ManagedLapack.QLDecompose Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

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
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  Span<Complex<Double>>
C# 
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
C# 
LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).
tau  Span<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(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
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  Span<Double>
C# 
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
C# 
LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).
tau  Span<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(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