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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  1. type CosSin = (Double, Double)

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  12. def givens(y: Double, z: Double): (Double, Double)

    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.

  13. def givensColUpdate(a: MatrixD, j: Int, k: Int, cs: (Double, Double)): 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

  14. def givensRo(i: Int, k: Int, n: Int, cs: (Double, Double)): 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

  15. def givensRoT(i: Int, k: Int, n: Int, cs: (Double, Double)): 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

  16. def givensRowUpdate(a: MatrixD, i: Int, k: Int, cs: (Double, Double)): 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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