GenericDecompositionOperations<T>.LQDecompose Method

public override void LQDecompose(
	int m,
	int n,
	Span<T> a,
	int lda,
	Span<T> tau,
	out int info
)

Public Overrides Sub LQDecompose ( 
	m As Integer,
	n As Integer,
	a As Span(Of T),
	lda As Integer,
	tau As Span(Of T),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void LQDecompose(
	int m, 
	int n, 
	Span<T> a, 
	int lda, 
	Span<T> tau, 
	[OutAttribute] int% info
) override

abstract LQDecompose : 
        m : int * 
        n : int * 
        a : Span<'T> * 
        lda : int * 
        tau : Span<'T> * 
        info : int byref -> unit 
override LQDecompose : 
        m : int * 
        n : int * 
        a : Span<'T> * 
        lda : int * 
        tau : Span<'T> * 
        info : int byref -> unit 

Parameters

m  Int32

C# Copy

M is INTEGER
The number of rows of the matrix A.  M >= 0.

n  Int32

C# Copy

N is INTEGER
The number of columns of the matrix A.  N >= 0.

a  Span<T>

C# Copy

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# Copy

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

tau  Span<T>

C# Copy

TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

info  Int32

C# Copy

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

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

public override void LQDecompose(
	int m,
	int n,
	Span<Complex<T>> a,
	int lda,
	Span<Complex<T>> tau,
	out int info
)

Public Overrides Sub LQDecompose ( 
	m As Integer,
	n As Integer,
	a As Span(Of Complex(Of T)),
	lda As Integer,
	tau As Span(Of Complex(Of T)),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void LQDecompose(
	int m, 
	int n, 
	Span<Complex<T>> a, 
	int lda, 
	Span<Complex<T>> tau, 
	[OutAttribute] int% info
) override

abstract LQDecompose : 
        m : int * 
        n : int * 
        a : Span<Complex<'T>> * 
        lda : int * 
        tau : Span<Complex<'T>> * 
        info : int byref -> unit 
override LQDecompose : 
        m : int * 
        n : int * 
        a : Span<Complex<'T>> * 
        lda : int * 
        tau : Span<Complex<'T>> * 
        info : int byref -> unit 

Parameters

m  Int32

C# Copy

M is INTEGER
The number of rows of the matrix A.  M >= 0.

n  Int32

C# Copy

N is INTEGER
The number of columns of the matrix A.  N >= 0.

a  Span<Complex<T>>

C# Copy

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# Copy

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

tau  Span<Complex<T>>

C# Copy

TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

info  Int32

C# Copy

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

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

Reference