Generic Decomposition Operations<T>.QLDecompose Method
Definition
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.3
Overload List
QLDecompose( | |
QLDecompose( | |
QLDecompose( | Computes a QL factorization of a complex M-by-N matrix A: A = Q * L. |
QLDecompose( | Computes a QL factorization of a complex M-by-N matrix A: A = Q * L. |
QLDecompose( | Computes a QL factorization of a complex M-by-N matrix A: A = Q * L. |
QLDecompose( | Computes a QL factorization of a complex M-by-N matrix A: A = Q * L. |
QLDecompose(Int32, Int32, Span<T>, Int32, Span<T>, Int32)
Computes a QL factorization of a complex M-by-N matrix A: A = Q * L.
public override void QLDecompose(
int m,
int n,
Span<T> a,
int lda,
Span<T> 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<T>
-
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<T>
-
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:
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<Complex<T>>, Int32, Span<Complex<T>>, Int32)
Computes a QL factorization of a complex M-by-N matrix A: A = Q * L.
public override void QLDecompose(
int m,
int n,
Span<Complex<T>> a,
int lda,
Span<Complex<T>> 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<T>>
-
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<T>>
-
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:
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