Annotation of rpl/lapack/lapack/zlaqge.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLAQGE
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAQGE + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqge.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqge.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqge.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAQGE( 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 C( * ), R( * )
! 31: * COMPLEX*16 A( LDA, * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZLAQGE equilibrates a general M by N matrix A using the row and
! 41: *> column scaling factors in the vectors R and C.
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] M
! 48: *> \verbatim
! 49: *> M is INTEGER
! 50: *> The number of rows of the matrix A. M >= 0.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] N
! 54: *> \verbatim
! 55: *> N is INTEGER
! 56: *> The number of columns of the matrix A. N >= 0.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in,out] A
! 60: *> \verbatim
! 61: *> A is COMPLEX*16 array, dimension (LDA,N)
! 62: *> On entry, the M by N matrix A.
! 63: *> On exit, the equilibrated matrix. See EQUED for the form of
! 64: *> the equilibrated matrix.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] LDA
! 68: *> \verbatim
! 69: *> LDA is INTEGER
! 70: *> The leading dimension of the array A. LDA >= max(M,1).
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] R
! 74: *> \verbatim
! 75: *> R is DOUBLE PRECISION array, dimension (M)
! 76: *> The row scale factors for A.
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] C
! 80: *> \verbatim
! 81: *> C is DOUBLE PRECISION array, dimension (N)
! 82: *> The column scale factors for A.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] ROWCND
! 86: *> \verbatim
! 87: *> ROWCND is DOUBLE PRECISION
! 88: *> Ratio of the smallest R(i) to the largest R(i).
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in] COLCND
! 92: *> \verbatim
! 93: *> COLCND is DOUBLE PRECISION
! 94: *> Ratio of the smallest C(i) to the largest C(i).
! 95: *> \endverbatim
! 96: *>
! 97: *> \param[in] AMAX
! 98: *> \verbatim
! 99: *> AMAX is DOUBLE PRECISION
! 100: *> Absolute value of largest matrix entry.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[out] EQUED
! 104: *> \verbatim
! 105: *> EQUED is CHARACTER*1
! 106: *> Specifies the form of equilibration that was done.
! 107: *> = 'N': No equilibration
! 108: *> = 'R': Row equilibration, i.e., A has been premultiplied by
! 109: *> diag(R).
! 110: *> = 'C': Column equilibration, i.e., A has been postmultiplied
! 111: *> by diag(C).
! 112: *> = 'B': Both row and column equilibration, i.e., A has been
! 113: *> replaced by diag(R) * A * diag(C).
! 114: *> \endverbatim
! 115: *
! 116: *> \par Internal Parameters:
! 117: * =========================
! 118: *>
! 119: *> \verbatim
! 120: *> THRESH is a threshold value used to decide if row or column scaling
! 121: *> should be done based on the ratio of the row or column scaling
! 122: *> factors. If ROWCND < THRESH, row scaling is done, and if
! 123: *> COLCND < THRESH, column scaling is done.
! 124: *>
! 125: *> LARGE and SMALL are threshold values used to decide if row scaling
! 126: *> should be done based on the absolute size of the largest matrix
! 127: *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
! 128: *> \endverbatim
! 129: *
! 130: * Authors:
! 131: * ========
! 132: *
! 133: *> \author Univ. of Tennessee
! 134: *> \author Univ. of California Berkeley
! 135: *> \author Univ. of Colorado Denver
! 136: *> \author NAG Ltd.
! 137: *
! 138: *> \date November 2011
! 139: *
! 140: *> \ingroup complex16GEauxiliary
! 141: *
! 142: * =====================================================================
1.1 bertrand 143: SUBROUTINE ZLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
144: $ EQUED )
145: *
1.8 ! bertrand 146: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 147: * -- LAPACK is a software package provided by Univ. of Tennessee, --
148: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 149: * November 2011
1.1 bertrand 150: *
151: * .. Scalar Arguments ..
152: CHARACTER EQUED
153: INTEGER LDA, M, N
154: DOUBLE PRECISION AMAX, COLCND, ROWCND
155: * ..
156: * .. Array Arguments ..
157: DOUBLE PRECISION C( * ), R( * )
158: COMPLEX*16 A( LDA, * )
159: * ..
160: *
161: * =====================================================================
162: *
163: * .. Parameters ..
164: DOUBLE PRECISION ONE, THRESH
165: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
166: * ..
167: * .. Local Scalars ..
168: INTEGER I, J
169: DOUBLE PRECISION CJ, LARGE, SMALL
170: * ..
171: * .. External Functions ..
172: DOUBLE PRECISION DLAMCH
173: EXTERNAL DLAMCH
174: * ..
175: * .. Executable Statements ..
176: *
177: * Quick return if possible
178: *
179: IF( M.LE.0 .OR. N.LE.0 ) THEN
180: EQUED = 'N'
181: RETURN
182: END IF
183: *
184: * Initialize LARGE and SMALL.
185: *
186: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
187: LARGE = ONE / SMALL
188: *
189: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
190: $ THEN
191: *
192: * No row scaling
193: *
194: IF( COLCND.GE.THRESH ) THEN
195: *
196: * No column scaling
197: *
198: EQUED = 'N'
199: ELSE
200: *
201: * Column scaling
202: *
203: DO 20 J = 1, N
204: CJ = C( J )
205: DO 10 I = 1, M
206: A( I, J ) = CJ*A( I, J )
207: 10 CONTINUE
208: 20 CONTINUE
209: EQUED = 'C'
210: END IF
211: ELSE IF( COLCND.GE.THRESH ) THEN
212: *
213: * Row scaling, no column scaling
214: *
215: DO 40 J = 1, N
216: DO 30 I = 1, M
217: A( I, J ) = R( I )*A( I, J )
218: 30 CONTINUE
219: 40 CONTINUE
220: EQUED = 'R'
221: ELSE
222: *
223: * Row and column scaling
224: *
225: DO 60 J = 1, N
226: CJ = C( J )
227: DO 50 I = 1, M
228: A( I, J ) = CJ*R( I )*A( I, J )
229: 50 CONTINUE
230: 60 CONTINUE
231: EQUED = 'B'
232: END IF
233: *
234: RETURN
235: *
236: * End of ZLAQGE
237: *
238: END
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