z_spm_norm.c File Reference

#include "common.h"
#include <lapacke.h>
#include <cblas.h>
#include "frobeniusupdate.h"

Go to the source code of this file.

#define	LAPACKE_zlassq_work(_n_, _X_, _incx_, _scale_, _sumsq_)    __spm_zlassq( (_n_), (_X_), (_incx_), (_scale_), (_sumsq_) )
	TODO.
static int	__spm_zlassq (spm_int_t n, spm_complex64_t *x, spm_int_t incx, double *scale, double *sumsq)
	Updates the values scale and sumsq such that.
static void	z_spm_frobenius_elt_sym_diag (spm_int_t dofs, const double *valptr, double *data)
	Compute the Frobenius norm of a diagonal element within a symmetric/hermitian matrix with column/row major storage.
static void	z_spm_frobenius_elt_sym_offd (spm_int_t nbelts, const double *valptr, double *data)
	Compute the Frobenius norm of an off-diagonal element matrix in the symmetric/hermitian case.
static void	z_spm_frobenius_elt_sym (spm_int_t row, spm_int_t dofi, spm_int_t col, spm_int_t dofj, const spm_complex64_t *valptr, double *data)
	Compute the Frobenius norm of any element matrix in the symmetric/hermitian case.
static void	z_spmFrobeniusNorm_csc (const spmatrix_t *spm, double *data)
	Compute the Frobenius norm of a symmetrix/hermitian CSC matrix.
static void	z_spmFrobeniusNorm_csr (const spmatrix_t *spm, double *data)
	Compute the Frobenius norm of a symmetrix/hermitian CSR matrix.
static void	z_spmFrobeniusNorm_ijv (const spmatrix_t *spm, double *data)
	Compute the Frobenius norm of a symmetrix/hermitian IJV matrix.
double	z_spmFrobeniusNorm (const spmatrix_t *spm)
	Compute the Frobenius norm of the given spm structure.
double	z_spmMaxNorm (const spmatrix_t *spm)
	Compute the Max norm of the given spm structure.
static void	z_spm_oneinf_elt_sym_diag (spm_int_t row, spm_int_t dofi, const spm_complex64_t *valptr, double *sumtab)
	Compute the sum array for the one/inf norms of a diagonal element within a symmetric/hermitian matrix with column/row major storage.
static void	z_spm_oneinf_elt_gen_A (spm_int_t dofi, spm_int_t dofj, const spm_complex64_t *valptr, double *sumtab)
	Compute the sum array for the one/inf norms of a general element.
static void	z_spm_oneinf_elt_gen_B (spm_int_t dofi, spm_int_t dofj, const spm_complex64_t *valptr, double *sumtab)
	Compute the sum array for the one/inf norms of a general element.
static void	z_spm_oneinf_elt_gen_AB (spm_int_t row, spm_int_t dofi, spm_int_t col, spm_int_t dofj, const spm_complex64_t *valptr, double *sumtab)
	Compute the sum array for both the one and inf norms for the off-diagonal elements of symmetric/hermitian element matrices.
static void	z_spm_oneinf_elt_gen (spm_layout_t layout, spm_int_t row, spm_int_t dofi, spm_int_t col, spm_int_t dofj, const spm_complex64_t *valptr, spm_normtype_t ntype, double *sumtab)
	Compute the sum array for the one and inf norms of a general element.
static void	z_spm_oneinf_elt_sym_offd (spm_layout_t layout, spm_int_t row, spm_int_t dofi, spm_int_t col, spm_int_t dofj, const spm_complex64_t *valptr, double *sumtab)
	Compute the sum array for both the one and inf norms for the off-diagonal elements of symmetric/hermitian element matrices in either column or row major layout.
static void	z_spm_oneinf_elt (spm_mtxtype_t mtxtype, spm_layout_t layout, spm_int_t row, spm_int_t dofi, spm_int_t col, spm_int_t dofj, const spm_complex64_t *valptr, spm_normtype_t ntype, double *sumtab)
	Compute the sum array for the one/inf norm for an element matrix.
static void	z_spmOneInfNorm_csc (spm_normtype_t ntype, const spmatrix_t *spm, double *sumtab)
	Compute the one/inf norm of an spm CSC structure.
static void	z_spmOneInfNorm_csr (spm_normtype_t ntype, const spmatrix_t *spm, double *sumtab)
	Compute the one/inf norm of an spm CSR structure.
static void	z_spmOneInfNorm_ijv (spm_normtype_t ntype, const spmatrix_t *spm, double *sumtab)
	Compute the one/inf norm of an spm IJV structure.
static double	z_spmOneInfNorm (spm_normtype_t ntype, const spmatrix_t *spm)
	Compute the one/inf norm of the given spm structure given by the maximum row sum.
double	z_spmNorm (spm_normtype_t ntype, const spmatrix_t *spm)
	Compute the norm of an spm matrix.
double	z_spmNormMat (spm_normtype_t ntype, const spmatrix_t *spm, spm_int_t n, const spm_complex64_t *A, spm_int_t lda)
	Compute the norm of a dense matrix that follows the distribution of an spm matrix.

