Decomposition Operations<TReal, TComplex>.RQDecompose Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2
Overload List
RQDecompose( | Computes an RQ factorization of a real M-by-N matrix A: A = R * Q. |
RQDecompose( | Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q. |
RQDecompose( | Computes an RQ factorization of a real M-by-N matrix A: A = R * Q. |
RQDecompose( | Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q. |
RQDecompose( | Computes an RQ factorization of a real M-by-N matrix A: A = R * Q. |
RQDecompose( | Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q. |
RQDecompose(Int32, Int32, Array2D<TReal>, Array1D<TReal>, Int32)
Computes an RQ factorization of a real M-by-N matrix A: A = R * Q.
public void RQDecompose(
int m,
int n,
Array2D<TReal> a,
Array1D<TReal> 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 Array2D<TReal>
-
C# A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
- tau Array1D<TReal>
-
C# TAU is DOUBLE PRECISION 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
RQDecompose(Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Int32)
Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.
public void RQDecompose(
int m,
int n,
Array2D<TComplex> a,
Array1D<TComplex> 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 Array2D<TComplex>
-
C# A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
- tau Array1D<TComplex>
-
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(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
RQDecompose(Int32, Int32, Span2D<TReal>, Span<TReal>, Int32)
Computes an RQ factorization of a real M-by-N matrix A: A = R * Q.
public void RQDecompose(
int m,
int n,
Span2D<TReal> a,
Span<TReal> 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 Span2D<TReal>
-
C# A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
- tau Span<TReal>
-
C# TAU is DOUBLE PRECISION 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
RQDecompose(Int32, Int32, Span2D<TComplex>, Span<TComplex>, Int32)
Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.
public void RQDecompose(
int m,
int n,
Span2D<TComplex> a,
Span<TComplex> 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 Span2D<TComplex>
-
C# A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
- tau Span<TComplex>
-
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(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
RQDecompose(Int32, Int32, Span<TReal>, Int32, Span<TReal>, Int32)
Computes an RQ factorization of a real M-by-N matrix A: A = R * Q.
public abstract void RQDecompose(
int m,
int n,
Span<TReal> a,
int lda,
Span<TReal> 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<TReal>
-
C# A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
- lda Int32
-
C# LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
- tau Span<TReal>
-
C# TAU is DOUBLE PRECISION 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
RQDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32)
Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.
public abstract void RQDecompose(
int m,
int n,
Span<TComplex> a,
int lda,
Span<TComplex> 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<TComplex>
-
C# A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
- lda Int32
-
C# LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
- tau Span<TComplex>
-
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(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011