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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"
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