Annotation of rpl/lapack/lapack/dlaqr1.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLAQR1
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAQR1 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr1.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr1.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr1.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * DOUBLE PRECISION SI1, SI2, SR1, SR2
! 25: * INTEGER LDH, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION H( LDH, * ), V( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a
! 38: *> scalar multiple of the first column of the product
! 39: *>
! 40: *> (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
! 41: *>
! 42: *> scaling to avoid overflows and most underflows. It
! 43: *> is assumed that either
! 44: *>
! 45: *> 1) sr1 = sr2 and si1 = -si2
! 46: *> or
! 47: *> 2) si1 = si2 = 0.
! 48: *>
! 49: *> This is useful for starting double implicit shift bulges
! 50: *> in the QR algorithm.
! 51: *> \endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] N
! 57: *> \verbatim
! 58: *> N is integer
! 59: *> Order of the matrix H. N must be either 2 or 3.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] H
! 63: *> \verbatim
! 64: *> H is DOUBLE PRECISION array of dimension (LDH,N)
! 65: *> The 2-by-2 or 3-by-3 matrix H in (*).
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] LDH
! 69: *> \verbatim
! 70: *> LDH is integer
! 71: *> The leading dimension of H as declared in
! 72: *> the calling procedure. LDH.GE.N
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] SR1
! 76: *> \verbatim
! 77: *> SR1 is DOUBLE PRECISION
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] SI1
! 81: *> \verbatim
! 82: *> SI1 is DOUBLE PRECISION
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] SR2
! 86: *> \verbatim
! 87: *> SR2 is DOUBLE PRECISION
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] SI2
! 91: *> \verbatim
! 92: *> SI2 is DOUBLE PRECISION
! 93: *> The shifts in (*).
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[out] V
! 97: *> \verbatim
! 98: *> V is DOUBLE PRECISION array of dimension N
! 99: *> A scalar multiple of the first column of the
! 100: *> matrix K in (*).
! 101: *> \endverbatim
! 102: *
! 103: * Authors:
! 104: * ========
! 105: *
! 106: *> \author Univ. of Tennessee
! 107: *> \author Univ. of California Berkeley
! 108: *> \author Univ. of Colorado Denver
! 109: *> \author NAG Ltd.
! 110: *
! 111: *> \date November 2011
! 112: *
! 113: *> \ingroup doubleOTHERauxiliary
! 114: *
! 115: *> \par Contributors:
! 116: * ==================
! 117: *>
! 118: *> Karen Braman and Ralph Byers, Department of Mathematics,
! 119: *> University of Kansas, USA
! 120: *>
! 121: * =====================================================================
1.1 bertrand 122: SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
123: *
1.8 ! bertrand 124: * -- LAPACK auxiliary routine (version 3.4.0) --
! 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 127: * November 2011
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: DOUBLE PRECISION SI1, SI2, SR1, SR2
131: INTEGER LDH, N
132: * ..
133: * .. Array Arguments ..
134: DOUBLE PRECISION H( LDH, * ), V( * )
135: * ..
136: *
1.8 ! bertrand 137: * ================================================================
1.1 bertrand 138: *
139: * .. Parameters ..
140: DOUBLE PRECISION ZERO
141: PARAMETER ( ZERO = 0.0d0 )
142: * ..
143: * .. Local Scalars ..
144: DOUBLE PRECISION H21S, H31S, S
145: * ..
146: * .. Intrinsic Functions ..
147: INTRINSIC ABS
148: * ..
149: * .. Executable Statements ..
150: IF( N.EQ.2 ) THEN
151: S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) )
152: IF( S.EQ.ZERO ) THEN
153: V( 1 ) = ZERO
154: V( 2 ) = ZERO
155: ELSE
156: H21S = H( 2, 1 ) / S
157: V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )*
158: $ ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S )
159: V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 )
160: END IF
161: ELSE
162: S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) +
163: $ ABS( H( 3, 1 ) )
164: IF( S.EQ.ZERO ) THEN
165: V( 1 ) = ZERO
166: V( 2 ) = ZERO
167: V( 3 ) = ZERO
168: ELSE
169: H21S = H( 2, 1 ) / S
170: H31S = H( 3, 1 ) / S
171: V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) -
172: $ SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S
173: V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) +
174: $ H( 2, 3 )*H31S
175: V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
176: $ H21S*H( 3, 2 )
177: END IF
178: END IF
179: END
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