Detailed Description

SParse Matrix package norm routine.

Copyright

2016-2024 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.

Version

1.2.4

Author

Mathieu Faverge

Pierre Ramet

Tony Delarue

Matias Hastaran

Alycia Lisito

Date

2024-06-25

Generated arithmetic file from /builds/2mk6rsew/0/fpruvost/spm/src/z_spm_norm.c, normal z -> z, Fri Nov 29 11:34:31 2024

Definition in file z_spm_norm.c.

Macro Definition Documentation

LAPACKE_zlassq_work

#define LAPACKE_zlassq_work	(		_n_,
			_X_,
			_incx_,
			_scale_,
			_sumsq_
	)		__spm_zlassq( (_n_), (_X_), (_incx_), (_scale_), (_sumsq_) )

TODO.

Definition at line 88 of file z_spm_norm.c.

Function Documentation

__spm_zlassq()

static int __spm_zlassq ( spm_int_t  n, spm_complex64_t *  x, spm_int_t  incx, double *  scale, double *  sumsq  )

static

Updates the values scale and sumsq such that.

( scale**2 )*sumsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,

This routine is inspired from LAPACK zlassq function.

Parameters

[in]	n	The number of elements in the vector
[in]	x	The vector of size abs(n * incx)
[in]	incx	The increment between two elements in the vector x.
[in,out]	scale	On entry, the former scale On exit, the update scale to take into account the value
[in,out]	sumsq	On entry, the former sumsq On exit, the update sumsq to take into account the value

Returns

SPM_SUCESS to match the prototype of LAPACKE_zlassq_work

Definition at line 63 of file z_spm_norm.c.

z_spm_frobenius_elt_sym_diag()

static void z_spm_frobenius_elt_sym_diag ( spm_int_t  dofs, const double *  valptr, double *  data  )

static

Compute the Frobenius norm of a diagonal element within a symmetric/hermitian matrix with column/row major storage.

Note that column major is using the low triangular part only of the diagonal element matrices, and row major, by symmetry, is using only the upper triangular part.

The comments in the code are made for column major storage.

Parameters

[in]	dofs	TODO
[in]	valptr	TODO
[in,out]	data	TODO

Definition at line 152 of file z_spm_norm.c.

Referenced by z_spm_frobenius_elt_sym().

z_spm_frobenius_elt_sym_offd()

static void z_spm_frobenius_elt_sym_offd ( spm_int_t  nbelts, const double *  valptr, double *  data  )

static

Compute the Frobenius norm of an off-diagonal element matrix in the symmetric/hermitian case.

Parameters

[in]	nbelts	TODO
[in]	valptr	TODO
[in,out]	data

Definition at line 206 of file z_spm_norm.c.

Referenced by z_spm_frobenius_elt_sym().

z_spm_frobenius_elt_sym()

static void z_spm_frobenius_elt_sym ( spm_int_t  row, spm_int_t  dofi, spm_int_t  col, spm_int_t  dofj, const spm_complex64_t *  valptr, double *  data  )

static

Compute the Frobenius norm of any element matrix in the symmetric/hermitian case.

Parameters

[in]	row	TODO
[in]	dofi	TODO
[in]	col	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in,out]	data	TODO

Definition at line 252 of file z_spm_norm.c.

References z_spm_frobenius_elt_sym_diag(), and z_spm_frobenius_elt_sym_offd().

