ManagedLapack.QRDecompose Method

ZGEQRF computes a QR decomposition of a real M-by-N matrix A: A = Q * R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Zetails). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Zetails). WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Zetails =============== 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' 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:m) is stored on exit inthis. A(i+1:m,i), and tau inthis. TAU(i).

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

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

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

abstract QRDecompose : 
        m : int * 
        n : int * 
        a : Span<Complex<float>> * 
        lda : int * 
        tau : Span<Complex<float>> * 
        info : int byref -> unit 
override QRDecompose : 
        m : int * 
        n : int * 
        a : Span<Complex<float>> * 
        lda : int * 
        tau : Span<Complex<float>> * 
        info : int byref -> unit 

ZGEQRF computes a QR decomposition of a real M-by-N matrix A: A = Q * R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Zetails). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Zetails). WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Zetails =============== 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' 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:m) is stored on exit inthis. A(i+1:m,i), and tau inthis. TAU(i).

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

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

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

abstract QRDecompose : 
        m : int * 
        n : int * 
        a : Span<float> * 
        lda : int * 
        tau : Span<float> * 
        info : int byref -> unit 
override QRDecompose : 
        m : int * 
        n : int * 
        a : Span<float> * 
        lda : int * 
        tau : Span<float> * 
        info : int byref -> unit 

public override void QRDecompose(
	int m,
	int n,
	Span<double> a,
	int lda,
	Span<int> jpvt,
	Span<double> tau,
	out int info
)

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

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

abstract QRDecompose : 
        m : int * 
        n : int * 
        a : Span<float> * 
        lda : int * 
        jpvt : Span<int> * 
        tau : Span<float> * 
        info : int byref -> unit 
override QRDecompose : 
        m : int * 
        n : int * 
        a : Span<float> * 
        lda : int * 
        jpvt : Span<int> * 
        tau : Span<float> * 
        info : int byref -> unit 

            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/complex scalar, and v is a real/complex vector
            with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
            A(i+1:m,i), and tau in TAU(i).