n,&cgls->vwork_n);
 26:   }
 27:   KSPCreateVecs(ksp,cgls->nwork_n,&cgls->vwork_n,cgls->nwork_m,&cgls->vwork_m);
 28:   return(0);
 29: }

 31: static PetscErrorCode KSPSolve_CGLS(KSP ksp)
 32: {
 34:   KSP_CGLS       *cgls = (KSP_CGLS*)ksp->data;
 35:   Mat            A;
 36:   Vec            x,b,r,p,q,ss;
 37:   PetscScalar    beta;
 38:   PetscReal      alpha,gamma,oldgamma;
 39:   PetscInt       maxiter_ls = 15;
 40: 
 42:   KSPGetOperators(ksp,&A,NULL); /* Matrix of the system */
 43: 
 44:   /* vectors of length n, where system size is mxn */
 45:   x  = ksp->vec_sol; /* Solution vector */
 46:   p  = cgls->vwork_n[0];
 47:   ss  = cgls->vwork_n[1];
 48: 
 49:   /* vectors of length m, where system size is mxn */
 50:   b  = ksp->vec_rhs; /* Right-hand side vector */
 51:   r  = cgls->vwork_m[0];
 52:   q  = cgls->vwork_m[1];
 53: 
 54:   /* Minimization with the CGLS method */
 55:   ksp->its = 0;
 56:   MatMult(A,x,r);
 57:   VecAYPX(r,-1,b);         /* r_0 = b - A * x_0  */
 58:   MatMultTranspose(A,r,p); /* p_0 = A^T * r_0    */
 59:   VecCopy(p,ss);           /* s_0 = p_0          */
 60:   VecNorm(ss,NORM_2,&gamma);
 61:   ksp->rnorm = gamma;
 62:   (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
 63:   gamma = gamma*gamma;                          /* gamma = norm2(s)^2 */

 65:   do {
 66:     MatMult(A,p,q);           /* q = A * p               */
 67:     VecNorm(q,NORM_2,&alpha);
 68:     KSPCheckNorm(ksp,alpha);
 69:     alpha = alpha*alpha;                           /* alpha = norm2(q)^2      */
 70:     alpha = gamma / alpha;                         /* alpha = gamma / alpha   */
 71:     VecAXPY(x,alpha,p);       /* x += alpha * p          */
 72:     VecAXPY(r,-alpha,q);      /* r -= alpha * q          */
 73:     MatMultTranspose(A,r,ss); /* ss = A^T * r            */
 74:     oldgamma = gamma;                              /* oldgamma = gamma        */
 75:     VecNorm(ss,NORM_2,&gamma);
 76:     KSPCheckNorm(ksp,gamma);
 77:     ksp->its++;
 78:     ksp->rnorm = gamma;
 79:     KSPMonitor(ksp,ksp->its,ksp->rnorm);
 80:     (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
 81:     gamma = gamma*gamma;                           /* gamma = norm2(s)^2      */
 82:     beta = gamma/oldgamma;                         /* beta = gamma / oldgamma */
 83:     VecAYPX(p,beta,ss);       /* p = s + beta * p        */
 84:   } while (ksp->its<ksp->max_it && !ksp->reason);
 85: 
 86:   if (ksp->its>=maxiter_ls && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
 87:   return(0);
 88: }

 90: static PetscErrorCode KSPDestroy_CGLS(KSP ksp)
 91: {
 92:   KSP_CGLS       *cgls = (KSP_CGLS*)ksp->data;

 96:   /* Free work vectors */
 97:   if (cgls->vwork_n) {
 98:     VecDestroyVecs(cgls->nwork_n,&cgls->vwork_n);
 99:   }
100:   if (cgls->vwork_m) {
101:     VecDestroyVecs(cgls->nwork_m,&cgls->vwork_m);
102:   }
103:   PetscFree(ksp->data);
104:   return(0);
105: }

107: /*MC
108:      KSPCGLS - Conjugate Gradient method for Least-Squares problems

110:    Level: beginner

112:    Supports non-square (rectangular) matrices.

114:    Notes:
115:     This does not use the preconditioner, so one should probably use KSPLSQR instead.

117: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
118:            KSPCGSetType(), KSPCGUseSingleReduction(), KSPPIPECG, KSPGROPPCG

120: M*/
121: PETSC_EXTERN PetscErrorCode KSPCreate_CGLS(KSP ksp)
122: {
124:   KSP_CGLS       *cgls;
125: 
127:   PetscNewLog(ksp,&cgls);
128:   ksp->data                = (void*)cgls;
129:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,3);
130:   ksp->ops->setup          = KSPSetUp_CGLS;
131:   ksp->ops->solve          = KSPSolve_CGLS;
132:   ksp->ops->destroy        = KSPDestroy_CGLS;
133:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
134:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
135:   ksp->ops->setfromoptions = 0;
136:   ksp->ops->view           = 0;
137: #if defined(PETSC_USE_COMPLEX)
138:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"This is not supported for complex numbers");
139: #endif
140:   return(0);
141: }