impls/svd/svd.c

#include <petsc/private/pcimpl.h> /*I "petscpc.h" I*/
#include <petscblaslapack.h>

/*
   Private context (data structure) for the SVD preconditioner.
*/
typedef struct {
  Vec               diag, work;
  Mat               A, U, Vt;
  PetscInt          nzero;
  PetscReal         zerosing; /* measure of smallest singular value treated as nonzero */
  PetscInt          essrank;  /* essential rank of operator */
  VecScatter        left2red, right2red;
  Vec               leftred, rightred;
  PetscViewer       monitor;
  PetscViewerFormat monitorformat;
} PC_SVD;

typedef enum {
  READ       = 1,
  WRITE      = 2,
  READ_WRITE = 3
} AccessMode;

/*
   PCSetUp_SVD - Prepares for the use of the SVD preconditioner
                    by setting data structures and options.

   Input Parameter:
.  pc - the preconditioner context

   Application Interface Routine: PCSetUp()

   Note:
   The interface routine PCSetUp() is not usually called directly by
   the user, but instead is called by PCApply() if necessary.
*/
static PetscErrorCode PCSetUp_SVD(PC pc)
{
  PC_SVD      *jac = (PC_SVD *)pc->data;
  PetscScalar *a, *u, *v, *d, *work;
  PetscBLASInt nb, lwork;
  PetscInt     i, n;
  PetscMPIInt  size;

  PetscFunctionBegin;
  PetscCall(MatDestroy(&jac->A));
  PetscCallMPI(MPI_Comm_size(((PetscObject)pc->pmat)->comm, &size));
  if (size > 1) {
    Mat redmat;

