Various estimates of how `wild' a matrix is. More...

#include <stdlib.h>
#include "anamod.h"
#include "anamodsalsamodules.h"
#include "petscerror.h"
#include "petscmat.h"

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Functions
static PetscErrorCode	ComputeVariability (Mat A)
static PetscErrorCode	RowVariability (AnaModNumericalProblem prob, AnalysisItem rv, int lv, PetscBool *flg)
static PetscErrorCode	ColVariability (AnaModNumericalProblem prob, AnalysisItem rv, int lv, PetscBool *flg)
static PetscErrorCode	ComputeDiagonal (Mat A)
static PetscErrorCode	DiagonalAverage (AnaModNumericalProblem prob, AnalysisItem rv, int lv, PetscBool *flg)
static PetscErrorCode	DiagonalVariance (AnaModNumericalProblem prob, AnalysisItem rv, int lv, PetscBool *flg)
static PetscErrorCode	DiagonalSign (AnaModNumericalProblem prob, AnalysisItem rv, int lv, PetscBool *flg)
PetscErrorCode	RegisterVarianceModules ()
PetscErrorCode	DeRegisterVarianceModules (void)

Detailed Description

Various estimates of how `wild' a matrix is.

Measurements of element variance

This module contains various estimates of how different elements in a matrix are. These measures are completely heuristic, and do not relate to any known mathematical theory.

Usage

Activate this module with

PetscErrorCode RegisterVarianceModules();

Compute these elements with

ComputeQuantity("variance",<element>,A,(AnalysisItem*)&res,&flg);

Available elements are:

"row-variability" : $\max_i \log_{10} {\max_j|a_{ij}|\over\min_j|a_{ij}|}$ , computed by RowVariability()
"col-variability" : $\max_j \log_{10} {\max_i|a_{ij}|\over\min_i|a_{ij}|}$ , computed by ColVariability()
"diagonal-average" : average value of absolute diagonal elements, by DiagonalAverage()
"diagonal-variance" : standard deviation of diagonal average, by DiagonalVariance()
"diagonal-sign" : indicator of diagonal sign pattern, by DiagonalSign(): -10 all zero, -2 all negative, -1 nonpositive, 0 indefinite, 1 nonnegative, 2 all positive

Definition in file variance.c.

Function Documentation

static PetscErrorCode ColVariability	(	AnaModNumericalProblem	prob,
		AnalysisItem *	rv,
		int *	lv,
		PetscBool *	flg
	)		`[static]`

This routine relies on a call to ComputeVariability()

Definition at line 146 of file variance.c.

References ComputeVariability(), GetDataID(), HASTOEXIST, id, and AnalysisItem::r.

Referenced by RegisterVarianceModules().

{
  Mat A = (Mat)prob;
  PetscReal v=0.; PetscBool has; int id; PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = GetDataID("variance","col-variability",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataGetReal
    ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
  if (*flg) rv->r = v;
  else {
    ierr = ComputeVariability(A); CHKERRQ(ierr);
    ierr = PetscObjectComposedDataGetReal
      ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
    if (*flg) rv->r = v;
  }
  
  PetscFunctionReturn(0);
}

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static PetscErrorCode ComputeDiagonal ( Mat A ) [static]

This is a computational routine; it computes the value of several modules

Definition at line 173 of file variance.c.

References DIAGONAL_INDEFINITE, DIAGONAL_NEGATIVE, DIAGONAL_NONNEGATIVE, DIAGONAL_NONPOSITIVE, DIAGONAL_POSITIVE, DIAGONAL_ZERO, GetDataID(), HASTOEXIST, and id.

Referenced by DiagonalAverage(), DiagonalSign(), and DiagonalVariance().