Referenced by z_spmFrobeniusNorm_csc(), z_spmFrobeniusNorm_csr(), and z_spmFrobeniusNorm_ijv().

z_spmFrobeniusNorm_csc()

static void z_spmFrobeniusNorm_csc ( const spmatrix_t *  spm, double *  data  )

static

Compute the Frobenius norm of a symmetrix/hermitian CSC matrix.

Parameters

[in]	spm	The spm from which the norm need to be computed.
[in,out]	data	TODO

Definition at line 283 of file z_spm_norm.c.

References spmatrix_s::baseval, spmatrix_s::colptr, spmatrix_s::dof, spmatrix_s::dofs, spmatrix_s::flttype, spmatrix_s::fmttype, spmatrix_s::loc2glob, spmatrix_s::n, spmatrix_s::replicated, spmatrix_s::rowptr, SpmComplex64, SpmCSC, spmatrix_s::values, and z_spm_frobenius_elt_sym().

Referenced by z_spmFrobeniusNorm().

z_spmFrobeniusNorm_csr()

static void z_spmFrobeniusNorm_csr ( const spmatrix_t *  spm, double *  data  )

static

Compute the Frobenius norm of a symmetrix/hermitian CSR matrix.

Parameters

[in]	spm	The spm from which the norm need to be computed.
[in,out]	data	TODO

Definition at line 350 of file z_spm_norm.c.

References spmatrix_s::baseval, spmatrix_s::colptr, spmatrix_s::dof, spmatrix_s::dofs, spmatrix_s::flttype, spmatrix_s::fmttype, spmatrix_s::loc2glob, spmatrix_s::n, spmatrix_s::replicated, spmatrix_s::rowptr, SpmComplex64, SpmCSR, spmatrix_s::values, and z_spm_frobenius_elt_sym().

Referenced by z_spmFrobeniusNorm().

z_spmFrobeniusNorm_ijv()

static void z_spmFrobeniusNorm_ijv ( const spmatrix_t *  spm, double *  data  )

static

Compute the Frobenius norm of a symmetrix/hermitian IJV matrix.

Parameters

[in]	spm	The spm from which the norm need to be computed.
[in,out]	data	TODO

Definition at line 418 of file z_spm_norm.c.

References spmatrix_s::baseval, spmatrix_s::colptr, spmatrix_s::dof, spmatrix_s::dofs, spmatrix_s::flttype, spmatrix_s::fmttype, spmatrix_s::nnz, spmatrix_s::rowptr, SpmComplex64, SpmIJV, spmatrix_s::values, and z_spm_frobenius_elt_sym().

Referenced by z_spmFrobeniusNorm().

z_spmFrobeniusNorm()

double z_spmFrobeniusNorm

(

const spmatrix_t *

spm

)

Compute the Frobenius norm of the given spm structure.

||A|| = sqrt( sum( a_ij ^ 2 ) )

Parameters

[in]

spm

The spm from which the norm need to be computed.

Returns

The computed frobenius norm

Definition at line 480 of file z_spm_norm.c.

References spmatrix_s::clustnbr, spmatrix_s::comm, spmatrix_s::fmttype, spmatrix_s::mtxtype, spmatrix_s::nnzexp, spmatrix_s::replicated, SpmCSC, SpmCSR, SpmGeneral, SpmIJV, spmatrix_s::values, z_spmFrobeniusNorm_csc(), z_spmFrobeniusNorm_csr(), and z_spmFrobeniusNorm_ijv().

Referenced by z_spmNorm().

z_spmMaxNorm()

double z_spmMaxNorm

(

const spmatrix_t *

spm

)

Compute the Max norm of the given spm structure.

||A|| = max( abs(a_ij) )

Parameters

[in]

spm

The spm from which the norm need to be computed.

Returns

The computed max norm

Definition at line 543 of file z_spm_norm.c.

References spmatrix_s::clustnbr, spmatrix_s::comm, spmatrix_s::nnzexp, spmatrix_s::replicated, and spmatrix_s::values.

Referenced by z_spmNorm().

z_spm_oneinf_elt_sym_diag()

static void z_spm_oneinf_elt_sym_diag ( spm_int_t  row, spm_int_t  dofi, const spm_complex64_t *  valptr, double *  sumtab  )

static

Compute the sum array for the one/inf norms of a diagonal element within a symmetric/hermitian matrix with column/row major storage.