    PetscCall(MatCreateRedundantMatrix(pc->pmat, size, PETSC_COMM_SELF, MAT_INITIAL_MATRIX, &redmat));
    PetscCall(MatConvert(redmat, MATSEQDENSE, MAT_INITIAL_MATRIX, &jac->A));
    PetscCall(MatDestroy(&redmat));
  } else {
    PetscCall(MatConvert(pc->pmat, MATSEQDENSE, MAT_INITIAL_MATRIX, &jac->A));
  }
  if (!jac->diag) { /* assume square matrices */
    PetscCall(MatCreateVecs(jac->A, &jac->diag, &jac->work));
  }
  if (!jac->U) {
    PetscCall(MatDuplicate(jac->A, MAT_DO_NOT_COPY_VALUES, &jac->U));
    PetscCall(MatDuplicate(jac->A, MAT_DO_NOT_COPY_VALUES, &jac->Vt));
  }
  PetscCall(MatGetSize(jac->A, &n, NULL));
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(PetscBLASIntCast(n, &nb));
  lwork = 5 * nb;
  PetscCall(PetscMalloc1(lwork, &work));
  PetscCall(MatDenseGetArray(jac->A, &a));
  PetscCall(MatDenseGetArray(jac->U, &u));
  PetscCall(MatDenseGetArray(jac->Vt, &v));
  PetscCall(VecGetArray(jac->diag, &d));
#if !defined(PETSC_USE_COMPLEX)
  {
    PetscBLASInt lierr;
    PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("A", "A", &nb, &nb, a, &nb, d, u, &nb, v, &nb, work, &lwork, &lierr));
    PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "gesvd() error %" PetscBLASInt_FMT, lierr);
    PetscCall(PetscFPTrapPop());
  }
#else
  {
    PetscBLASInt lierr;
    PetscReal   *rwork, *dd;
    PetscCall(PetscMalloc1(5 * nb, &rwork));
    PetscCall(PetscMalloc1(nb, &dd));
    PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("A", "A", &nb, &nb, a, &nb, dd, u, &nb, v, &nb, work, &lwork, rwork, &lierr));
    PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "gesv() error %" PetscBLASInt_FMT, lierr);
    PetscCall(PetscFree(rwork));
    for (i = 0; i < n; i++) d[i] = dd[i];
    PetscCall(PetscFree(dd));
    PetscCall(PetscFPTrapPop());
  }
#endif
  PetscCall(MatDenseRestoreArray(jac->A, &a));
  PetscCall(MatDenseRestoreArray(jac->U, &u));
  PetscCall(MatDenseRestoreArray(jac->Vt, &v));
  for (i = n - 1; i >= 0; i--)
    if (PetscRealPart(d[i]) > jac->zerosing) break;
  jac->nzero = n - 1 - i;
  if (jac->monitor) {
    PetscCall(PetscViewerASCIIAddTab(jac->monitor, ((PetscObject)pc)->tablevel));
    PetscCall(PetscViewerASCIIPrintf(jac->monitor, "    SVD: condition number %14.12e, %" PetscInt_FMT " of %" PetscInt_FMT " singular values are (nearly) zero\n", (double)PetscRealPart(d[0] / d[n - 1]), jac->nzero, n));
    if (n < 10 || jac->monitorformat == PETSC_VIEWER_ALL) {
      PetscCall(PetscViewerASCIIPrintf(jac->monitor, "    SVD: singular values:\n"));
      for (i = 0; i < n; i++) {
        if (i % 5 == 0) {
          if (i != 0) PetscCall(PetscViewerASCIIPrintf(jac->monitor, "\n"));
          PetscCall(PetscViewerASCIIPrintf(jac->monitor, "        "));
        }
        PetscCall(PetscViewerASCIIPrintf(jac->monitor, " %14.12e", (double)PetscRealPart(d[i])));
      }
      PetscCall(PetscViewerASCIIPrintf(jac->monitor, "\n"));
    } else { /* print 5 smallest and 5 largest */
      PetscCall(PetscViewerASCIIPrintf(jac->monitor, "    SVD: smallest singular values: %14.12e %14.12e %14.12e %14.12e %14.12e\n", (double)PetscRealPart(d[n - 1]), (double)PetscRealPart(d[n - 2]), (double)PetscRealPart(d[n - 3]), (double)PetscRealPart(d[n - 4]), (double)PetscRealPart(d[n - 5])));
      PetscCall(PetscViewerASCIIPrintf(jac->monitor, "    SVD: largest singular values : %14.12e %14.12e %14.12e %14.12e %14.12e\n", (double)PetscRealPart(d[4]), (double)PetscRealPart(d[3]), (double)PetscRealPart(d[2]), (double)PetscRealPart(d[1]), (double)PetscRealPart(d[0])));
    }
    PetscCall(PetscViewerASCIISubtractTab(jac->monitor, ((PetscObject)pc)->tablevel));
  }
  PetscCall(PetscInfo(pc, "Largest and smallest singular values %14.12e %14.12e\n", (double)PetscRealPart(d[0]), (double)PetscRealPart(d[n - 1])));
  for (i = 0; i < n - jac->nzero; i++) d[i] = 1.0 / d[i];
  for (; i < n; i++) d[i] = 0.0;
  if (jac->essrank > 0)
    for (i = 0; i < n - jac->nzero - jac->essrank; i++) d[i] = 0.0; /* Skip all but essrank eigenvalues */
  PetscCall(PetscInfo(pc, "Number of zero or nearly singular values %" PetscInt_FMT "\n", jac->nzero));
  PetscCall(VecRestoreArray(jac->diag, &d));
  PetscCall(PetscFree(work));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSVDGetVec(PC pc, PCSide side, AccessMode amode, Vec x, Vec *xred)
{
  PC_SVD     *jac = (PC_SVD *)pc->data;
  PetscMPIInt size;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
  *xred = NULL;
  switch (side) {
  case PC_LEFT:
    if (size == 1) *xred = x;
    else {
      if (!jac->left2red) PetscCall(VecScatterCreateToAll(x, &jac->left2red, &jac->leftred));
      if (amode & READ) {
        PetscCall(VecScatterBegin(jac->left2red, x, jac->leftred, INSERT_VALUES, SCATTER_FORWARD));
        PetscCall(VecScatterEnd(jac->left2red, x, jac->leftred, INSERT_VALUES, SCATTER_FORWARD));
      }
      *xred = jac->leftred;
    }
    break;
  case PC_RIGHT:
    if (size == 1) *xred = x;
    else {
      if (!jac->right2red) PetscCall(VecScatterCreateToAll(x, &jac->right2red, &jac->rightred));
      if (amode & READ) {
        PetscCall(VecScatterBegin(jac->right2red, x, jac->rightred, INSERT_VALUES, SCATTER_FORWARD));
        PetscCall(VecScatterEnd(jac->right2red, x, jac->rightred, INSERT_VALUES, SCATTER_FORWARD));
      }
      *xred = jac->rightred;
    }
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Side must be LEFT or RIGHT");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSVDRestoreVec(PC pc, PCSide side, AccessMode amode, Vec x, Vec *xred)
{
  PC_SVD     *jac = (PC_SVD *)pc->data;
  PetscMPIInt size;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
  switch (side) {
  case PC_LEFT:
    if (size != 1 && amode & WRITE) {
      PetscCall(VecScatterBegin(jac->left2red, jac->leftred, x, INSERT_VALUES, SCATTER_REVERSE));
      PetscCall(VecScatterEnd(jac->left2red, jac->leftred, x, INSERT_VALUES, SCATTER_REVERSE));
    }
    break;
  case PC_RIGHT:
    if (size != 1 && amode & WRITE) {
      PetscCall(VecScatterBegin(jac->right2red, jac->rightred, x, INSERT_VALUES, SCATTER_REVERSE));
      PetscCall(VecScatterEnd(jac->right2red, jac->rightred, x, INSERT_VALUES, SCATTER_REVERSE));
    }
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Side must be LEFT or RIGHT");
  }
  *xred = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   PCApply_SVD - Applies the SVD preconditioner to a vector.