{
  int sign;
  Vec V; PetscScalar *v; MPI_Comm comm;
  PetscReal average,g_average,variance,g_variance;
  int local,nn,nz,np,gnn,gnz,gnp,row,id, N;
  PetscBool has; PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)A,&comm); CHKERRQ(ierr);
  ierr = MatGetLocalSize(A,&local,PETSC_NULL); CHKERRQ(ierr);
  ierr = MatGetSize(A,&N,PETSC_NULL); CHKERRQ(ierr);
  ierr = VecCreateMPI(comm,local,PETSC_DECIDE,&V); CHKERRQ(ierr);
  ierr = MatGetDiagonal(A,V); CHKERRQ(ierr);
  ierr = VecGetArray(V,&v); CHKERRQ(ierr);

  average = 0; nn = np = nz = 0;
  for (row=0; row<local; row++) {
    if (v[row]>0) np++; else if (v[row]<0) nn++; else nz++;
    average += PetscAbsScalar(v[row]);
  }
  ierr = MPI_Allreduce((void*)&nn,(void*)&gnn,1,MPI_INT,MPI_SUM,comm);
  ierr = MPI_Allreduce((void*)&nz,(void*)&gnz,1,MPI_INT,MPI_SUM,comm);
  ierr = MPI_Allreduce((void*)&np,(void*)&gnp,1,MPI_INT,MPI_SUM,comm);
  if (np==N) sign = DIAGONAL_POSITIVE;
  else if (nn==0) {
    if (np==0) sign = DIAGONAL_ZERO; else sign = DIAGONAL_NONNEGATIVE;}
  else if (nn==N) sign = DIAGONAL_NEGATIVE;
  else if (np==0) sign = DIAGONAL_NONPOSITIVE;
  else sign = DIAGONAL_INDEFINITE;
  ierr = MPI_Allreduce((void*)&average,(void*)&g_average,1,MPIU_REAL,MPI_SUM,comm);
  average = g_average / N; variance = 0;
  for (row=0; row<local; row++) {
    PetscReal d = PetscAbsScalar(v[row])-average;
    variance += d*d;
  }
  ierr = MPI_Allreduce((void*)&variance,(void*)&g_variance,1,MPIU_REAL,MPI_SUM,comm);
  variance = sqrt(g_variance / N);
  ierr = GetDataID("variance","diagonal-average",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataSetReal
    ((PetscObject)A,id,average); CHKERRQ(ierr);

  ierr = GetDataID("variance","diagonal-variance",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataSetReal
    ((PetscObject)A,id,variance); CHKERRQ(ierr);

  ierr = GetDataID("variance","diagonal-sign",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataSetInt
    ((PetscObject)A,id,sign); CHKERRQ(ierr);

  ierr = VecRestoreArray(V,&v); CHKERRQ(ierr);
  ierr = VecDestroy(&V); CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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static PetscErrorCode ComputeVariability ( Mat A ) [static]

Variability in rows and columns.

This is a computational routine.

Definition at line 42 of file variance.c.

References GetDataID(), HASTOEXIST, and id.

Referenced by ColVariability(), and RowVariability().

{
  MPI_Comm comm;
  PetscReal rr,cr;
  PetscReal *rmax,*rmin,*cmax,*cmin,*cmaxx,*cminn,rr_local;
  int m,n,M,N,first,last,i,id,row; 
  PetscBool has; PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)A,&comm); CHKERRQ(ierr);
  ierr = MatGetSize(A,&M,&N); CHKERRQ(ierr);
  ierr = MatGetLocalSize(A,&m,&n); CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(A,&first,&last); CHKERRQ(ierr);
  ierr = PetscMalloc(m*sizeof(PetscReal),&rmax); CHKERRQ(ierr);
  ierr = PetscMalloc(m*sizeof(PetscReal),&rmin); CHKERRQ(ierr);
  ierr = PetscMalloc(N*sizeof(PetscReal),&cmax); CHKERRQ(ierr);
  ierr = PetscMalloc(N*sizeof(PetscReal),&cmin); CHKERRQ(ierr);
  ierr = PetscMalloc(N*sizeof(PetscReal),&cmaxx); CHKERRQ(ierr);
  ierr = PetscMalloc(N*sizeof(PetscReal),&cminn); CHKERRQ(ierr);