Note that column major is using the low triangular part only of the diagonal element matrices, and row major, by symmetry, is using only the upper triangular part.

The comments in the code are made for column major storage.

Parameters

[in]	row	TODO
[in]	dofi	TODO
[in]	valptr	TODO
[in,out]	sumtab	TODO

Definition at line 591 of file z_spm_norm.c.

Referenced by z_spm_oneinf_elt().

z_spm_oneinf_elt_gen_A()

static void z_spm_oneinf_elt_gen_A ( spm_int_t  dofi, spm_int_t  dofj, const spm_complex64_t *  valptr, double *  sumtab  )

static

Compute the sum array for the one/inf norms of a general element.

We can observe two cases A and B;

---

| | | | | | |________| | | | | | | |A| OR |________| |B| |__|__|__| |_| |________| |_|

---

|___B____| |___A____|

          | One Norm | Inf norm |

----------—+-------—+-------—+ Column Major | B | A | ----------—+-------—+-------—+ Row Major | A | B | ----------—+-------—+-------—+

Warning

: The sumtab must be shifted at the right place on input

Parameters

[in]	dofi	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in,out]	sumtab	TODO

Definition at line 659 of file z_spm_norm.c.

Referenced by z_spm_oneinf_elt_gen().

z_spm_oneinf_elt_gen_B()

static void z_spm_oneinf_elt_gen_B ( spm_int_t  dofi, spm_int_t  dofj, const spm_complex64_t *  valptr, double *  sumtab  )

static

Compute the sum array for the one/inf norms of a general element.

See z_spm_oneinf_elt_gen_A()

Parameters

[in]	dofi	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in,out]	sumtab	TODO

Definition at line 698 of file z_spm_norm.c.

Referenced by z_spm_oneinf_elt_gen().

z_spm_oneinf_elt_gen_AB()

static void z_spm_oneinf_elt_gen_AB ( spm_int_t  row, spm_int_t  dofi, spm_int_t  col, spm_int_t  dofj, const spm_complex64_t *  valptr, double *  sumtab  )

static

Compute the sum array for both the one and inf norms for the off-diagonal elements of symmetric/hermitian element matrices.

See z_spm_oneinf_elt_gen_A()

Parameters

[in]	row	TODO
[in]	dofi	TODO
[in]	col	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in,out]	sumtab	TODO

Definition at line 744 of file z_spm_norm.c.

Referenced by z_spm_oneinf_elt_sym_offd().

z_spm_oneinf_elt_gen()

static void z_spm_oneinf_elt_gen ( spm_layout_t  layout, spm_int_t  row, spm_int_t  dofi, spm_int_t  col, spm_int_t  dofj, const spm_complex64_t *  valptr, spm_normtype_t  ntype, double *  sumtab  )

static

Compute the sum array for the one and inf norms of a general element.

Parameters

[in]	layout	TODO
[in]	row	TODO
[in]	dofi	TODO
[in]	col	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in]	ntype	TODO
[in,out]	sumtab	TODO

Definition at line 799 of file z_spm_norm.c.

References SpmColMajor, SpmInfNorm, SpmOneNorm, z_spm_oneinf_elt_gen_A(), and z_spm_oneinf_elt_gen_B().

Referenced by z_spm_oneinf_elt().

z_spm_oneinf_elt_sym_offd()

static void z_spm_oneinf_elt_sym_offd ( spm_layout_t  layout, spm_int_t  row, spm_int_t  dofi, spm_int_t  col, spm_int_t  dofj, const spm_complex64_t *  valptr, double *  sumtab  )

static

Compute the sum array for both the one and inf norms for the off-diagonal elements of symmetric/hermitian element matrices in either column or row major layout.

Parameters

[in]	layout	TODO
[in]	row	TODO
[in]	dofi	TODO
[in]	col	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in,out]	sumtab	TODO

Definition at line 860 of file z_spm_norm.c.

References SpmColMajor, and z_spm_oneinf_elt_gen_AB().

