Annotation of rpl/lapack/lapack/zlaqsb.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZLAQSB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAQSB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqsb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqsb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqsb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER EQUED, UPLO
! 25: * INTEGER KD, LDAB, N
! 26: * DOUBLE PRECISION AMAX, SCOND
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION S( * )
! 30: * COMPLEX*16 AB( LDAB, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZLAQSB equilibrates a symmetric band matrix A using the scaling
! 40: *> factors in the vector S.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] UPLO
! 47: *> \verbatim
! 48: *> UPLO is CHARACTER*1
! 49: *> Specifies whether the upper or lower triangular part of the
! 50: *> symmetric matrix A is stored.
! 51: *> = 'U': Upper triangular
! 52: *> = 'L': Lower triangular
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] N
! 56: *> \verbatim
! 57: *> N is INTEGER
! 58: *> The order of the matrix A. N >= 0.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] KD
! 62: *> \verbatim
! 63: *> KD is INTEGER
! 64: *> The number of super-diagonals of the matrix A if UPLO = 'U',
! 65: *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in,out] AB
! 69: *> \verbatim
! 70: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 71: *> On entry, the upper or lower triangle of the symmetric band
! 72: *> matrix A, stored in the first KD+1 rows of the array. The
! 73: *> j-th column of A is stored in the j-th column of the array AB
! 74: *> as follows:
! 75: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 76: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 77: *>
! 78: *> On exit, if INFO = 0, the triangular factor U or L from the
! 79: *> Cholesky factorization A = U**H *U or A = L*L**H of the band
! 80: *> matrix A, in the same storage format as A.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] LDAB
! 84: *> \verbatim
! 85: *> LDAB is INTEGER
! 86: *> The leading dimension of the array AB. LDAB >= KD+1.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] S
! 90: *> \verbatim
! 91: *> S is DOUBLE PRECISION array, dimension (N)
! 92: *> The scale factors for A.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] SCOND
! 96: *> \verbatim
! 97: *> SCOND is DOUBLE PRECISION
! 98: *> Ratio of the smallest S(i) to the largest S(i).
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] AMAX
! 102: *> \verbatim
! 103: *> AMAX is DOUBLE PRECISION
! 104: *> Absolute value of largest matrix entry.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[out] EQUED
! 108: *> \verbatim
! 109: *> EQUED is CHARACTER*1
! 110: *> Specifies whether or not equilibration was done.
! 111: *> = 'N': No equilibration.
! 112: *> = 'Y': Equilibration was done, i.e., A has been replaced by
! 113: *> diag(S) * A * diag(S).
! 114: *> \endverbatim
! 115: *
! 116: *> \par Internal Parameters:
! 117: * =========================
! 118: *>
! 119: *> \verbatim
! 120: *> THRESH is a threshold value used to decide if scaling should be done
! 121: *> based on the ratio of the scaling factors. If SCOND < THRESH,
! 122: *> scaling is done.
! 123: *>
! 124: *> LARGE and SMALL are threshold values used to decide if scaling should
! 125: *> be done based on the absolute size of the largest matrix element.
! 126: *> If AMAX > LARGE or AMAX < SMALL, 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 complex16OTHERauxiliary
! 140: *
! 141: * =====================================================================
1.1 bertrand 142: SUBROUTINE ZLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
143: *
1.9 ! bertrand 144: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 145: * -- LAPACK is a software package provided by Univ. of Tennessee, --
146: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 147: * November 2011
1.1 bertrand 148: *
149: * .. Scalar Arguments ..
150: CHARACTER EQUED, UPLO
151: INTEGER KD, LDAB, N
152: DOUBLE PRECISION AMAX, SCOND
153: * ..
154: * .. Array Arguments ..
155: DOUBLE PRECISION S( * )
156: COMPLEX*16 AB( LDAB, * )
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: LOGICAL LSAME
171: DOUBLE PRECISION DLAMCH
172: EXTERNAL LSAME, DLAMCH
173: * ..
174: * .. Intrinsic Functions ..
175: INTRINSIC MAX, MIN
176: * ..
177: * .. Executable Statements ..
178: *
179: * Quick return if possible
180: *
181: IF( N.LE.0 ) THEN
182: EQUED = 'N'
183: RETURN
184: END IF
185: *
186: * Initialize LARGE and SMALL.
187: *
188: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
189: LARGE = ONE / SMALL
190: *
191: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
192: *
193: * No equilibration
194: *
195: EQUED = 'N'
196: ELSE
197: *
198: * Replace A by diag(S) * A * diag(S).
199: *
200: IF( LSAME( UPLO, 'U' ) ) THEN
201: *
202: * Upper triangle of A is stored in band format.
203: *
204: DO 20 J = 1, N
205: CJ = S( J )
206: DO 10 I = MAX( 1, J-KD ), J
207: AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
208: 10 CONTINUE
209: 20 CONTINUE
210: ELSE
211: *
212: * Lower triangle of A is stored.
213: *
214: DO 40 J = 1, N
215: CJ = S( J )
216: DO 30 I = J, MIN( N, J+KD )
217: AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
218: 30 CONTINUE
219: 40 CONTINUE
220: END IF
221: EQUED = 'Y'
222: END IF
223: *
224: RETURN
225: *
226: * End of ZLAQSB
227: *
228: END
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