Managed Lapack Of Single.LQDecompose Method
Definition
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.0.1
Overload List
LQDecompose( | |
LQDecompose( | |
LQDecompose( | Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. |
LQDecompose( | Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. |
LQDecompose( | Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. |
LQDecompose( | Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. |
LQDecompose(Int32, Int32, Span<Complex<Single>>, Int32, Span<Complex<Single>>, Int32)
Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.
public override void LQDecompose(
int m,
int n,
Span<Complex<float>> a,
int lda,
Span<Complex<float>> 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<Single>>
-
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).
- lda Int32
-
C# LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
- tau Span<Complex<Single>>
-
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 . . . 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, Span<Single>, Int32, Span<Single>, Int32)
Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.
public override void LQDecompose(
int m,
int n,
Span<float> a,
int lda,
Span<float> 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<Single>
-
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).
- lda Int32
-
C# LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
- tau Span<Single>
-
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 . . . 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