Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLAEV2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAEV2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaev2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaev2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaev2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * DOUBLE PRECISION CS1, RT1, RT2
! 25: * COMPLEX*16 A, B, C, SN1
! 26: * ..
! 27: *
! 28: *
! 29: *> \par Purpose:
! 30: * =============
! 31: *>
! 32: *> \verbatim
! 33: *>
! 34: *> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
! 35: *> [ A B ]
! 36: *> [ CONJG(B) C ].
! 37: *> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
! 38: *> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
! 39: *> eigenvector for RT1, giving the decomposition
! 40: *>
! 41: *> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
! 42: *> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] A
! 49: *> \verbatim
! 50: *> A is COMPLEX*16
! 51: *> The (1,1) element of the 2-by-2 matrix.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] B
! 55: *> \verbatim
! 56: *> B is COMPLEX*16
! 57: *> The (1,2) element and the conjugate of the (2,1) element of
! 58: *> the 2-by-2 matrix.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] C
! 62: *> \verbatim
! 63: *> C is COMPLEX*16
! 64: *> The (2,2) element of the 2-by-2 matrix.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[out] RT1
! 68: *> \verbatim
! 69: *> RT1 is DOUBLE PRECISION
! 70: *> The eigenvalue of larger absolute value.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[out] RT2
! 74: *> \verbatim
! 75: *> RT2 is DOUBLE PRECISION
! 76: *> The eigenvalue of smaller absolute value.
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[out] CS1
! 80: *> \verbatim
! 81: *> CS1 is DOUBLE PRECISION
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[out] SN1
! 85: *> \verbatim
! 86: *> SN1 is COMPLEX*16
! 87: *> The vector (CS1, SN1) is a unit right eigenvector for RT1.
! 88: *> \endverbatim
! 89: *
! 90: * Authors:
! 91: * ========
! 92: *
! 93: *> \author Univ. of Tennessee
! 94: *> \author Univ. of California Berkeley
! 95: *> \author Univ. of Colorado Denver
! 96: *> \author NAG Ltd.
! 97: *
! 98: *> \date November 2011
! 99: *
! 100: *> \ingroup complex16OTHERauxiliary
! 101: *
! 102: *> \par Further Details:
! 103: * =====================
! 104: *>
! 105: *> \verbatim
! 106: *>
! 107: *> RT1 is accurate to a few ulps barring over/underflow.
! 108: *>
! 109: *> RT2 may be inaccurate if there is massive cancellation in the
! 110: *> determinant A*C-B*B; higher precision or correctly rounded or
! 111: *> correctly truncated arithmetic would be needed to compute RT2
! 112: *> accurately in all cases.
! 113: *>
! 114: *> CS1 and SN1 are accurate to a few ulps barring over/underflow.
! 115: *>
! 116: *> Overflow is possible only if RT1 is within a factor of 5 of overflow.
! 117: *> Underflow is harmless if the input data is 0 or exceeds
! 118: *> underflow_threshold / macheps.
! 119: *> \endverbatim
! 120: *>
! 121: * =====================================================================
1.1 bertrand 122: SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
123: *
1.8 ! bertrand 124: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 127: * November 2011
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: DOUBLE PRECISION CS1, RT1, RT2
131: COMPLEX*16 A, B, C, SN1
132: * ..
133: *
134: * =====================================================================
135: *
136: * .. Parameters ..
137: DOUBLE PRECISION ZERO
138: PARAMETER ( ZERO = 0.0D0 )
139: DOUBLE PRECISION ONE
140: PARAMETER ( ONE = 1.0D0 )
141: * ..
142: * .. Local Scalars ..
143: DOUBLE PRECISION T
144: COMPLEX*16 W
145: * ..
146: * .. External Subroutines ..
147: EXTERNAL DLAEV2
148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC ABS, DBLE, DCONJG
151: * ..
152: * .. Executable Statements ..
153: *
154: IF( ABS( B ).EQ.ZERO ) THEN
155: W = ONE
156: ELSE
157: W = DCONJG( B ) / ABS( B )
158: END IF
159: CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
160: SN1 = W*T
161: RETURN
162: *
163: * End of ZLAEV2
164: *
165: END
CVSweb interface <joel.bertrand@systella.fr>