Annotation of rpl/lapack/lapack/dlas2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLAS2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAS2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlas2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlas2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlas2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * DOUBLE PRECISION F, G, H, SSMAX, SSMIN
! 25: * ..
! 26: *
! 27: *
! 28: *> \par Purpose:
! 29: * =============
! 30: *>
! 31: *> \verbatim
! 32: *>
! 33: *> DLAS2 computes the singular values of the 2-by-2 matrix
! 34: *> [ F G ]
! 35: *> [ 0 H ].
! 36: *> On return, SSMIN is the smaller singular value and SSMAX is the
! 37: *> larger singular value.
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] F
! 44: *> \verbatim
! 45: *> F is DOUBLE PRECISION
! 46: *> The (1,1) element of the 2-by-2 matrix.
! 47: *> \endverbatim
! 48: *>
! 49: *> \param[in] G
! 50: *> \verbatim
! 51: *> G is DOUBLE PRECISION
! 52: *> The (1,2) element of the 2-by-2 matrix.
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] H
! 56: *> \verbatim
! 57: *> H is DOUBLE PRECISION
! 58: *> The (2,2) element of the 2-by-2 matrix.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[out] SSMIN
! 62: *> \verbatim
! 63: *> SSMIN is DOUBLE PRECISION
! 64: *> The smaller singular value.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[out] SSMAX
! 68: *> \verbatim
! 69: *> SSMAX is DOUBLE PRECISION
! 70: *> The larger singular value.
! 71: *> \endverbatim
! 72: *
! 73: * Authors:
! 74: * ========
! 75: *
! 76: *> \author Univ. of Tennessee
! 77: *> \author Univ. of California Berkeley
! 78: *> \author Univ. of Colorado Denver
! 79: *> \author NAG Ltd.
! 80: *
! 81: *> \date November 2011
! 82: *
! 83: *> \ingroup auxOTHERauxiliary
! 84: *
! 85: *> \par Further Details:
! 86: * =====================
! 87: *>
! 88: *> \verbatim
! 89: *>
! 90: *> Barring over/underflow, all output quantities are correct to within
! 91: *> a few units in the last place (ulps), even in the absence of a guard
! 92: *> digit in addition/subtraction.
! 93: *>
! 94: *> In IEEE arithmetic, the code works correctly if one matrix element is
! 95: *> infinite.
! 96: *>
! 97: *> Overflow will not occur unless the largest singular value itself
! 98: *> overflows, or is within a few ulps of overflow. (On machines with
! 99: *> partial overflow, like the Cray, overflow may occur if the largest
! 100: *> singular value is within a factor of 2 of overflow.)
! 101: *>
! 102: *> Underflow is harmless if underflow is gradual. Otherwise, results
! 103: *> may correspond to a matrix modified by perturbations of size near
! 104: *> the underflow threshold.
! 105: *> \endverbatim
! 106: *>
! 107: * =====================================================================
1.1 bertrand 108: SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
109: *
1.8 ! bertrand 110: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 111: * -- LAPACK is a software package provided by Univ. of Tennessee, --
112: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 113: * November 2011
1.1 bertrand 114: *
115: * .. Scalar Arguments ..
116: DOUBLE PRECISION F, G, H, SSMAX, SSMIN
117: * ..
118: *
119: * ====================================================================
120: *
121: * .. Parameters ..
122: DOUBLE PRECISION ZERO
123: PARAMETER ( ZERO = 0.0D0 )
124: DOUBLE PRECISION ONE
125: PARAMETER ( ONE = 1.0D0 )
126: DOUBLE PRECISION TWO
127: PARAMETER ( TWO = 2.0D0 )
128: * ..
129: * .. Local Scalars ..
130: DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA
131: * ..
132: * .. Intrinsic Functions ..
133: INTRINSIC ABS, MAX, MIN, SQRT
134: * ..
135: * .. Executable Statements ..
136: *
137: FA = ABS( F )
138: GA = ABS( G )
139: HA = ABS( H )
140: FHMN = MIN( FA, HA )
141: FHMX = MAX( FA, HA )
142: IF( FHMN.EQ.ZERO ) THEN
143: SSMIN = ZERO
144: IF( FHMX.EQ.ZERO ) THEN
145: SSMAX = GA
146: ELSE
147: SSMAX = MAX( FHMX, GA )*SQRT( ONE+
148: $ ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 )
149: END IF
150: ELSE
151: IF( GA.LT.FHMX ) THEN
152: AS = ONE + FHMN / FHMX
153: AT = ( FHMX-FHMN ) / FHMX
154: AU = ( GA / FHMX )**2
155: C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) )
156: SSMIN = FHMN*C
157: SSMAX = FHMX / C
158: ELSE
159: AU = FHMX / GA
160: IF( AU.EQ.ZERO ) THEN
161: *
162: * Avoid possible harmful underflow if exponent range
163: * asymmetric (true SSMIN may not underflow even if
164: * AU underflows)
165: *
166: SSMIN = ( FHMN*FHMX ) / GA
167: SSMAX = GA
168: ELSE
169: AS = ONE + FHMN / FHMX
170: AT = ( FHMX-FHMN ) / FHMX
171: C = ONE / ( SQRT( ONE+( AS*AU )**2 )+
172: $ SQRT( ONE+( AT*AU )**2 ) )
173: SSMIN = ( FHMN*C )*AU
174: SSMIN = SSMIN + SSMIN
175: SSMAX = GA / ( C+C )
176: END IF
177: END IF
178: END IF
179: RETURN
180: *
181: * End of DLAS2
182: *
183: END
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