Annotation of rpl/lapack/lapack/zlaqgb.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLAQGB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAQGB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqgb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqgb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqgb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAQGB( 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 C( * ), R( * )
! 31: * COMPLEX*16 AB( LDAB, * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZLAQGB equilibrates a general M by N band matrix A with KL
! 41: *> subdiagonals and KU superdiagonals using the row and scaling factors
! 42: *> in the vectors R and C.
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] M
! 49: *> \verbatim
! 50: *> M is INTEGER
! 51: *> The number of rows of the matrix A. M >= 0.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] N
! 55: *> \verbatim
! 56: *> N is INTEGER
! 57: *> The number of columns of the matrix A. N >= 0.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] KL
! 61: *> \verbatim
! 62: *> KL is INTEGER
! 63: *> The number of subdiagonals within the band of A. KL >= 0.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] KU
! 67: *> \verbatim
! 68: *> KU is INTEGER
! 69: *> The number of superdiagonals within the band of A. KU >= 0.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in,out] AB
! 73: *> \verbatim
! 74: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 75: *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 76: *> The j-th column of A is stored in the j-th column of the
! 77: *> array AB as follows:
! 78: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
! 79: *>
! 80: *> On exit, the equilibrated matrix, in the same storage format
! 81: *> as A. See EQUED for the form of the equilibrated matrix.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] LDAB
! 85: *> \verbatim
! 86: *> LDAB is INTEGER
! 87: *> The leading dimension of the array AB. LDA >= KL+KU+1.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] R
! 91: *> \verbatim
! 92: *> R is DOUBLE PRECISION array, dimension (M)
! 93: *> The row scale factors for A.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] C
! 97: *> \verbatim
! 98: *> C is DOUBLE PRECISION array, dimension (N)
! 99: *> The column scale factors for A.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] ROWCND
! 103: *> \verbatim
! 104: *> ROWCND is DOUBLE PRECISION
! 105: *> Ratio of the smallest R(i) to the largest R(i).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] COLCND
! 109: *> \verbatim
! 110: *> COLCND is DOUBLE PRECISION
! 111: *> Ratio of the smallest C(i) to the largest C(i).
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in] AMAX
! 115: *> \verbatim
! 116: *> AMAX is DOUBLE PRECISION
! 117: *> Absolute value of largest matrix entry.
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[out] EQUED
! 121: *> \verbatim
! 122: *> EQUED is CHARACTER*1
! 123: *> Specifies the form of equilibration that was done.
! 124: *> = 'N': No equilibration
! 125: *> = 'R': Row equilibration, i.e., A has been premultiplied by
! 126: *> diag(R).
! 127: *> = 'C': Column equilibration, i.e., A has been postmultiplied
! 128: *> by diag(C).
! 129: *> = 'B': Both row and column equilibration, i.e., A has been
! 130: *> replaced by diag(R) * A * diag(C).
! 131: *> \endverbatim
! 132: *
! 133: *> \par Internal Parameters:
! 134: * =========================
! 135: *>
! 136: *> \verbatim
! 137: *> THRESH is a threshold value used to decide if row or column scaling
! 138: *> should be done based on the ratio of the row or column scaling
! 139: *> factors. If ROWCND < THRESH, row scaling is done, and if
! 140: *> COLCND < THRESH, column scaling is done.
! 141: *>
! 142: *> LARGE and SMALL are threshold values used to decide if row scaling
! 143: *> should be done based on the absolute size of the largest matrix
! 144: *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
! 145: *> \endverbatim
! 146: *
! 147: * Authors:
! 148: * ========
! 149: *
! 150: *> \author Univ. of Tennessee
! 151: *> \author Univ. of California Berkeley
! 152: *> \author Univ. of Colorado Denver
! 153: *> \author NAG Ltd.
! 154: *
! 155: *> \date November 2011
! 156: *
! 157: *> \ingroup complex16GBauxiliary
! 158: *
! 159: * =====================================================================
1.1 bertrand 160: SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
161: $ AMAX, EQUED )
162: *
1.8 ! bertrand 163: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 164: * -- LAPACK is a software package provided by Univ. of Tennessee, --
165: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 166: * November 2011
1.1 bertrand 167: *
168: * .. Scalar Arguments ..
169: CHARACTER EQUED
170: INTEGER KL, KU, LDAB, M, N
171: DOUBLE PRECISION AMAX, COLCND, ROWCND
172: * ..
173: * .. Array Arguments ..
174: DOUBLE PRECISION C( * ), R( * )
175: COMPLEX*16 AB( LDAB, * )
176: * ..
177: *
178: * =====================================================================
179: *
180: * .. Parameters ..
181: DOUBLE PRECISION ONE, THRESH
182: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
183: * ..
184: * .. Local Scalars ..
185: INTEGER I, J
186: DOUBLE PRECISION CJ, LARGE, SMALL
187: * ..
188: * .. External Functions ..
189: DOUBLE PRECISION DLAMCH
190: EXTERNAL DLAMCH
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC MAX, MIN
194: * ..
195: * .. Executable Statements ..
196: *
197: * Quick return if possible
198: *
199: IF( M.LE.0 .OR. N.LE.0 ) THEN
200: EQUED = 'N'
201: RETURN
202: END IF
203: *
204: * Initialize LARGE and SMALL.
205: *
206: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
207: LARGE = ONE / SMALL
208: *
209: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
210: $ THEN
211: *
212: * No row scaling
213: *
214: IF( COLCND.GE.THRESH ) THEN
215: *
216: * No column scaling
217: *
218: EQUED = 'N'
219: ELSE
220: *
221: * Column scaling
222: *
223: DO 20 J = 1, N
224: CJ = C( J )
225: DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
226: AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
227: 10 CONTINUE
228: 20 CONTINUE
229: EQUED = 'C'
230: END IF
231: ELSE IF( COLCND.GE.THRESH ) THEN
232: *
233: * Row scaling, no column scaling
234: *
235: DO 40 J = 1, N
236: DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
237: AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
238: 30 CONTINUE
239: 40 CONTINUE
240: EQUED = 'R'
241: ELSE
242: *
243: * Row and column scaling
244: *
245: DO 60 J = 1, N
246: CJ = C( J )
247: DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
248: AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
249: 50 CONTINUE
250: 60 CONTINUE
251: EQUED = 'B'
252: END IF
253: *
254: RETURN
255: *
256: * End of ZLAQGB
257: *
258: END
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