--- 
:name: dlaic1
:md5sum: c5939e302aa2582a21e74047f303bb4a
:category: :subroutine
:arguments: 
- job: 
    :type: integer
    :intent: input
- j: 
    :type: integer
    :intent: input
- x: 
    :type: doublereal
    :intent: input
    :dims: 
    - j
- sest: 
    :type: doublereal
    :intent: input
- w: 
    :type: doublereal
    :intent: input
    :dims: 
    - j
- gamma: 
    :type: doublereal
    :intent: input
- sestpr: 
    :type: doublereal
    :intent: output
- s: 
    :type: doublereal
    :intent: output
- c: 
    :type: doublereal
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  DLAIC1 applies one step of incremental condition estimation in\n\
  *  its simplest version:\n\
  *\n\
  *  Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j\n\
  *  lower triangular matrix L, such that\n\
  *           twonorm(L*x) = sest\n\
  *  Then DLAIC1 computes sestpr, s, c such that\n\
  *  the vector\n\
  *                  [ s*x ]\n\
  *           xhat = [  c  ]\n\
  *  is an approximate singular vector of\n\
  *                  [ L     0  ]\n\
  *           Lhat = [ w' gamma ]\n\
  *  in the sense that\n\
  *           twonorm(Lhat*xhat) = sestpr.\n\
  *\n\
  *  Depending on JOB, an estimate for the largest or smallest singular\n\
  *  value is computed.\n\
  *\n\
  *  Note that [s c]' and sestpr**2 is an eigenpair of the system\n\
  *\n\
  *      diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]\n\
  *                                            [ gamma ]\n\
  *\n\
  *  where  alpha =  x'*w.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  JOB     (input) INTEGER\n\
  *          = 1: an estimate for the largest singular value is computed.\n\
  *          = 2: an estimate for the smallest singular value is computed.\n\
  *\n\
  *  J       (input) INTEGER\n\
  *          Length of X and W\n\
  *\n\
  *  X       (input) DOUBLE PRECISION array, dimension (J)\n\
  *          The j-vector x.\n\
  *\n\
  *  SEST    (input) DOUBLE PRECISION\n\
  *          Estimated singular value of j by j matrix L\n\
  *\n\
  *  W       (input) DOUBLE PRECISION array, dimension (J)\n\
  *          The j-vector w.\n\
  *\n\
  *  GAMMA   (input) DOUBLE PRECISION\n\
  *          The diagonal element gamma.\n\
  *\n\
  *  SESTPR  (output) DOUBLE PRECISION\n\
  *          Estimated singular value of (j+1) by (j+1) matrix Lhat.\n\
  *\n\
  *  S       (output) DOUBLE PRECISION\n\
  *          Sine needed in forming xhat.\n\
  *\n\
  *  C       (output) DOUBLE PRECISION\n\
  *          Cosine needed in forming xhat.\n\
  *\n\n\
  *  =====================================================================\n\
  *\n"
