DecompositionOperations<TReal, TComplex>.QLDecompose Method

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

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

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

member QLDecompose : 
        m : int * 
        n : int * 
        a : Array2D<'TReal> * 
        tau : Array1D<'TReal> * 
        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  Array2D<TReal>

C# Copy

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

C# Copy

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

tau  Array1D<TReal>

C# Copy

TAU is DOUBLE PRECISION 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(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(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

public void QLDecompose(
	int m,
	int n,
	Array2D<TComplex> a,
	Array1D<TComplex> tau,
	out int info
)

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

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

member QLDecompose : 
        m : int * 
        n : int * 
        a : Array2D<'TComplex> * 
        tau : Array1D<'TComplex> * 
        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  Array2D<TComplex>

C# Copy

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).

C# Copy

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

tau  Array1D<TComplex>

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(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

public void QLDecompose(
	int m,
	int n,
	Span2D<TReal> a,
	Span<TReal> tau,
	out int info
)

Public Sub QLDecompose ( 
	m As Integer,
	n As Integer,
	a As Span2D(Of TReal),
	tau As Span(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void QLDecompose(
	int m, 
	int n, 
	Span2D<TReal> a, 
	Span<TReal> tau, 
	[OutAttribute] int% info
)

member QLDecompose : 
        m : int * 
        n : int * 
        a : Span2D<'TReal> * 
        tau : Span<'TReal> * 
        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  Span2D<TReal>

C# Copy

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

C# Copy

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

tau  Span<TReal>

C# Copy

TAU is DOUBLE PRECISION 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(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(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

public void QLDecompose(
	int m,
	int n,
	Span2D<TComplex> a,
	Span<TComplex> tau,
	out int info
)

Public Sub QLDecompose ( 
	m As Integer,
	n As Integer,
	a As Span2D(Of TComplex),
	tau As Span(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
void QLDecompose(
	int m, 
	int n, 
	Span2D<TComplex> a, 
	Span<TComplex> tau, 
	[OutAttribute] int% info
)

member QLDecompose : 
        m : int * 
        n : int * 
        a : Span2D<'TComplex> * 
        tau : Span<'TComplex> * 
        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  Span2D<TComplex>

C# Copy

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).

C# Copy

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

tau  Span<TComplex>

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(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

public abstract void QLDecompose(
	int m,
	int n,
	Span<TReal> a,
	int lda,
	Span<TReal> tau,
	out int info
)

Public MustOverride Sub QLDecompose ( 
	m As Integer,
	n As Integer,
	a As Span(Of TReal),
	lda As Integer,
	tau As Span(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void QLDecompose(
	int m, 
	int n, 
	Span<TReal> a, 
	int lda, 
	Span<TReal> tau, 
	[OutAttribute] int% info
) abstract

abstract QLDecompose : 
        m : int * 
        n : int * 
        a : Span<'TReal> * 
        lda : int * 
        tau : Span<'TReal> * 
        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<TReal>

C# Copy

A is DOUBLE PRECISION 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
orthogonal 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<TReal>

C# Copy

TAU is DOUBLE PRECISION 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(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(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

public abstract void QLDecompose(
	int m,
	int n,
	Span<TComplex> a,
	int lda,
	Span<TComplex> tau,
	out int info
)

Public MustOverride Sub QLDecompose ( 
	m As Integer,
	n As Integer,
	a As Span(Of TComplex),
	lda As Integer,
	tau As Span(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void QLDecompose(
	int m, 
	int n, 
	Span<TComplex> a, 
	int lda, 
	Span<TComplex> tau, 
	[OutAttribute] int% info
) abstract

abstract QLDecompose : 
        m : int * 
        n : int * 
        a : Span<'TComplex> * 
        lda : int * 
        tau : Span<'TComplex> * 
        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<TComplex>

C# Copy

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# Copy

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

tau  Span<TComplex>

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(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

Reference