PLASMA 2.8.0 PLASMA - Parallel Linear Algebra for Scalable Multi-core Architectures

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int PLASMA_cgesdd | ( | PLASMA_enum | jobu,
|  | PLASMA_enum | jobvt,
|  | int | M,
|  | int | N,
|  | PLASMA_Complex32_t * | A,
|  | int | LDA,
|  | float * | S,
|  | PLASMA_desc * | descT,
|  | PLASMA_Complex32_t * | U,
|  | int | LDU,
|  | PLASMA_Complex32_t * | VT,
|  | int | LDVT
| ) |  |

PLASMA_cgesdd - 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 * SIGMA * conjfugate-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 = V**H, 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.

NOTE that the input parameter of this function differ from the LAPACK CGESDD. We have jobu and jobvt instead of only jobz first to be consistent with CGESVD and second to allow a computation of only U or VT.

Parameters

  [in] | jobu | Specifies options for computing all or part of the matrix U. Intended usage: = PlasmaVec = 'A'(lapack): all M columns of U are returned in array U; = PlasmaNoVec = 'N': no columns of U (no left singular vectors) are computed. = PlasmaSVec = 'S': the first min(m,n) columns of U (the left singular vectors) are returned in the array U; NOT SUPPORTTED YET = PlasmaOVec = 'O': the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; NOT SUPPORTTED YET
  [in] | jobvt | Specifies options for computing all or part of the matrix V**H. Intended usage: = PlasmaVec = 'A'(lapack): all N rows of V**H are returned in the array VT; = PlasmaNoVec = 'N': no rows of V**H (no right singular vectors) are computed. = PlasmaSVec = 'S': the first min(m,n) rows of V**H (the right singular vectors) are returned in the array VT; NOT SUPPORTTED YET = PlasmaOVec = 'O': the first min(m,n) rows of V**H (the right singular vectors) are overwritten on the array A; NOT SUPPORTTED YET

Note: jobu and jobvt cannot both be PlasmaOVec.

Parameters

  [in] | M | The number of rows of the matrix A. M >= 0.
  [in] | N | The number of columns of the matrix A. N >= 0.
  [in,out] | A | On entry, the M-by-N matrix A. On exit, if JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**H (the right singular vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.
  [in] | LDA | The leading dimension of the array A. LDA >= max(1,M).
  [out] | S | The real singular values of A, sorted so that S(i) >= S(i+1).
  [in,out] | descT | On entry, descriptor as return by PLASMA_Alloc_Workspace_cgesdd On exit, contains auxiliary factorization data.
  [out] | U | (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains the M-by-M unitary matrix U; if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBU = 'N' or 'O', U is not referenced.
  [in] | LDU | The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.
  [out] | VT | If JOBVT = 'A', VT contains the N-by-N unitary matrix V**H; if JOBVT = 'S', VT contains the first min(m,n) rows of V**H (the right singular vectors, stored rowwise); if JOBVT = 'N' or 'O', VT is not referenced.
  [in] | LDVT | The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).

Returns

Return values

  PLASMA_SUCCESS | successful exit
  <0 | if -i, the i-th argument had an illegal value

See also
  PLASMA_cgesdd_Tile
  PLASMA_cgesdd_Tile_Async
  PLASMA_cgesdd
  PLASMA_dgesdd
  PLASMA_sgesdd