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