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().