File: dlaqr1

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--- 
:name: dlaqr1
:md5sum: ad34e252476d8fc18eea40e0f25e76ec
:category: :subroutine
:arguments: 
- n: 
    :type: integer
    :intent: input
- h: 
    :type: doublereal
    :intent: input
    :dims: 
    - ldh
    - n
- ldh: 
    :type: integer
    :intent: input
- sr1: 
    :type: doublereal
    :intent: input
- si1: 
    :type: doublereal
    :intent: input
- sr2: 
    :type: doublereal
    :intent: input
- si2: 
    :type: doublereal
    :intent: input
- v: 
    :type: doublereal
    :intent: output
    :dims: 
    - n
:substitutions: {}

:fortran_help: "      SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )\n\n\
  *       Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a\n\
  *       scalar multiple of the first column of the product\n\
  *\n\
  *       (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)\n\
  *\n\
  *       scaling to avoid overflows and most underflows. It\n\
  *       is assumed that either\n\
  *\n\
  *               1) sr1 = sr2 and si1 = -si2\n\
  *           or\n\
  *               2) si1 = si2 = 0.\n\
  *\n\
  *       This is useful for starting double implicit shift bulges\n\
  *       in the QR algorithm.\n\
  *\n\
  *\n\n\
  *       N      (input) integer\n\
  *              Order of the matrix H. N must be either 2 or 3.\n\
  *\n\
  *       H      (input) DOUBLE PRECISION array of dimension (LDH,N)\n\
  *              The 2-by-2 or 3-by-3 matrix H in (*).\n\
  *\n\
  *       LDH    (input) integer\n\
  *              The leading dimension of H as declared in\n\
  *              the calling procedure.  LDH.GE.N\n\
  *\n\
  *       SR1    (input) DOUBLE PRECISION\n\
  *       SI1    The shifts in (*).\n\
  *       SR2\n\
  *       SI2\n\
  *\n\
  *       V      (output) DOUBLE PRECISION array of dimension N\n\
  *              A scalar multiple of the first column of the\n\
  *              matrix K in (*).\n\
  *\n\n\
  *     ================================================================\n\
  *     Based on contributions by\n\
  *        Karen Braman and Ralph Byers, Department of Mathematics,\n\
  *        University of Kansas, USA\n\
  *\n\
  *     ================================================================\n\
  *\n"