Lapack++: lasvd.h File Reference

void LaSVD_IP	(	LaGenMatComplex &	A,
		LaVectorDouble &	Sigma,
		LaGenMatComplex &	U,
		LaGenMatComplex &	VT
	)

Compute the Singular Value Decomposition.

Compute the singular value decomposition (SVD) of a complex M-by-N matrix A, also computing the left and right singular vectors, by using a divide-and-conquer method.

In lapack this is zgesdd. zgesdd computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written

$A = U \cdot Sigma \cdot V^T$

where Sigma is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non- negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns VT = V**H (conjugate-transpose), not V.

Parameters:

	A	The M-by-N input matrix to be decomposed. It will be destroyed during the computation.
	Sigma	A real-valued vector of length `min(M,N)` that will return the singular values. WATCH OUT: The length has to be exactly `min(M,N)` or else an exception will be thrown.
	U	The M-by-M matrix of the left singular vectors.
	VT	The N-by-N matrix of the right singular vectors.

void LaSVD_IP	(	LaGenMatComplex &	A,
		LaVectorDouble &	Sigma
	)

Compute the Singular Values.

Compute the singular values of a singular value decomposition (SVD) of a complex M-by-N matrix A.

In lapack this is zgesdd. zgesdd computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written

$A = U \cdot Sigma \cdot V^T$

where Sigma is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non- negative, and are returned in descending order.

Parameters:

	A	The M-by-N input matrix to be decomposed. It will be destroyed during the computation.
	Sigma	A real-valued vector of length `min(M,N)` that will return the singular values. WATCH OUT: The length has to be exactly `min(M,N)` or else an exception will be thrown.

void LaSVD_IP	(	LaGenMatDouble &	A,
		LaVectorDouble &	Sigma,
		LaGenMatDouble &	U,
		LaGenMatDouble &	VT
	)

Compute the Singular Value Decomposition.

Compute the singular value decomposition (SVD) of a complex M-by-N matrix A, also computing the left and right singular vectors, by using a divide-and-conquer method.

In lapack this is dgesdd. dgesdd computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written

$A = U \cdot Sigma \cdot V^T$

where Sigma is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non- negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns VT = V**T (transposed), not V.

Now watch out: This routine has several modes of operation, depending on the size of the input matrices U and VT. This is:

If U is M-by-M and VT is N-by-N (the normal mode), then all left and right singular vectors are calculated and are returned in U and VT.

If U is M-by-min(M,N) and VT is min(M,N)-by-N, then the first min(M,N) left and right singular vectors are calculated, respectively, and are returned in U and VT. FIXME: needs verification.

If M >= N, U is of size 0, and VT is N-by-N, then the first N left singular vectors are calculated and returned in the first columns of A, and all right singular vectors are calculated and returned in VT. In this mode, U is unused. FIXME: needs verification.

If M < N, U is M-by-M, and VT is of size 0, then all left singular vectors are calculated and returned in U, and the first M right singular vectors are calculated and returned in the first M rows of A. In this mode, VT is unused. FIXME: needs verification.

In any other combination of matrix sizes, an exception is thrown.

Parameters:

	A	The M-by-N input matrix to be decomposed. It will be destroyed during the computation.
	Sigma	A real-valued vector of length `min(M,N)` that will return the singular values. WATCH OUT: The length has to be exactly `min(M,N)` or else an exception will be thrown.
	U	In the normal mode of calculation, the M-by-M matrix of the left singular vectors. In other modes this might be unused.
	VT	In the normal mode of calculation, the N-by-N matrix of the right singular vectors. In other modes this might be unused.

void LaSVD_IP	(	LaGenMatDouble &	A,
		LaVectorDouble &	Sigma
	)

Compute the Singular Values.

Compute the singular values of a singular value decomposition (SVD) of a complex M-by-N matrix A.

In lapack this is dgesdd. dgesdd computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written

$A = U \cdot Sigma \cdot V^T$

where Sigma is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non- negative, and are returned in descending order.

Parameters:

	A	The M-by-N input matrix to be decomposed. It will be destroyed during the computation.
	Sigma	A real-valued vector of length `min(M,N)` that will return the singular values. WATCH OUT: The length has to be exactly `min(M,N)` or else an exception will be thrown.


Complex-valued matrices
void	LaSVD_IP (LaGenMatComplex &A, LaVectorDouble &Sigma, LaGenMatComplex &U, LaGenMatComplex &VT)
void	LaSVD_IP (LaGenMatComplex &A, LaVectorDouble &Sigma)
Real-valued matrices
void	LaSVD_IP (LaGenMatDouble &A, LaVectorDouble &Sigma, LaGenMatDouble &U, LaGenMatDouble &VT)
void	LaSVD_IP (LaGenMatDouble &A, LaVectorDouble &Sigma)

lasvd.h File Reference

Complex-valued matrices

Real-valued matrices

Detailed Description

Function Documentation