Annotation of rpl/lapack/lapack/dlaqgb.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLAQGB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAQGB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqgb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqgb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqgb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 22: * AMAX, EQUED )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER EQUED
! 26: * INTEGER KL, KU, LDAB, M, N
! 27: * DOUBLE PRECISION AMAX, COLCND, ROWCND
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DLAQGB equilibrates a general M by N band matrix A with KL
! 40: *> subdiagonals and KU superdiagonals using the row and scaling factors
! 41: *> 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] KL
! 60: *> \verbatim
! 61: *> KL is INTEGER
! 62: *> The number of subdiagonals within the band of A. KL >= 0.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] KU
! 66: *> \verbatim
! 67: *> KU is INTEGER
! 68: *> The number of superdiagonals within the band of A. KU >= 0.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in,out] AB
! 72: *> \verbatim
! 73: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
! 74: *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 75: *> The j-th column of A is stored in the j-th column of the
! 76: *> array AB as follows:
! 77: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
! 78: *>
! 79: *> On exit, the equilibrated matrix, in the same storage format
! 80: *> as A. See EQUED for the form of the equilibrated matrix.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] LDAB
! 84: *> \verbatim
! 85: *> LDAB is INTEGER
! 86: *> The leading dimension of the array AB. LDA >= KL+KU+1.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] R
! 90: *> \verbatim
! 91: *> R is DOUBLE PRECISION array, dimension (M)
! 92: *> The row scale factors for A.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] C
! 96: *> \verbatim
! 97: *> C is DOUBLE PRECISION array, dimension (N)
! 98: *> The column scale factors for A.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] ROWCND
! 102: *> \verbatim
! 103: *> ROWCND is DOUBLE PRECISION
! 104: *> Ratio of the smallest R(i) to the largest R(i).
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in] COLCND
! 108: *> \verbatim
! 109: *> COLCND is DOUBLE PRECISION
! 110: *> Ratio of the smallest C(i) to the largest C(i).
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] AMAX
! 114: *> \verbatim
! 115: *> AMAX is DOUBLE PRECISION
! 116: *> Absolute value of largest matrix entry.
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[out] EQUED
! 120: *> \verbatim
! 121: *> EQUED is CHARACTER*1
! 122: *> Specifies the form of equilibration that was done.
! 123: *> = 'N': No equilibration
! 124: *> = 'R': Row equilibration, i.e., A has been premultiplied by
! 125: *> diag(R).
! 126: *> = 'C': Column equilibration, i.e., A has been postmultiplied
! 127: *> by diag(C).
! 128: *> = 'B': Both row and column equilibration, i.e., A has been
! 129: *> replaced by diag(R) * A * diag(C).
! 130: *> \endverbatim
! 131: *
! 132: *> \par Internal Parameters:
! 133: * =========================
! 134: *>
! 135: *> \verbatim
! 136: *> THRESH is a threshold value used to decide if row or column scaling
! 137: *> should be done based on the ratio of the row or column scaling
! 138: *> factors. If ROWCND < THRESH, row scaling is done, and if
! 139: *> COLCND < THRESH, column scaling is done.
! 140: *>
! 141: *> LARGE and SMALL are threshold values used to decide if row scaling
! 142: *> should be done based on the absolute size of the largest matrix
! 143: *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
! 144: *> \endverbatim
! 145: *
! 146: * Authors:
! 147: * ========
! 148: *
! 149: *> \author Univ. of Tennessee
! 150: *> \author Univ. of California Berkeley
! 151: *> \author Univ. of Colorado Denver
! 152: *> \author NAG Ltd.
! 153: *
! 154: *> \date November 2011
! 155: *
! 156: *> \ingroup doubleGBauxiliary
! 157: *
! 158: * =====================================================================
1.1 bertrand 159: SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
160: $ AMAX, EQUED )
161: *
1.8 ! bertrand 162: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 163: * -- LAPACK is a software package provided by Univ. of Tennessee, --
164: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 165: * November 2011
1.1 bertrand 166: *
167: * .. Scalar Arguments ..
168: CHARACTER EQUED
169: INTEGER KL, KU, LDAB, M, N
170: DOUBLE PRECISION AMAX, COLCND, ROWCND
171: * ..
172: * .. Array Arguments ..
173: DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
174: * ..
175: *
176: * =====================================================================
177: *
178: * .. Parameters ..
179: DOUBLE PRECISION ONE, THRESH
180: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
181: * ..
182: * .. Local Scalars ..
183: INTEGER I, J
184: DOUBLE PRECISION CJ, LARGE, SMALL
185: * ..
186: * .. External Functions ..
187: DOUBLE PRECISION DLAMCH
188: EXTERNAL DLAMCH
189: * ..
190: * .. Intrinsic Functions ..
191: INTRINSIC MAX, MIN
192: * ..
193: * .. Executable Statements ..
194: *
195: * Quick return if possible
196: *
197: IF( M.LE.0 .OR. N.LE.0 ) THEN
198: EQUED = 'N'
199: RETURN
200: END IF
201: *
202: * Initialize LARGE and SMALL.
203: *
204: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
205: LARGE = ONE / SMALL
206: *
207: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
208: $ THEN
209: *
210: * No row scaling
211: *
212: IF( COLCND.GE.THRESH ) THEN
213: *
214: * No column scaling
215: *
216: EQUED = 'N'
217: ELSE
218: *
219: * Column scaling
220: *
221: DO 20 J = 1, N
222: CJ = C( J )
223: DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
224: AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
225: 10 CONTINUE
226: 20 CONTINUE
227: EQUED = 'C'
228: END IF
229: ELSE IF( COLCND.GE.THRESH ) THEN
230: *
231: * Row scaling, no column scaling
232: *
233: DO 40 J = 1, N
234: DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
235: AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
236: 30 CONTINUE
237: 40 CONTINUE
238: EQUED = 'R'
239: ELSE
240: *
241: * Row and column scaling
242: *
243: DO 60 J = 1, N
244: CJ = C( J )
245: DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
246: AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
247: 50 CONTINUE
248: 60 CONTINUE
249: EQUED = 'B'
250: END IF
251: *
252: RETURN
253: *
254: * End of DLAQGB
255: *
256: END
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