Annotation of rpl/lapack/lapack/dlaqge.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLAQGE
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAQGE + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqge.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqge.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqge.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
! 22: * EQUED )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER EQUED
! 26: * INTEGER LDA, M, N
! 27: * DOUBLE PRECISION AMAX, COLCND, ROWCND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DLAQGE equilibrates a general M by N matrix A using the row and
! 40: *> column scaling factors in the vectors R and C.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] M
! 47: *> \verbatim
! 48: *> M is INTEGER
! 49: *> The number of rows of the matrix A. M >= 0.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] N
! 53: *> \verbatim
! 54: *> N is INTEGER
! 55: *> The number of columns of the matrix A. N >= 0.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in,out] A
! 59: *> \verbatim
! 60: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 61: *> On entry, the M by N matrix A.
! 62: *> On exit, the equilibrated matrix. See EQUED for the form of
! 63: *> the equilibrated matrix.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] LDA
! 67: *> \verbatim
! 68: *> LDA is INTEGER
! 69: *> The leading dimension of the array A. LDA >= max(M,1).
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] R
! 73: *> \verbatim
! 74: *> R is DOUBLE PRECISION array, dimension (M)
! 75: *> The row scale factors for A.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] C
! 79: *> \verbatim
! 80: *> C is DOUBLE PRECISION array, dimension (N)
! 81: *> The column scale factors for A.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] ROWCND
! 85: *> \verbatim
! 86: *> ROWCND is DOUBLE PRECISION
! 87: *> Ratio of the smallest R(i) to the largest R(i).
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] COLCND
! 91: *> \verbatim
! 92: *> COLCND is DOUBLE PRECISION
! 93: *> Ratio of the smallest C(i) to the largest C(i).
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] AMAX
! 97: *> \verbatim
! 98: *> AMAX is DOUBLE PRECISION
! 99: *> Absolute value of largest matrix entry.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[out] EQUED
! 103: *> \verbatim
! 104: *> EQUED is CHARACTER*1
! 105: *> Specifies the form of equilibration that was done.
! 106: *> = 'N': No equilibration
! 107: *> = 'R': Row equilibration, i.e., A has been premultiplied by
! 108: *> diag(R).
! 109: *> = 'C': Column equilibration, i.e., A has been postmultiplied
! 110: *> by diag(C).
! 111: *> = 'B': Both row and column equilibration, i.e., A has been
! 112: *> replaced by diag(R) * A * diag(C).
! 113: *> \endverbatim
! 114: *
! 115: *> \par Internal Parameters:
! 116: * =========================
! 117: *>
! 118: *> \verbatim
! 119: *> THRESH is a threshold value used to decide if row or column scaling
! 120: *> should be done based on the ratio of the row or column scaling
! 121: *> factors. If ROWCND < THRESH, row scaling is done, and if
! 122: *> COLCND < THRESH, column scaling is done.
! 123: *>
! 124: *> LARGE and SMALL are threshold values used to decide if row scaling
! 125: *> should be done based on the absolute size of the largest matrix
! 126: *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
! 127: *> \endverbatim
! 128: *
! 129: * Authors:
! 130: * ========
! 131: *
! 132: *> \author Univ. of Tennessee
! 133: *> \author Univ. of California Berkeley
! 134: *> \author Univ. of Colorado Denver
! 135: *> \author NAG Ltd.
! 136: *
! 137: *> \date November 2011
! 138: *
! 139: *> \ingroup doubleGEauxiliary
! 140: *
! 141: * =====================================================================
1.1 bertrand 142: SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
143: $ EQUED )
144: *
1.8 ! bertrand 145: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 146: * -- LAPACK is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 148: * November 2011
1.1 bertrand 149: *
150: * .. Scalar Arguments ..
151: CHARACTER EQUED
152: INTEGER LDA, M, N
153: DOUBLE PRECISION AMAX, COLCND, ROWCND
154: * ..
155: * .. Array Arguments ..
156: DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: DOUBLE PRECISION ONE, THRESH
163: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
164: * ..
165: * .. Local Scalars ..
166: INTEGER I, J
167: DOUBLE PRECISION CJ, LARGE, SMALL
168: * ..
169: * .. External Functions ..
170: DOUBLE PRECISION DLAMCH
171: EXTERNAL DLAMCH
172: * ..
173: * .. Executable Statements ..
174: *
175: * Quick return if possible
176: *
177: IF( M.LE.0 .OR. N.LE.0 ) THEN
178: EQUED = 'N'
179: RETURN
180: END IF
181: *
182: * Initialize LARGE and SMALL.
183: *
184: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
185: LARGE = ONE / SMALL
186: *
187: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
188: $ THEN
189: *
190: * No row scaling
191: *
192: IF( COLCND.GE.THRESH ) THEN
193: *
194: * No column scaling
195: *
196: EQUED = 'N'
197: ELSE
198: *
199: * Column scaling
200: *
201: DO 20 J = 1, N
202: CJ = C( J )
203: DO 10 I = 1, M
204: A( I, J ) = CJ*A( I, J )
205: 10 CONTINUE
206: 20 CONTINUE
207: EQUED = 'C'
208: END IF
209: ELSE IF( COLCND.GE.THRESH ) THEN
210: *
211: * Row scaling, no column scaling
212: *
213: DO 40 J = 1, N
214: DO 30 I = 1, M
215: A( I, J ) = R( I )*A( I, J )
216: 30 CONTINUE
217: 40 CONTINUE
218: EQUED = 'R'
219: ELSE
220: *
221: * Row and column scaling
222: *
223: DO 60 J = 1, N
224: CJ = C( J )
225: DO 50 I = 1, M
226: A( I, J ) = CJ*R( I )*A( I, J )
227: 50 CONTINUE
228: 60 CONTINUE
229: EQUED = 'B'
230: END IF
231: *
232: RETURN
233: *
234: * End of DLAQGE
235: *
236: END
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