  /* init; we take logs, so 1.e+5 is beyond infinity */
  for (i=0; i<m; i++) {rmax[i] = 0; rmin[i] = 1.e+5;}
  for (i=0; i<N; i++) {cmax[i] = 0; cmin[i] = 1.e+5;}
  for (row=first; row<last; row++) {
    int irow=row-first,ncols,icol; const int *cols; const PetscScalar *vals;
    ierr = MatGetRow(A,row,&ncols,&cols,&vals); CHKERRQ(ierr);
    for (icol=0; icol<ncols; icol++) {
      int col=cols[icol];
      if (vals[icol]) {
        PetscReal logval = (PetscReal) log10(PetscAbsScalar(vals[icol]));
        if (logval>rmax[irow]) rmax[irow] = logval;
        if (logval<rmin[irow]) rmin[irow] = logval;
        if (logval>cmax[col]) cmax[col] = logval;
        if (logval<cmin[col]) cmin[col] = logval;
      }
    }
    ierr = MatRestoreRow(A,row,&ncols,&cols,&vals); CHKERRQ(ierr);
  }

  /*
   * now get global row spread
   */
  for (i=0; i<m; i++) rmax[i] -= rmin[i];
  for (i=1; i<m; i++) if (rmax[i]>rmax[0]) rmax[0] = rmax[i];
  rr_local = rmax[0];
  ierr = MPI_Allreduce(&rr_local,&rr,1,MPIU_SCALAR,MPI_MAX,comm);
  ierr = GetDataID("variance","row-variability",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataSetReal
    ((PetscObject)A,id,rr); CHKERRQ(ierr);

  /*
   * global column spread: reduce the full length row of values,
   * then local max is global
   */
  ierr = MPI_Allreduce(cmax,cmaxx,N,MPIU_SCALAR,MPI_MAX,comm);
  ierr = MPI_Allreduce(cmin,cminn,N,MPIU_SCALAR,MPI_MIN,comm);
  for (i=0; i<N; i++) cmaxx[i] -= cminn[i];
  for (i=1; i<N; i++) if (cmaxx[i]>cmaxx[0]) cmaxx[0] = cmaxx[i];
  cr = cmaxx[0];
  ierr = GetDataID("variance","col-variability",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataSetReal
    ((PetscObject)A,id,cr); CHKERRQ(ierr);

  ierr = PetscFree(rmax); CHKERRQ(ierr);
  ierr = PetscFree(cmax); CHKERRQ(ierr);
  ierr = PetscFree(cmaxx); CHKERRQ(ierr);
  ierr = PetscFree(rmin); CHKERRQ(ierr);
  ierr = PetscFree(cmin); CHKERRQ(ierr);
  ierr = PetscFree(cminn); CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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PetscErrorCode DeRegisterVarianceModules ( void )

Definition at line 333 of file variance.c.

Referenced by AnaModDeregisterSalsaModules().

{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

static PetscErrorCode DiagonalAverage	(	AnaModNumericalProblem	prob,
		AnalysisItem *	rv,
		int *	lv,
		PetscBool *	flg
	)		`[static]`

This routine relies on a call to ComputeDiagonal()

Definition at line 237 of file variance.c.

References ComputeDiagonal(), GetDataID(), HASTOEXIST, id, and AnalysisItem::r.

Referenced by RegisterVarianceModules().

{
  Mat A = (Mat)prob;
  PetscReal v=0.; PetscBool has; int id; PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = GetDataID("variance","diagonal-average",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataGetReal
    ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
  if (*flg) rv->r = v;
  else {
    ierr = ComputeDiagonal(A); CHKERRQ(ierr);
    ierr = PetscObjectComposedDataGetReal
      ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
    if (*flg) rv->r = v;
  }
  
  PetscFunctionReturn(0);
}

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static PetscErrorCode DiagonalSign	(	AnaModNumericalProblem	prob,
		AnalysisItem *	rv,
		int *	lv,
		PetscBool *	flg
	)		`[static]`

This routine relies on a call to ComputeDiagonal()

Definition at line 289 of file variance.c.

