LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dlaqsb()

subroutine dlaqsb ( character  UPLO,
integer  N,
integer  KD,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( * )  S,
double precision  SCOND,
double precision  AMAX,
character  EQUED 
)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Download DLAQSB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLAQSB equilibrates a symmetric band matrix A using the scaling
 factors in the vector S.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
[in,out]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          On entry, the upper or lower triangle of the symmetric band
          matrix A, stored in the first KD+1 rows of the array.  The
          j-th column of A is stored in the j-th column of the array AB
          as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

          On exit, if INFO = 0, the triangular factor U or L from the
          Cholesky factorization A = U**T*U or A = L*L**T of the band
          matrix A, in the same storage format as A.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]S
          S is DOUBLE PRECISION array, dimension (N)
          The scale factors for A.
[in]SCOND
          SCOND is DOUBLE PRECISION
          Ratio of the smallest S(i) to the largest S(i).
[in]AMAX
          AMAX is DOUBLE PRECISION
          Absolute value of largest matrix entry.
[out]EQUED
          EQUED is CHARACTER*1
          Specifies whether or not equilibration was done.
          = 'N':  No equilibration.
          = 'Y':  Equilibration was done, i.e., A has been replaced by
                  diag(S) * A * diag(S).
Internal Parameters:
  THRESH is a threshold value used to decide if scaling should be done
  based on the ratio of the scaling factors.  If SCOND < THRESH,
  scaling is done.

  LARGE and SMALL are threshold values used to decide if scaling should
  be done based on the absolute size of the largest matrix element.
  If AMAX > LARGE or AMAX < SMALL, scaling is done.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 142 of file dlaqsb.f.

142 *
143 * -- LAPACK auxiliary routine (version 3.7.0) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * December 2016
147 *
148 * .. Scalar Arguments ..
149  CHARACTER equed, uplo
150  INTEGER kd, ldab, n
151  DOUBLE PRECISION amax, scond
152 * ..
153 * .. Array Arguments ..
154  DOUBLE PRECISION ab( ldab, * ), s( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  DOUBLE PRECISION one, thresh
161  parameter( one = 1.0d+0, thresh = 0.1d+0 )
162 * ..
163 * .. Local Scalars ..
164  INTEGER i, j
165  DOUBLE PRECISION cj, large, small
166 * ..
167 * .. External Functions ..
168  LOGICAL lsame
169  DOUBLE PRECISION dlamch
170  EXTERNAL lsame, dlamch
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC max, min
174 * ..
175 * .. Executable Statements ..
176 *
177 * Quick return if possible
178 *
179  IF( 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( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
190 *
191 * No equilibration
192 *
193  equed = 'N'
194  ELSE
195 *
196 * Replace A by diag(S) * A * diag(S).
197 *
198  IF( lsame( uplo, 'U' ) ) THEN
199 *
200 * Upper triangle of A is stored in band format.
201 *
202  DO 20 j = 1, n
203  cj = s( j )
204  DO 10 i = max( 1, j-kd ), j
205  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
206  10 CONTINUE
207  20 CONTINUE
208  ELSE
209 *
210 * Lower triangle of A is stored.
211 *
212  DO 40 j = 1, n
213  cj = s( j )
214  DO 30 i = j, min( n, j+kd )
215  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
216  30 CONTINUE
217  40 CONTINUE
218  END IF
219  equed = 'Y'
220  END IF
221 *
222  RETURN
223 *
224 * End of DLAQSB
225 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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