ManagedLapack.QLDecompose Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.3.0

Overload List

QLDecompose(Int32, Int32, Span<Complex<Double>>, Int32, Span<Complex<Double>>, Int32)

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

C# 
public override void QLDecompose(
	int m,
	int n,
	Span<Complex<double>> a,
	int lda,
	Span<Complex<double>> tau,
	out int info
)

Parameters

m  Int32
M is INTEGER The number of rows of the matrix A. M >= 0.
n  Int32
N is INTEGER The number of columns of the matrix A. N >= 0.
a  Span<Complex<Double>>
A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
lda  Int32
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
tau  Span<Complex<Double>>
TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
info  Int32
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Remarks

Further Details:

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**H where tau is a complex scalar, and v is a complex vector with v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

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

Date: November 2011

QLDecompose(Int32, Int32, Span<Double>, Int32, Span<Double>, Int32)

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

C# 
public override void QLDecompose(
	int m,
	int n,
	Span<double> a,
	int lda,
	Span<double> tau,
	out int info
)

Parameters

m  Int32
M is INTEGER The number of rows of the matrix A. M >= 0.
n  Int32
N is INTEGER The number of columns of the matrix A. N >= 0.
a  Span<Double>
A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
lda  Int32
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
tau  Span<Double>
TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
info  Int32
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Remarks

Further Details:

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**H where tau is a complex scalar, and v is a complex vector with v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

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

Date: November 2011

See Also