--- 
:name: sgesvd
:md5sum: d1b4d1842f793e4c465046572749c3b6
:category: :subroutine
:arguments: 
- jobu: 
    :type: char
    :intent: input
- jobvt: 
    :type: char
    :intent: input
- m: 
    :type: integer
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: real
    :intent: input/output
    :dims: 
    - lda
    - n
    :outdims:
    - lda
    - MIN(m,n)
- lda: 
    :type: integer
    :intent: input
- s: 
    :type: real
    :intent: output
    :dims: 
    - MIN(m,n)
- u: 
    :type: real
    :intent: output
    :dims: 
    - ldu
    - "lsame_(&jobu,\"A\") ? m : lsame_(&jobu,\"S\") ? MIN(m,n) : 0"
- ldu: 
    :type: integer
    :intent: input
- vt: 
    :type: real
    :intent: output
    :dims: 
    - ldvt
    - n
- ldvt: 
    :type: integer
    :intent: input
- work: 
    :type: real
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: MAX(MAX(1, 3*MIN(m,n)+MAX(m,n)), 5*MIN(m,n))
- info: 
    :type: integer
    :intent: output
:substitutions: 
  m: lda
  ldvt: "lsame_(&jobvt,\"A\") ? n : lsame_(&jobvt,\"S\") ? MIN(m,n) : 1"
  ldu: "((lsame_(&jobu,\"S\")) || (lsame_(&jobu,\"A\"))) ? m : 1"
:fortran_help: "      SUBROUTINE SGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  SGESVD computes the singular value decomposition (SVD) of a real\n\
  *  M-by-N matrix A, optionally computing the left and/or right singular\n\
  *  vectors. The SVD is written\n\
  *\n\
  *       A = U * SIGMA * transpose(V)\n\
  *\n\
  *  where SIGMA is an M-by-N matrix which is zero except for its\n\
  *  min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and\n\
  *  V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA\n\
  *  are the singular values of A; they are real and non-negative, and\n\
  *  are returned in descending order.  The first min(m,n) columns of\n\
  *  U and V are the left and right singular vectors of A.\n\
  *\n\
  *  Note that the routine returns V**T, not V.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  JOBU    (input) CHARACTER*1\n\
  *          Specifies options for computing all or part of the matrix U:\n\
  *          = 'A':  all M columns of U are returned in array U:\n\
  *          = 'S':  the first min(m,n) columns of U (the left singular\n\
  *                  vectors) are returned in the array U;\n\
  *          = 'O':  the first min(m,n) columns of U (the left singular\n\
  *                  vectors) are overwritten on the array A;\n\
  *          = 'N':  no columns of U (no left singular vectors) are\n\
  *                  computed.\n\
  *\n\
  *  JOBVT   (input) CHARACTER*1\n\
  *          Specifies options for computing all or part of the matrix\n\
  *          V**T:\n\
  *          = 'A':  all N rows of V**T are returned in the array VT;\n\
  *          = 'S':  the first min(m,n) rows of V**T (the right singular\n\
  *                  vectors) are returned in the array VT;\n\
  *          = 'O':  the first min(m,n) rows of V**T (the right singular\n\
  *                  vectors) are overwritten on the array A;\n\
  *          = 'N':  no rows of V**T (no right singular vectors) are\n\
  *                  computed.\n\
  *\n\
  *          JOBVT and JOBU cannot both be 'O'.\n\
  *\n\
  *  M       (input) INTEGER\n\
  *          The number of rows of the input matrix A.  M >= 0.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The number of columns of the input matrix A.  N >= 0.\n\
  *\n\
  *  A       (input/output) REAL array, dimension (LDA,N)\n\
  *          On entry, the M-by-N matrix A.\n\
  *          On exit,\n\
  *          if JOBU = 'O',  A is overwritten with the first min(m,n)\n\
  *                          columns of U (the left singular vectors,\n\
  *                          stored columnwise);\n\
  *          if JOBVT = 'O', A is overwritten with the first min(m,n)\n\
  *                          rows of V**T (the right singular vectors,\n\
  *                          stored rowwise);\n\
  *          if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A\n\
  *                          are destroyed.\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A.  LDA >= max(1,M).\n\
  *\n\
  *  S       (output) REAL array, dimension (min(M,N))\n\
  *          The singular values of A, sorted so that S(i) >= S(i+1).\n\
  *\n\
  *  U       (output) REAL array, dimension (LDU,UCOL)\n\
  *          (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.\n\
  *          If JOBU = 'A', U contains the M-by-M orthogonal matrix U;\n\
  *          if JOBU = 'S', U contains the first min(m,n) columns of U\n\
  *          (the left singular vectors, stored columnwise);\n\
  *          if JOBU = 'N' or 'O', U is not referenced.\n\
  *\n\
  *  LDU     (input) INTEGER\n\
  *          The leading dimension of the array U.  LDU >= 1; if\n\
  *          JOBU = 'S' or 'A', LDU >= M.\n\
  *\n\
  *  VT      (output) REAL array, dimension (LDVT,N)\n\
  *          If JOBVT = 'A', VT contains the N-by-N orthogonal matrix\n\
  *          V**T;\n\
  *          if JOBVT = 'S', VT contains the first min(m,n) rows of\n\
  *          V**T (the right singular vectors, stored rowwise);\n\
  *          if JOBVT = 'N' or 'O', VT is not referenced.\n\
  *\n\
  *  LDVT    (input) INTEGER\n\
  *          The leading dimension of the array VT.  LDVT >= 1; if\n\
  *          JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).\n\
  *\n\
  *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK;\n\
  *          if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged\n\
  *          superdiagonal elements of an upper bidiagonal matrix B\n\
  *          whose diagonal is in S (not necessarily sorted). B\n\
  *          satisfies A = U * B * VT, so it has the same singular values\n\
  *          as A, and singular vectors related by U and VT.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The dimension of the array WORK.\n\
  *          LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).\n\
  *          For good performance, LWORK should generally be larger.\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal size of the WORK array, returns\n\
  *          this value as the first entry of the WORK array, and no error\n\
  *          message related to LWORK is issued by XERBLA.\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit.\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value.\n\
  *          > 0:  if SBDSQR did not converge, INFO specifies how many\n\
  *                superdiagonals of an intermediate bidiagonal form B\n\
  *                did not converge to zero. See the description of WORK\n\
  *                above for details.\n\
  *\n\n\
  *  =====================================================================\n\
  *\n"