   Input Parameters:
.  pc - the preconditioner context
.  x - input vector

   Output Parameter:
.  y - output vector

   Application Interface Routine: PCApply()
 */
static PetscErrorCode PCApply_SVD(PC pc, Vec x, Vec y)
{
  PC_SVD *jac  = (PC_SVD *)pc->data;
  Vec     work = jac->work, xred, yred;

  PetscFunctionBegin;
  PetscCall(PCSVDGetVec(pc, PC_RIGHT, READ, x, &xred));
  PetscCall(PCSVDGetVec(pc, PC_LEFT, WRITE, y, &yred));
#if !defined(PETSC_USE_COMPLEX)
  PetscCall(MatMultTranspose(jac->U, xred, work));
#else
  PetscCall(MatMultHermitianTranspose(jac->U, xred, work));
#endif
  PetscCall(VecPointwiseMult(work, work, jac->diag));
#if !defined(PETSC_USE_COMPLEX)
  PetscCall(MatMultTranspose(jac->Vt, work, yred));
#else
  PetscCall(MatMultHermitianTranspose(jac->Vt, work, yred));
#endif
  PetscCall(PCSVDRestoreVec(pc, PC_RIGHT, READ, x, &xred));
  PetscCall(PCSVDRestoreVec(pc, PC_LEFT, WRITE, y, &yred));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCMatApply_SVD(PC pc, Mat X, Mat Y)
{
  PC_SVD *jac = (PC_SVD *)pc->data;
  Mat     W;

  PetscFunctionBegin;
  PetscCall(MatTransposeMatMult(jac->U, X, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &W));
  PetscCall(MatDiagonalScale(W, jac->diag, NULL));
  PetscCall(MatTransposeMatMult(jac->Vt, W, MAT_REUSE_MATRIX, PETSC_DETERMINE, &Y));
  PetscCall(MatDestroy(&W));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCApplyTranspose_SVD(PC pc, Vec x, Vec y)
{
  PC_SVD *jac  = (PC_SVD *)pc->data;
  Vec     work = jac->work, xred, yred;

  PetscFunctionBegin;
  PetscCall(PCSVDGetVec(pc, PC_LEFT, READ, x, &xred));
  PetscCall(PCSVDGetVec(pc, PC_RIGHT, WRITE, y, &yred));
  PetscCall(MatMult(jac->Vt, xred, work));
  PetscCall(VecPointwiseMult(work, work, jac->diag));
  PetscCall(MatMult(jac->U, work, yred));
  PetscCall(PCSVDRestoreVec(pc, PC_LEFT, READ, x, &xred));
  PetscCall(PCSVDRestoreVec(pc, PC_RIGHT, WRITE, y, &yred));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCReset_SVD(PC pc)
{
  PC_SVD *jac = (PC_SVD *)pc->data;

