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//------------------------------------------------------------------------------
// gb_norm: compute the norm of a GraphBLAS matrix
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
#include "gb_interface.h"
double gb_norm // compute norm (A,kind)
(
GrB_Matrix A,
int64_t norm_kind // 0, 1, 2, INT64_MAX, or INT64_MIN
)
{
//--------------------------------------------------------------------------
// get input matrix, select types and operators, and allocate X
//--------------------------------------------------------------------------
GrB_Index nrows, ncols, nvals ;
OK (GrB_Matrix_nvals (&nvals, A)) ;
if (nvals == 0) return ((double) 0) ;
GrB_Type atype, xtype ;
OK (GrB_Matrix_nrows (&nrows, A)) ;
OK (GrB_Matrix_ncols (&ncols, A)) ;
OK (GxB_Matrix_type (&atype, A)) ;
GrB_UnaryOp absop ;
GrB_Monoid sumop, maxop, minop ;
GrB_Vector t = NULL ;
GrB_Matrix X = NULL ;
bool is_complex = false ;
if (atype == GrB_FP32)
{
// if A is FP32, use the FP32 type and operators
xtype = GrB_FP32 ;
absop = GrB_ABS_FP32 ;
sumop = GrB_PLUS_MONOID_FP32 ;
maxop = GrB_MAX_MONOID_FP32 ;
minop = GrB_MIN_MONOID_FP32 ;
}
else if (atype == GxB_FC32)
{
// if A is FC32, use the FP32/FC32 type and operators
is_complex = true ;
xtype = GrB_FP32 ;
absop = GxB_ABS_FC32 ;
sumop = GrB_PLUS_MONOID_FP32 ;
maxop = GrB_MAX_MONOID_FP32 ;
minop = GrB_MIN_MONOID_FP32 ;
}
else if (atype == GxB_FC64)
{
// if A is FC64, use the FP64/FC64 type and operators
is_complex = true ;
xtype = GrB_FP64 ;
absop = GxB_ABS_FC64 ;
sumop = GrB_PLUS_MONOID_FP64 ;
maxop = GrB_MAX_MONOID_FP64 ;
minop = GrB_MIN_MONOID_FP64 ;
}
else
{
// otherwise, use FP64 type and operators; this will typecast the
// input matrix to FP64 if A is not of that type.
xtype = GrB_FP64 ;
absop = GrB_ABS_FP64 ;
sumop = GrB_PLUS_MONOID_FP64 ;
maxop = GrB_MAX_MONOID_FP64 ;
minop = GrB_MIN_MONOID_FP64 ;
}
OK (GrB_Matrix_new (&X, xtype, nrows, ncols)) ;
//--------------------------------------------------------------------------
// compute the norm
//--------------------------------------------------------------------------
double s = 0 ;
if (nrows == 1 || ncols == 1 || norm_kind == 0)
{
//----------------------------------------------------------------------
// vector or Frobenius norm
//----------------------------------------------------------------------
switch (norm_kind)
{
case 0 : // Frobenius norm
case 2 : // 2-norm
if (is_complex)
{
// X = abs (A)
OK1 (X, GrB_Matrix_apply (X, NULL, NULL, absop, A, NULL)) ;
// X = X.^2
if (atype == GxB_FC32)
{
OK1 (X, GrB_Matrix_apply_BinaryOp2nd_FP32 (X, NULL,
NULL, GxB_POW_FP32, X, (float) 2.0, NULL)) ;
}
else
{
OK1 (X, GrB_Matrix_apply_BinaryOp2nd_FP64 (X, NULL,
NULL, GxB_POW_FP64, X, (double) 2.0, NULL)) ;
}
}
else
{
// X = A.^2
OK1 (X, GrB_Matrix_apply_BinaryOp2nd_FP64 (X, NULL, NULL,
GxB_POW_FP64, A, (double) 2.0, NULL)) ;
}
// s = sum (X)
OK (GrB_Matrix_reduce_FP64 (&s, NULL, sumop, X, NULL)) ;
s = sqrt (s) ;
break ;
case 1 : // 1-norm
// X = abs (A)
OK1 (X, GrB_Matrix_apply (X, NULL, NULL, absop, A, NULL)) ;
// s = sum (X)
OK (GrB_Matrix_reduce_FP64 (&s, NULL, sumop, X, NULL)) ;
break ;
case INT64_MAX : // inf-norm
// X = abs (A)
OK1 (X, GrB_Matrix_apply (X, NULL, NULL, absop, A, NULL)) ;
// s = max (X)
OK (GrB_Matrix_reduce_FP64 (&s, NULL, maxop, X, NULL)) ;
break ;
case INT64_MIN : // (-inf)-norm
if (GB_is_dense (A))
{
// X = abs (A)
OK1 (X, GrB_Matrix_apply (X, NULL, NULL, absop, A, NULL)) ;
// s = min (X)
OK (GrB_Matrix_reduce_FP64 (&s, NULL, minop, X, NULL)) ;
}
break ;
default:
ERROR ("unknown norm") ;
break ;
}
}
else
{
//----------------------------------------------------------------------
// matrix norm
//----------------------------------------------------------------------
switch (norm_kind)
{
case 2 : // 2-norm
ERROR ("2-norm not available for GrB matrices") ;
break ;
case 1 : // 1-norm: max sum of columns of abs (A)
// X = abs (A)
OK1 (X, GrB_Matrix_apply (X, NULL, NULL, absop, A, NULL)) ;
// t = zeros (ncols,1)
OK (GrB_Vector_new (&t, xtype, ncols)) ;
// t(j) = sum of the ith column, X(:,j)
OK (GrB_Matrix_reduce_Monoid (t, NULL, NULL, sumop, X,
GrB_DESC_T0)) ;
// s = max (t)
OK (GrB_Vector_reduce_FP64 (&s, NULL, maxop, t, NULL)) ;
break ;
case INT64_MAX : // inf-norm: max sum of rows of abs (A)
// X = abs (A)
OK1 (X, GrB_Matrix_apply (X, NULL, NULL, absop, A, NULL)) ;
// t = zeros (nrows,1)
OK (GrB_Vector_new (&t, xtype, nrows)) ;
// t(i) = sum of the ith row, X(i,:)
OK (GrB_Matrix_reduce_Monoid (t, NULL, NULL, sumop, X, NULL)) ;
// s = max (t)
OK (GrB_Vector_reduce_FP64 (&s, NULL, maxop, t, NULL)) ;
break ;
case INT64_MIN :
ERROR ("(-inf)-norm not available for GrB matrices") ;
break ;
default :
ERROR ("unknown norm") ;
break ;
}
}
//--------------------------------------------------------------------------
// free workspace and return result
//--------------------------------------------------------------------------
OK (GrB_Matrix_free (&X)) ;
OK (GrB_Vector_free (&t)) ;
return (s) ;
}
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