LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ slaqsb()

subroutine slaqsb ( character  UPLO,
integer  N,
integer  KD,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( * )  S,
real  SCOND,
real  AMAX,
character  EQUED 
)

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

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

Purpose:
 SLAQSB 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 REAL 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 REAL array, dimension (N)
          The scale factors for A.
[in]SCOND
          SCOND is REAL
          Ratio of the smallest S(i) to the largest S(i).
[in]AMAX
          AMAX is REAL
          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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.

Definition at line 139 of file slaqsb.f.

140 *
141 * -- LAPACK auxiliary routine --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 *
145 * .. Scalar Arguments ..
146  CHARACTER EQUED, UPLO
147  INTEGER KD, LDAB, N
148  REAL AMAX, SCOND
149 * ..
150 * .. Array Arguments ..
151  REAL AB( LDAB, * ), S( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  REAL ONE, THRESH
158  parameter( one = 1.0e+0, thresh = 0.1e+0 )
159 * ..
160 * .. Local Scalars ..
161  INTEGER I, J
162  REAL CJ, LARGE, SMALL
163 * ..
164 * .. External Functions ..
165  LOGICAL LSAME
166  REAL SLAMCH
167  EXTERNAL lsame, slamch
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max, min
171 * ..
172 * .. Executable Statements ..
173 *
174 * Quick return if possible
175 *
176  IF( n.LE.0 ) THEN
177  equed = 'N'
178  RETURN
179  END IF
180 *
181 * Initialize LARGE and SMALL.
182 *
183  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
184  large = one / small
185 *
186  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
187 *
188 * No equilibration
189 *
190  equed = 'N'
191  ELSE
192 *
193 * Replace A by diag(S) * A * diag(S).
194 *
195  IF( lsame( uplo, 'U' ) ) THEN
196 *
197 * Upper triangle of A is stored in band format.
198 *
199  DO 20 j = 1, n
200  cj = s( j )
201  DO 10 i = max( 1, j-kd ), j
202  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
203  10 CONTINUE
204  20 CONTINUE
205  ELSE
206 *
207 * Lower triangle of A is stored.
208 *
209  DO 40 j = 1, n
210  cj = s( j )
211  DO 30 i = j, min( n, j+kd )
212  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
213  30 CONTINUE
214  40 CONTINUE
215  END IF
216  equed = 'Y'
217  END IF
218 *
219  RETURN
220 *
221 * End of SLAQSB
222 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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