  PetscFunctionBegin;
  PetscCall(MatDestroy(&jac->A));
  PetscCall(MatDestroy(&jac->U));
  PetscCall(MatDestroy(&jac->Vt));
  PetscCall(VecDestroy(&jac->diag));
  PetscCall(VecDestroy(&jac->work));
  PetscCall(VecScatterDestroy(&jac->right2red));
  PetscCall(VecScatterDestroy(&jac->left2red));
  PetscCall(VecDestroy(&jac->rightred));
  PetscCall(VecDestroy(&jac->leftred));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   PCDestroy_SVD - Destroys the private context for the SVD preconditioner
   that was created with PCCreate_SVD().

   Input Parameter:
.  pc - the preconditioner context

   Application Interface Routine: PCDestroy()
*/
static PetscErrorCode PCDestroy_SVD(PC pc)
{
  PC_SVD *jac = (PC_SVD *)pc->data;

  PetscFunctionBegin;
  PetscCall(PCReset_SVD(pc));
  PetscCall(PetscViewerDestroy(&jac->monitor));
  PetscCall(PetscFree(pc->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSetFromOptions_SVD(PC pc, PetscOptionItems PetscOptionsObject)
{
  PC_SVD   *jac = (PC_SVD *)pc->data;
  PetscBool flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "SVD options");
  PetscCall(PetscOptionsReal("-pc_svd_zero_sing", "Singular values smaller than this treated as zero", "None", jac->zerosing, &jac->zerosing, NULL));
  PetscCall(PetscOptionsInt("-pc_svd_ess_rank", "Essential rank of operator (0 to use entire operator)", "None", jac->essrank, &jac->essrank, NULL));
  PetscCall(PetscOptionsViewer("-pc_svd_monitor", "Monitor the conditioning, and extremal singular values", "None", &jac->monitor, &jac->monitorformat, &flg));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCView_SVD(PC pc, PetscViewer viewer)
{
  PC_SVD   *svd = (PC_SVD *)pc->data;
  PetscBool isascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
  if (isascii) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "  All singular values smaller than %g treated as zero\n", (double)svd->zerosing));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Provided essential rank of the matrix %" PetscInt_FMT " (all other eigenvalues are zeroed)\n", svd->essrank));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   PCCreate_SVD - Creates a SVD preconditioner context, PC_SVD,
   and sets this as the private data within the generic preconditioning
   context, PC, that was created within PCCreate().

   Input Parameter:
.  pc - the preconditioner context

   Application Interface Routine: PCCreate()
*/

/*MC
   PCSVD - Use pseudo inverse defined by SVD of operator

   Level: advanced

  Options Database Keys:
+  -pc_svd_zero_sing <rtol> - Singular values smaller than this are treated as zero
-  -pc_svd_monitor          - Print information on the extreme singular values of the operator

  Developer Note:
  This implementation automatically creates a redundant copy of the
  matrix on each process and uses a sequential SVD solve. Why does it do this instead
  of using the composable `PCREDUNDANT` object?

.seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCREDUNDANT`
M*/

PETSC_EXTERN PetscErrorCode PCCreate_SVD(PC pc)
{
  PC_SVD     *jac;
  PetscMPIInt size = 0;

  PetscFunctionBegin;
  /*
     Creates the private data structure for this preconditioner and
     attach it to the PC object.
  */
  PetscCall(PetscNew(&jac));
  jac->zerosing = 1.e-12;
  pc->data      = (void *)jac;

  /*
      Set the pointers for the functions that are provided above.
      Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
      are called, they will automatically call these functions.  Note we
      choose not to provide a couple of these functions since they are
      not needed.
  */

#if defined(PETSC_HAVE_COMPLEX)
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
#endif
  if (size == 1) pc->ops->matapply = PCMatApply_SVD;
  pc->ops->apply           = PCApply_SVD;
  pc->ops->applytranspose  = PCApplyTranspose_SVD;
  pc->ops->setup           = PCSetUp_SVD;
  pc->ops->reset           = PCReset_SVD;
  pc->ops->destroy         = PCDestroy_SVD;
  pc->ops->setfromoptions  = PCSetFromOptions_SVD;
  pc->ops->view            = PCView_SVD;
  pc->ops->applyrichardson = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}