Annotation of rpl/lapack/lapack/zlaqhe.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLAQHE
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAQHE + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqhe.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqhe.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqhe.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER EQUED, UPLO
! 25: * INTEGER LDA, N
! 26: * DOUBLE PRECISION AMAX, SCOND
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION S( * )
! 30: * COMPLEX*16 A( LDA, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
! 40: *> in the vector S.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] UPLO
! 47: *> \verbatim
! 48: *> UPLO is CHARACTER*1
! 49: *> Specifies whether the upper or lower triangular part of the
! 50: *> Hermitian matrix A is stored.
! 51: *> = 'U': Upper triangular
! 52: *> = 'L': Lower triangular
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] N
! 56: *> \verbatim
! 57: *> N is INTEGER
! 58: *> The order of the matrix A. N >= 0.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in,out] A
! 62: *> \verbatim
! 63: *> A is COMPLEX*16 array, dimension (LDA,N)
! 64: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 65: *> n by n upper triangular part of A contains the upper
! 66: *> triangular part of the matrix A, and the strictly lower
! 67: *> triangular part of A is not referenced. If UPLO = 'L', the
! 68: *> leading n by n lower triangular part of A contains the lower
! 69: *> triangular part of the matrix A, and the strictly upper
! 70: *> triangular part of A is not referenced.
! 71: *>
! 72: *> On exit, if EQUED = 'Y', the equilibrated matrix:
! 73: *> diag(S) * A * diag(S).
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] LDA
! 77: *> \verbatim
! 78: *> LDA is INTEGER
! 79: *> The leading dimension of the array A. LDA >= max(N,1).
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] S
! 83: *> \verbatim
! 84: *> S is DOUBLE PRECISION array, dimension (N)
! 85: *> The scale factors for A.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] SCOND
! 89: *> \verbatim
! 90: *> SCOND is DOUBLE PRECISION
! 91: *> Ratio of the smallest S(i) to the largest S(i).
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in] AMAX
! 95: *> \verbatim
! 96: *> AMAX is DOUBLE PRECISION
! 97: *> Absolute value of largest matrix entry.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[out] EQUED
! 101: *> \verbatim
! 102: *> EQUED is CHARACTER*1
! 103: *> Specifies whether or not equilibration was done.
! 104: *> = 'N': No equilibration.
! 105: *> = 'Y': Equilibration was done, i.e., A has been replaced by
! 106: *> diag(S) * A * diag(S).
! 107: *> \endverbatim
! 108: *
! 109: *> \par Internal Parameters:
! 110: * =========================
! 111: *>
! 112: *> \verbatim
! 113: *> THRESH is a threshold value used to decide if scaling should be done
! 114: *> based on the ratio of the scaling factors. If SCOND < THRESH,
! 115: *> scaling is done.
! 116: *>
! 117: *> LARGE and SMALL are threshold values used to decide if scaling should
! 118: *> be done based on the absolute size of the largest matrix element.
! 119: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
! 120: *> \endverbatim
! 121: *
! 122: * Authors:
! 123: * ========
! 124: *
! 125: *> \author Univ. of Tennessee
! 126: *> \author Univ. of California Berkeley
! 127: *> \author Univ. of Colorado Denver
! 128: *> \author NAG Ltd.
! 129: *
! 130: *> \date November 2011
! 131: *
! 132: *> \ingroup complex16HEauxiliary
! 133: *
! 134: * =====================================================================
1.1 bertrand 135: SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
136: *
1.8 ! bertrand 137: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 138: * -- LAPACK is a software package provided by Univ. of Tennessee, --
139: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 140: * November 2011
1.1 bertrand 141: *
142: * .. Scalar Arguments ..
143: CHARACTER EQUED, UPLO
144: INTEGER LDA, N
145: DOUBLE PRECISION AMAX, SCOND
146: * ..
147: * .. Array Arguments ..
148: DOUBLE PRECISION S( * )
149: COMPLEX*16 A( LDA, * )
150: * ..
151: *
152: * =====================================================================
153: *
154: * .. Parameters ..
155: DOUBLE PRECISION ONE, THRESH
156: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
157: * ..
158: * .. Local Scalars ..
159: INTEGER I, J
160: DOUBLE PRECISION CJ, LARGE, SMALL
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: DOUBLE PRECISION DLAMCH
165: EXTERNAL LSAME, DLAMCH
166: * ..
167: * .. Intrinsic Functions ..
168: INTRINSIC DBLE
169: * ..
170: * .. Executable Statements ..
171: *
172: * Quick return if possible
173: *
174: IF( N.LE.0 ) THEN
175: EQUED = 'N'
176: RETURN
177: END IF
178: *
179: * Initialize LARGE and SMALL.
180: *
181: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
182: LARGE = ONE / SMALL
183: *
184: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
185: *
186: * No equilibration
187: *
188: EQUED = 'N'
189: ELSE
190: *
191: * Replace A by diag(S) * A * diag(S).
192: *
193: IF( LSAME( UPLO, 'U' ) ) THEN
194: *
195: * Upper triangle of A is stored.
196: *
197: DO 20 J = 1, N
198: CJ = S( J )
199: DO 10 I = 1, J - 1
200: A( I, J ) = CJ*S( I )*A( I, J )
201: 10 CONTINUE
202: A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
203: 20 CONTINUE
204: ELSE
205: *
206: * Lower triangle of A is stored.
207: *
208: DO 40 J = 1, N
209: CJ = S( J )
210: A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
211: DO 30 I = J + 1, N
212: A( I, J ) = CJ*S( I )*A( I, J )
213: 30 CONTINUE
214: 40 CONTINUE
215: END IF
216: EQUED = 'Y'
217: END IF
218: *
219: RETURN
220: *
221: * End of ZLAQHE
222: *
223: END
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