Annotation of rpl/lapack/lapack/zlaqhp.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLAQHP
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAQHP + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqhp.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqhp.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqhp.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER EQUED, UPLO
! 25: * INTEGER N
! 26: * DOUBLE PRECISION AMAX, SCOND
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION S( * )
! 30: * COMPLEX*16 AP( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZLAQHP 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] AP
! 62: *> \verbatim
! 63: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 64: *> On entry, the upper or lower triangle of the Hermitian matrix
! 65: *> A, packed columnwise in a linear array. The j-th column of A
! 66: *> is stored in the array AP as follows:
! 67: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 68: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 69: *>
! 70: *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in
! 71: *> the same storage format as A.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] S
! 75: *> \verbatim
! 76: *> S is DOUBLE PRECISION array, dimension (N)
! 77: *> The scale factors for A.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] SCOND
! 81: *> \verbatim
! 82: *> SCOND is DOUBLE PRECISION
! 83: *> Ratio of the smallest S(i) to the largest S(i).
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] AMAX
! 87: *> \verbatim
! 88: *> AMAX is DOUBLE PRECISION
! 89: *> Absolute value of largest matrix entry.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] EQUED
! 93: *> \verbatim
! 94: *> EQUED is CHARACTER*1
! 95: *> Specifies whether or not equilibration was done.
! 96: *> = 'N': No equilibration.
! 97: *> = 'Y': Equilibration was done, i.e., A has been replaced by
! 98: *> diag(S) * A * diag(S).
! 99: *> \endverbatim
! 100: *
! 101: *> \par Internal Parameters:
! 102: * =========================
! 103: *>
! 104: *> \verbatim
! 105: *> THRESH is a threshold value used to decide if scaling should be done
! 106: *> based on the ratio of the scaling factors. If SCOND < THRESH,
! 107: *> scaling is done.
! 108: *>
! 109: *> LARGE and SMALL are threshold values used to decide if scaling should
! 110: *> be done based on the absolute size of the largest matrix element.
! 111: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
! 112: *> \endverbatim
! 113: *
! 114: * Authors:
! 115: * ========
! 116: *
! 117: *> \author Univ. of Tennessee
! 118: *> \author Univ. of California Berkeley
! 119: *> \author Univ. of Colorado Denver
! 120: *> \author NAG Ltd.
! 121: *
! 122: *> \date November 2011
! 123: *
! 124: *> \ingroup complex16OTHERauxiliary
! 125: *
! 126: * =====================================================================
1.1 bertrand 127: SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
128: *
1.8 ! bertrand 129: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 130: * -- LAPACK is a software package provided by Univ. of Tennessee, --
131: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 132: * November 2011
1.1 bertrand 133: *
134: * .. Scalar Arguments ..
135: CHARACTER EQUED, UPLO
136: INTEGER N
137: DOUBLE PRECISION AMAX, SCOND
138: * ..
139: * .. Array Arguments ..
140: DOUBLE PRECISION S( * )
141: COMPLEX*16 AP( * )
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Parameters ..
147: DOUBLE PRECISION ONE, THRESH
148: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
149: * ..
150: * .. Local Scalars ..
151: INTEGER I, J, JC
152: DOUBLE PRECISION CJ, LARGE, SMALL
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: DOUBLE PRECISION DLAMCH
157: EXTERNAL LSAME, DLAMCH
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC DBLE
161: * ..
162: * .. Executable Statements ..
163: *
164: * Quick return if possible
165: *
166: IF( N.LE.0 ) THEN
167: EQUED = 'N'
168: RETURN
169: END IF
170: *
171: * Initialize LARGE and SMALL.
172: *
173: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
174: LARGE = ONE / SMALL
175: *
176: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
177: *
178: * No equilibration
179: *
180: EQUED = 'N'
181: ELSE
182: *
183: * Replace A by diag(S) * A * diag(S).
184: *
185: IF( LSAME( UPLO, 'U' ) ) THEN
186: *
187: * Upper triangle of A is stored.
188: *
189: JC = 1
190: DO 20 J = 1, N
191: CJ = S( J )
192: DO 10 I = 1, J - 1
193: AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
194: 10 CONTINUE
195: AP( JC+J-1 ) = CJ*CJ*DBLE( AP( JC+J-1 ) )
196: JC = JC + J
197: 20 CONTINUE
198: ELSE
199: *
200: * Lower triangle of A is stored.
201: *
202: JC = 1
203: DO 40 J = 1, N
204: CJ = S( J )
205: AP( JC ) = CJ*CJ*DBLE( AP( JC ) )
206: DO 30 I = J + 1, N
207: AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
208: 30 CONTINUE
209: JC = JC + N - J + 1
210: 40 CONTINUE
211: END IF
212: EQUED = 'Y'
213: END IF
214: *
215: RETURN
216: *
217: * End of ZLAQHP
218: *
219: END
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