References ComputeDiagonal(), GetDataID(), HASTOEXIST, AnalysisItem::i, and id.

Referenced by RegisterVarianceModules().

{
  Mat A = (Mat)prob;
  int v = 0; PetscBool has; int id; PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = GetDataID("variance","diagonal-sign",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataGetInt
    ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
  if (*flg) rv->i = v;
  else {
    ierr = ComputeDiagonal(A); CHKERRQ(ierr);
    ierr = PetscObjectComposedDataGetInt
      ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
    if (*flg) rv->i = v;
  }
  
  PetscFunctionReturn(0);
}

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static PetscErrorCode DiagonalVariance	(	AnaModNumericalProblem	prob,
		AnalysisItem *	rv,
		int *	lv,
		PetscBool *	flg
	)		`[static]`

This routine relies on a call to ComputeDiagonal()

Definition at line 263 of file variance.c.

References ComputeDiagonal(), GetDataID(), HASTOEXIST, id, and AnalysisItem::r.

Referenced by RegisterVarianceModules().

{
  Mat A = (Mat)prob;
  PetscReal v=0.; PetscBool has; int id; PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = GetDataID("variance","diagonal-variance",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataGetReal
    ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
  if (*flg) rv->r = v;
  else {
    ierr = ComputeDiagonal(A); CHKERRQ(ierr);
    ierr = PetscObjectComposedDataGetReal
      ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
    if (*flg) rv->r = v;
  }
  
  PetscFunctionReturn(0);
}

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PetscErrorCode RegisterVarianceModules ( void )

Definition at line 311 of file variance.c.

References ANALYSISDOUBLE, ANALYSISINTEGER, ColVariability(), DiagonalAverage(), DiagonalSign(), DiagonalVariance(), RegisterModule(), and RowVariability().

Referenced by AnaModRegisterSalsaModules(), and AnaModRegisterStandardModules().

{
  PetscErrorCode ierr;
  PetscFunctionBegin;

  ierr = RegisterModule
    ("variance","row-variability",ANALYSISDOUBLE,&RowVariability); CHKERRQ(ierr);
  ierr = RegisterModule
    ("variance","col-variability",ANALYSISDOUBLE,&ColVariability); CHKERRQ(ierr);

  ierr = RegisterModule
    ("variance","diagonal-average",ANALYSISDOUBLE,&DiagonalAverage); CHKERRQ(ierr);
  ierr = RegisterModule
    ("variance","diagonal-variance",ANALYSISDOUBLE,&DiagonalVariance); CHKERRQ(ierr);
  ierr = RegisterModule
    ("variance","diagonal-sign",ANALYSISINTEGER,&DiagonalSign); CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

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static PetscErrorCode RowVariability	(	AnaModNumericalProblem	prob,
		AnalysisItem *	rv,
		int *	lv,
		PetscBool *	flg
	)		`[static]`

This routine relies on a call to ComputeVariability()

Definition at line 121 of file variance.c.

References ComputeVariability(), GetDataID(), HASTOEXIST, id, and AnalysisItem::r.

Referenced by RegisterVarianceModules().

{
  Mat A = (Mat)prob;
  PetscReal v=0.; PetscBool has; int id; PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = GetDataID("variance","row-variability",&id,&has); CHKERRQ(ierr);
  HASTOEXIST(has);
  ierr = PetscObjectComposedDataGetReal
    ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
  if (*flg) rv->r = v;
  else {
    ierr = ComputeVariability(A); CHKERRQ(ierr);
    ierr = PetscObjectComposedDataGetReal
      ((PetscObject)A,id,v,*flg); CHKERRQ(ierr);
    if (*flg) rv->r = v;
  }
  
  PetscFunctionReturn(0);
}

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Functions

Detailed Description

Measurements of element variance

Usage

Function Documentation