Referenced by z_spm_oneinf_elt().

z_spm_oneinf_elt()

static void z_spm_oneinf_elt ( spm_mtxtype_t  mtxtype, spm_layout_t  layout, spm_int_t  row, spm_int_t  dofi, spm_int_t  col, spm_int_t  dofj, const spm_complex64_t *  valptr, spm_normtype_t  ntype, double *  sumtab  )

static

Compute the sum array for the one/inf norm for an element matrix.

Parameters

[in]	mtxtype	TODO
[in]	layout	TODO
[in]	row	TODO
[in]	dofi	TODO
[in]	col	TODO
[in]	dofj	TODO
[in]	valptr	TODO
[in]	ntype	TODO
[in,out]	sumtab	TODO

Definition at line 912 of file z_spm_norm.c.

References SpmGeneral, z_spm_oneinf_elt_gen(), z_spm_oneinf_elt_sym_diag(), and z_spm_oneinf_elt_sym_offd().

Referenced by z_spmOneInfNorm_csc(), z_spmOneInfNorm_csr(), and z_spmOneInfNorm_ijv().

z_spmOneInfNorm_csc()

static void z_spmOneInfNorm_csc ( spm_normtype_t  ntype, const spmatrix_t *  spm, double *  sumtab  )

static

Compute the one/inf norm of an spm CSC structure.

Parameters

[in]	ntype	TODO
[in]	spm	TODO
[in,out]	sumtab	TODO

Definition at line 953 of file z_spm_norm.c.

References spmatrix_s::baseval, spmatrix_s::colptr, spmatrix_s::dof, spmatrix_s::dofs, spmatrix_s::layout, spmatrix_s::loc2glob, spmatrix_s::mtxtype, spmatrix_s::n, spmatrix_s::replicated, spmatrix_s::rowptr, spmatrix_s::values, and z_spm_oneinf_elt().

Referenced by z_spmOneInfNorm().

z_spmOneInfNorm_csr()

static void z_spmOneInfNorm_csr ( spm_normtype_t  ntype, const spmatrix_t *  spm, double *  sumtab  )

static

Compute the one/inf norm of an spm CSR structure.

Parameters

[in]	ntype	TODO
[in]	spm	TODO
[in,out]	sumtab	TODO

Definition at line 1019 of file z_spm_norm.c.

References spmatrix_s::baseval, spmatrix_s::colptr, spmatrix_s::dof, spmatrix_s::dofs, spmatrix_s::layout, spmatrix_s::loc2glob, spmatrix_s::mtxtype, spmatrix_s::n, spmatrix_s::replicated, spmatrix_s::rowptr, spmatrix_s::values, and z_spm_oneinf_elt().

Referenced by z_spmOneInfNorm().

z_spmOneInfNorm_ijv()

static void z_spmOneInfNorm_ijv ( spm_normtype_t  ntype, const spmatrix_t *  spm, double *  sumtab  )

static

Compute the one/inf norm of an spm IJV structure.

Parameters

[in]	ntype	TODO
[in]	spm	TODO
[in,out]	sumtab	TODO

Definition at line 1085 of file z_spm_norm.c.

References spmatrix_s::baseval, spmatrix_s::colptr, spmatrix_s::dof, spmatrix_s::dofs, spmatrix_s::layout, spmatrix_s::mtxtype, spmatrix_s::nnz, spmatrix_s::rowptr, spmatrix_s::values, and z_spm_oneinf_elt().

Referenced by z_spmOneInfNorm().

z_spmOneInfNorm()

static double z_spmOneInfNorm ( spm_normtype_t  ntype, const spmatrix_t *  spm  )

static

Compute the one/inf norm of the given spm structure given by the maximum row sum.

• SpmOneNorm: ||A|| = max_j( sum_i(|a_ij|) )
• SpmInfNorm: ||A|| = max_i( sum_j(|a_ij|) )

Parameters

[in]	ntype	The type of norm to compute.
[in]	spm	The spm from which the norm need to be computed.

Returns

The computed one norm

Definition at line 1149 of file z_spm_norm.c.

References spmatrix_s::clustnbr, spmatrix_s::comm, spmatrix_s::fmttype, spmatrix_s::gNexp, spmatrix_s::replicated, SpmCSC, SpmCSR, SpmIJV, z_spmOneInfNorm_csc(), z_spmOneInfNorm_csr(), and z_spmOneInfNorm_ijv().

Referenced by z_spmNorm().