Managed Lapack Of Single.Singular Value Decompose Method
Definition
Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.0.3
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.0.3
Overload List
SingularValueDecompose(Char, Int32, Int32, Span<Complex<Single>>, Int32, Span<Single>, Span<Complex<Single>>, Int32, Span<Complex<Single>>, Int32, Int32)
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.
public override void SingularValueDecompose(
char jobz,
int m,
int n,
Span<Complex<float>> a,
int lda,
Span<float> s,
Span<Complex<float>> u,
int ldu,
Span<Complex<float>> vt,
int ldvt,
out int info
)
Parameters
- jobz Char
Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of VH are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of VH are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten in the array A and all rows of VH are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of VH are overwritten in the array A; = 'N': no columns of U or rows of VH are computed.
- m Int32
The number of rows of the input matrix A. M >= 0.
- n Int32
The number of columns of the input matrix A. N >= 0.
- a Span<Complex<Single>>
A is TComplex array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of VH (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed.
- lda Int32
The leading dimension of the array A. LDA >= max(1,M).
- s Span<Single>
S is TReal array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).
- u Span<Complex<Single>>
U is TComplex array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
- ldu Int32
The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
- vt Span<Complex<Single>>
VT is TComplex array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix VH; if JOBZ = 'S', VT contains the first min(M,N) rows of VH (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
- ldvt Int32
The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N).
- info Int32
= 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The updating process of DBDSDC did not converge.
Remarks
The SVD is written A = U * SIGMA * conjugate-transpose(V) 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 = VH, not V. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
SingularValueDecompose(Char, Int32, Int32, Span<Single>, Int32, Span<Single>, Span<Single>, Int32, Span<Single>, Int32, Int32)
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.
public override void SingularValueDecompose(
char jobz,
int m,
int n,
Span<float> a,
int lda,
Span<float> s,
Span<float> u,
int ldu,
Span<float> vt,
int ldvt,
out int info
)
Parameters
- jobz Char
Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of VH are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of VH are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten in the array A and all rows of VH are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of VH are overwritten in the array A; = 'N': no columns of U or rows of VH are computed.
- m Int32
The number of rows of the input matrix A. M >= 0.
- n Int32
The number of columns of the input matrix A. N >= 0.
- a Span<Single>
A is TComplex array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of VH (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed.
- lda Int32
The leading dimension of the array A. LDA >= max(1,M).
- s Span<Single>
S is TReal array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).
- u Span<Single>
U is TComplex array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
- ldu Int32
The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
- vt Span<Single>
VT is TComplex array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix VH; if JOBZ = 'S', VT contains the first min(M,N) rows of VH (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
- ldvt Int32
The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N).
- info Int32
= 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The updating process of DBDSDC did not converge.
Remarks
The SVD is written A = U * SIGMA * conjugate-transpose(V) 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 = VH, not V. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA