scalation.linalgebra

Givens

object Givens

The Givens objects has methods for determinng values 'c = cos(theta)' and 's = sin(theta) for Givens rotation matrices as well as methods for applying Givens rotations.

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type CosSin = (Double, Double)

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def givens(y: Double, z: Double): CosSin

Create the values for a Givens 2-by-2 rotation matrix.
Create the values for a Givens 2-by-2 rotation matrix. Given scalars 'y' and 'z', efficiently compute 'c = cos(theta)' and 's = sin(theta)' that can be used to form the rotation matrix.
y
the first scalar
z
the second scalar

See also
Algorithm 5.1.3 in Matrix Computation.
def givensColUpdate(a: MatrixD, j: Int, k: Int, cs: CosSin): Unit

Efficiently perform a Givens column update: a = a * g (i, k, theta).
Efficiently perform a Givens column update: a = a * g (i, k, theta). The update just affects two columns. FIX
a
the matrix to update
j
the first column ??
k
the second column ??
cs
the (cosine, sine) of theta
def givensRo(i: Int, k: Int, n: Int, cs: CosSin): MatrixD

Return a Givens rotation matrix with angle 'theta = atan(s/c)'.
Return a Givens rotation matrix with angle 'theta = atan(s/c)'. A matrix is post-multiplied by the Given matrix to clear element (i, k). The 2-by-2 rotation is embedded in an identity matrix of dimension 'n'.
i
the first diagonal position (i, i)
k
the second diagonal position (k, k)
n
the dimension of the resulting rotation matrix
cs
the (cosine, sine) of theta
def givensRoT(i: Int, k: Int, n: Int, cs: CosSin): MatrixD

Return a transposed Givens rotation matrix with angle 'theta = atan(s/c)'.
Return a transposed Givens rotation matrix with angle 'theta = atan(s/c)'. A matrix is pre-multiplied by the Given matrix to clear element (k, i). The 2-by-2 rotation is embedded in an identity matrix of dimension 'n'.
i
the first diagonal position (i, i)
k
the second diagonal position (k, k)
n
the dimension of the resulting rotation matrix
cs
the (cosine, sine) of theta
def givensRowUpdate(a: MatrixD, i: Int, k: Int, cs: CosSin): Unit

Efficiently perform a Givens row update: 'a = g (i, k, theta).
Efficiently perform a Givens row update: 'a = g (i, k, theta).t * a'. The update just affects two row. FIX
a
the matrix to update
i
the first row ??
k
the second row ??
cs
the (cosine, sine) of theta
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