ManagedLapack.LQDecompose Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

Overload List

LQDecompose(Int32, Int32, Array2D<Complex<Double>>, Array1D<Complex<Double>>, Int32)

Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.

LQDecompose(Int32, Int32, Array2D<Double>, Array1D<Double>, Int32)

Computes an LQ factorization of a real M-by-N matrix A: A = L * Q.

LQDecompose(Int32, Int32, Array2D<Complex<Double>>, Array1D<Complex<Double>>, Int32)

Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.

C#
public override void LQDecompose(
	int m,
	int n,
	Array2D<Complex<double>> a,
	Array1D<Complex<double>> tau,
	out int info
)

Parameters

m  Int32
C#
M is INTEGER
The number of rows of the matrix A.  M >= 0.
n  Int32
C#
N is INTEGER
The number of columns of the matrix A.  N >= 0.
a  Array2D<Complex<Double>>
C#
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors (see Further Details).
tau  Array1D<Complex<Double>>
C#
TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
info  Int32
C#
INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

Further Details:

C#
The matrix Q is represented as a product of elementary reflectors
   Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
Each H(i) has the form
   H(i) = I - tau * v * v**H
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

LQDecompose(Int32, Int32, Array2D<Double>, Array1D<Double>, Int32)

Computes an LQ factorization of a real M-by-N matrix A: A = L * Q.

C#
public override void LQDecompose(
	int m,
	int n,
	Array2D<double> a,
	Array1D<double> tau,
	out int info
)

Parameters

m  Int32
C#
M is INTEGER
The number of rows of the matrix A.  M >= 0.
n  Int32
C#
N is INTEGER
The number of columns of the matrix A.  N >= 0.
a  Array2D<Double>
C#
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors (see Further Details).
tau  Array1D<Double>
C#
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
info  Int32
C#
INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

Further Details:

C#
The matrix Q is represented as a product of elementary reflectors
   Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
   H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

See Also