 LAPACK  3.9.1 LAPACK: Linear Algebra PACKage

## ◆ zlaqsb()

 subroutine zlaqsb ( character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED )

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

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

Purpose:
``` ZLAQSB 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 COMPLEX*16 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**H *U or A = L*L**H 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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.```

Definition at line 140 of file zlaqsb.f.

141 *
142 * -- LAPACK auxiliary routine --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 *
146 * .. Scalar Arguments ..
147  CHARACTER EQUED, UPLO
148  INTEGER KD, LDAB, N
149  DOUBLE PRECISION AMAX, SCOND
150 * ..
151 * .. Array Arguments ..
152  DOUBLE PRECISION S( * )
153  COMPLEX*16 AB( LDAB, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  DOUBLE PRECISION ONE, THRESH
160  parameter( one = 1.0d+0, thresh = 0.1d+0 )
161 * ..
162 * .. Local Scalars ..
163  INTEGER I, J
164  DOUBLE PRECISION CJ, LARGE, SMALL
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  DOUBLE PRECISION DLAMCH
169  EXTERNAL lsame, dlamch
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC max, min
173 * ..
174 * .. Executable Statements ..
175 *
176 * Quick return if possible
177 *
178  IF( n.LE.0 ) THEN
179  equed = 'N'
180  RETURN
181  END IF
182 *
183 * Initialize LARGE and SMALL.
184 *
185  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
186  large = one / small
187 *
188  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
189 *
190 * No equilibration
191 *
192  equed = 'N'
193  ELSE
194 *
195 * Replace A by diag(S) * A * diag(S).
196 *
197  IF( lsame( uplo, 'U' ) ) THEN
198 *
199 * Upper triangle of A is stored in band format.
200 *
201  DO 20 j = 1, n
202  cj = s( j )
203  DO 10 i = max( 1, j-kd ), j
204  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
205  10 CONTINUE
206  20 CONTINUE
207  ELSE
208 *
209 * Lower triangle of A is stored.
210 *
211  DO 40 j = 1, n
212  cj = s( j )
213  DO 30 i = j, min( n, j+kd )
214  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
215  30 CONTINUE
216  40 CONTINUE
217  END IF
218  equed = 'Y'
219  END IF
220 *
221  RETURN
222 *
223 * End of ZLAQSB
224 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53