scamac_vector.h File Reference

Vector creation and manipulation. More...

#include "scamac_inttypes.h"
#include "scamac_defs.h"
#include "scamac_error.h"
#include <stdbool.h>
#include <complex.h>

Go to the source code of this file.

Functions
ScamacErrorCode	scamac_vectormem_alloc (ScamacInt nv, int m, ScamacValType valtype, ScamacVectorMem **v)
	Allocate vector(s)equivalent to calling scamac_vector_multiple_alloc with m=1. More...
ScamacErrorCode	scamac_vectormem_free (ScamacVectorMem *v)
ScamacErrorCode	scamac_vector_view (ScamacVectorMem *vm, ScamacVector **v)
ScamacErrorCode	scamac_vector_view_single (ScamacVectorMem *vm, int i, ScamacVector **v)
ScamacErrorCode	scamac_vector_free (ScamacVector *v)
ScamacErrorCode	scamac_vector_sub_single (const ScamacVector *v, int i, ScamacVector **w)
ScamacErrorCode	scamac_vector_complement (const ScamacVector *v, ScamacVector **w)
ScamacErrorCode	scamac_vector_align (ScamacVector *v)
ScamacErrorCode	scamac_vector_assign (const char *which, ScamacVector *v)
ScamacErrorCode	scamac_vector_copy (const ScamacVector *v, ScamacVector *w)
ScamacErrorCode	scamac_vector_dot (const ScamacVector *v1, const ScamacVector *v2, double *dot)
ScamacErrorCode	scamac_vector_nrm2 (const ScamacVector *v, double *nrm)
ScamacErrorCode	scamac_vector_dotmatrix (const ScamacVector *v1, const ScamacVector *v2, double *dotm)
ScamacErrorCode	scamac_vector_gram (const ScamacVector *v, double *gram)
ScamacErrorCode	scamac_mvector_axpby (const ScamacVector *x, ScamacVector *y, const double *a, const double *b)
ScamacErrorCode	scamac_mvector_scal (ScamacVector *x, const double *s)
ScamacErrorCode	scamac_vector_transform (const ScamacVector *x, const double *a, ScamacVector *y)
ScamacErrorCode	scamac_vector_orthogonalize (const ScamacVector *v, ScamacVector *w, double *r, int *p)

Detailed Description

Vector creation and manipulation.

Author

Andreas Alvermann (University of Greifswald)

Date

May 2018 — today

Function Documentation

scamac_mvector_axpby()

ScamacErrorCode scamac_mvector_axpby	(	const ScamacVector *	x,
		ScamacVector *	y,
		const double *	a,
		const double *	b
	)

y -> a*x + b*y

scamac_mvector_scal()

ScamacErrorCode scamac_mvector_scal	(	ScamacVector *	x,
		const double *	s
	)

x[i] -> s[i]*x[i] for all vectors i

scamac_vector_align()

ScamacErrorCode scamac_vector_align

(

ScamacVector *

v

)

move vectors in v to the front of vecmem - e.g. to guarantee consecutive arrangement in memory, or just to simplify bookkeeping

scamac_vector_assign()

ScamacErrorCode scamac_vector_assign	(	const char *	which,
		ScamacVector *	v
	)

for testing purposes: assign specify types of vectors which = "Hilbert", "Nearly_Dependent", "Unit"

scamac_vector_complement()

ScamacErrorCode scamac_vector_complement	(	const ScamacVector *	v,
		ScamacVector **	w
	)

set w to vectors not contained in v

scamac_vector_copy()

ScamacErrorCode scamac_vector_copy	(	const ScamacVector *	v,
		ScamacVector *	w
	)

get an actual copy of vectors v, w must be exclusive [scamac_vector_check_exclusivity(v,w) == TRUE]

scamac_vector_dot()

ScamacErrorCode scamac_vector_dot	(	const ScamacVector *	v1,
		const ScamacVector *	v2,
		double *	dot
	)

vector-by-vector dot product length v1 = length v2, length dot >= length v{1,2}

scamac_vector_dotmatrix()

ScamacErrorCode scamac_vector_dotmatrix	(	const ScamacVector *	v1,
		const ScamacVector *	v2,
		double *	dotm
	)

matrix of scalar products V1^+ V2 length dotm >= length v1 * length v2 on exit, dotm[i + j * (length v1) ] = < v1[i], v2[j] > for 0<=i < length v1, 0<=j < length v2

scamac_vector_free()

ScamacErrorCode scamac_vector_free

(

ScamacVector *

v

)

Note

: does nothing if v==NULL

scamac_vector_gram()

ScamacErrorCode scamac_vector_gram	(	const ScamacVector *	v,
		double *	gram
	)

matrix of scalar products V^+ W if V==W, this is the Gram matrix length gram >= length v ** 2 on exit, gram[i + j * (length v) ] = < v[i], v[j] > for 0<= i,j < length v

remark: identical to dotmatrix with v1=v2=v, but computes less dot products

scamac_vector_nrm2()

ScamacErrorCode scamac_vector_nrm2	(	const ScamacVector *	v,
		double *	nrm
	)

vector norm

scamac_vector_orthogonalize()

ScamacErrorCode scamac_vector_orthogonalize	(	const ScamacVector *	v,
		ScamacVector *	w,
		double *	r,
		int *	p
	)

orthogonalize vectors in w against vectors in v

vectors in v must be orthogonal + normalized

if v = (v1, ..., vm) and w = (w1, ..., wn): on return, vectors in w are normalized, and the full set (v1, ..., vm, w1, ..., wn) is orthogonal

in this basis, the original input vectors in w have the expansion W = (V W_out) R P with the upper trapezoidal (m+n) x n matrix R and the n x n permutation matrix P.

[up to a permutation, R is upper triangular. The permutation is returned in P]

scamac_vector_sub_single()

ScamacErrorCode scamac_vector_sub_single	(	const ScamacVector *	v,
		int	i,
		ScamacVector **	w
	)

get a (view of) a subsets of vectors

Note

: if *w == NULL, the ScamacVector object is allocated first. if *w != NULL, it is overwritten. No actual copy of vectors is produced . /// This is incorrect [ It is legitimate that v == w (in which case, v is overwritten). ]

scamac_vector_transform()

ScamacErrorCode scamac_vector_transform	(	const ScamacVector *	x,
		const double *	a,
		ScamacVector *	y
	)

Y = X A, that is y_i = sum_j a_ji x_j requires matrix A = m x n, where m: number of vectors in X n: number of vectors in Y

scamac_vector_view()

ScamacErrorCode scamac_vector_view	(	ScamacVectorMem *	vm,
		ScamacVector **	v
	)

construct the "identity view" of vm on first call with v, must have v==NULL

scamac_vector_view_single()

ScamacErrorCode scamac_vector_view_single	(	ScamacVectorMem *	vm,
		int	i,
		ScamacVector **	v
	)

construct a "single vector view" of vm

scamac_vectormem_alloc()

ScamacErrorCode scamac_vectormem_alloc	(	ScamacInt	nv,
		int	m,
		ScamacValType	valtype,
		ScamacVectorMem **	v
	)

Allocate vector(s)equivalent to calling scamac_vector_multiple_alloc with m=1.

Note

: throws an error if *v != NULL on invocation

scamac_vectormem_free()

ScamacErrorCode scamac_vectormem_free

(

ScamacVectorMem *

v

)

Note

: does nothing if v==NULL