DecompositionOperations<TReal, TComplex>.LQDecompose Method

public abstract void LQDecompose(
	int m,
	int n,
	Array2D<TReal> a,
	Array1D<TReal> tau,
	out int info
)

Public MustOverride Sub LQDecompose ( 
	m As Integer,
	n As Integer,
	a As Array2D(Of TReal),
	tau As Array1D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void LQDecompose(
	int m, 
	int n, 
	Array2D<TReal> a, 
	Array1D<TReal> tau, 
	[OutAttribute] int% info
) abstract

abstract LQDecompose : 
        m : int * 
        n : int * 
        a : Array2D<'TReal> * 
        tau : Array1D<'TReal> * 
        info : int byref -> unit 

Parameters

m  Int32

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

n  Int32

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

a  Array2D<TReal>

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A is DOUBLE PRECISION 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 orthogonal matrix Q as a
product of elementary reflectors (see Further Details).

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

tau  Array1D<TReal>

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

info  Int32

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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(2) H(1), where k = min(m,n).
Each H(i) has the form
   H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; 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 abstract void LQDecompose(
	int m,
	int n,
	Array2D<TComplex> a,
	Array1D<TComplex> tau,
	out int info
)

Public MustOverride Sub LQDecompose ( 
	m As Integer,
	n As Integer,
	a As Array2D(Of TComplex),
	tau As Array1D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void LQDecompose(
	int m, 
	int n, 
	Array2D<TComplex> a, 
	Array1D<TComplex> tau, 
	[OutAttribute] int% info
) abstract

abstract LQDecompose : 
        m : int * 
        n : int * 
        a : Array2D<'TComplex> * 
        tau : Array1D<'TComplex> * 
        info : int byref -> unit 

Parameters

m  Int32

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

n  Int32

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

a  Array2D<TComplex>

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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).

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

tau  Array1D<TComplex>

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

info  Int32

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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