AlgVector

Files
file	AlgVectorMath.c
	Basic vector arithmatic.

Functions
void	AlgVectorZero (double *aV, size_t n)
	sets all elements of the given vector to zero. More...
double	AlgVectorNorm (double *aV, size_t n)
	Computes the norm of the given vector \(\mathbf{a}\) with n elements: \[ \|\mathbf{a}\| = \sqrt{\mathbf{a} \cdot \mathbf{a}}. \] . More...
double	AlgVectorDot (double *aV, double *bV, size_t n)
	Computes the scalar (dot) product of the two vectors \(\mathbf{a}\) and \(\mathbf{b}\) each with n elements: \[ \mathbf{a} \cdot \mathbf{b} = \sum_{i = 0}^{n - 1}{a_i b_i} \] . More...
void	AlgVectorAdd (double *aV, double *bV, double *cV, size_t n)
	Adds vector \(\mathbf{b}\) to vector \(\mathbf{c}\). Computes \(a_i = b_i + c_i, \forall i \in [0 \ldots n - 1]\). More...
void	AlgVectorSub (double *aV, double *bV, double *cV, size_t n)
	Subtracts vector \(\mathbf{c}\) from vector \(\mathbf{b}\). Computes \(a_i = b_i - c_i, \forall i \in [0 \ldots n - 1]\). More...
void	AlgVectorCopy (double *aV, double *bV, size_t n)
	Copies one vector \(\mathbf{b}\) to vector \(\mathbf{a}\). \(a_i = b_i, \forall i \in [0 \ldots n - 1]\). More...

Detailed Description

Function Documentation

AlgVectorZero()

void AlgVectorZero	(	double *	aV,
		size_t	n
	)

sets all elements of the given vector to zero.

Parameters

aV	Given vector.
n	Number of elements.

Referenced by AlgMatrixTVectorMul().

AlgVectorNorm()

double AlgVectorNorm	(	double *	aV,
		size_t	n
	)

Computes the norm of the given vector \(\mathbf{a}\) with n elements:

\[ \|\mathbf{a}\| = \sqrt{\mathbf{a} \cdot \mathbf{a}}. \]

.

Returns

Norm of the vector.

Note

For efficiency the given parameters are not checked.

Vector size is limited only by address space.

Parameters

aV	Given vector \(\mathbf{a}\),
n	Number of elements in \(\mathbf{a}\).

References AlgVectorDot().

Referenced by AlgMatrixCGSolve(), and AlgMatrixSolveLSQR().

AlgVectorDot()

double AlgVectorDot	(	double *	aV,
		double *	bV,
		size_t	n
	)

Computes the scalar (dot) product of the two vectors \(\mathbf{a}\) and \(\mathbf{b}\) each with n elements:

\[ \mathbf{a} \cdot \mathbf{b} = \sum_{i = 0}^{n - 1}{a_i b_i} \]

.

Returns

Scalar (dot) product of the vectors.

Note

For efficiency the given parameters are not checked.

Vector size is limited only by address space.

Parameters

aV	Vector \(\mathbf{a}\).
bV	Vector \(\mathbf{b}\).
n	Number of elements in each of the vectors.

Referenced by AlgMatrixCGSolve(), and AlgVectorNorm().

AlgVectorAdd()

void AlgVectorAdd	(	double *	aV,
		double *	bV,
		double *	cV,
		size_t	n
	)

Adds vector \(\mathbf{b}\) to vector \(\mathbf{c}\). Computes \(a_i = b_i + c_i, \forall i \in [0 \ldots n - 1]\).

Returns

void

Note

For efficiency the given parameters are not checked.

Vector size is limited only by address space.

Parameters

aV	Vector \(\mathbf{a}\).
bV	Vector \(\mathbf{b}\).
cV	Vector \(\mathbf{c}\).
n	Number of elements in each of the vectors.

AlgVectorSub()

void AlgVectorSub	(	double *	aV,
		double *	bV,
		double *	cV,
		size_t	n
	)

Subtracts vector \(\mathbf{c}\) from vector \(\mathbf{b}\). Computes \(a_i = b_i - c_i, \forall i \in [0 \ldots n - 1]\).

Returns

void

Note

For efficiency the given parameters are not checked.

Vector size is limited only by address space.

Parameters

aV	Vector \(\mathbf{a}\).
bV	Vector \(\mathbf{b}\).
cV	Vector \(\mathbf{c}\).
n	Number of elements in each of the vectors.

Referenced by AlgMatrixCGSolve().

AlgVectorCopy()

void AlgVectorCopy	(	double *	aV,
		double *	bV,
		size_t	n
	)

Copies one vector \(\mathbf{b}\) to vector \(\mathbf{a}\). \(a_i = b_i, \forall i \in [0 \ldots n - 1]\).

Returns

void

Note

For efficiency the given parameters are not checked.

Vector size is limited only by address space.

Parameters

aV	Vector \(\mathbf{a}\).
bV	Vector \(\mathbf{b}\).
n	Number of elements in each of the vectors.

Referenced by AlgMatrixCGSolve(), AlgMatrixCopy(), AlgMatrixSolveLSQR(), and AlgMatrixTVectorMulAdd().