LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ cpbequ()

 subroutine cpbequ ( character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) S, real SCOND, real AMAX, integer INFO )

CPBEQU

Purpose:
``` CPBEQU computes row and column scalings intended to equilibrate a
Hermitian positive definite band matrix A and reduce its condition
number (with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.``` [in] AB ``` AB is COMPLEX array, dimension (LDAB,N) The upper or lower triangle of the Hermitian 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).``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array A. LDAB >= KD+1.``` [out] S ``` S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A.``` [out] SCOND ``` SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.``` [out] AMAX ``` AMAX is REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, the i-th diagonal element is nonpositive.```
Date
December 2016

Definition at line 132 of file cpbequ.f.

132 *
133 * -- LAPACK computational routine (version 3.7.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * December 2016
137 *
138 * .. Scalar Arguments ..
139  CHARACTER uplo
140  INTEGER info, kd, ldab, n
141  REAL amax, scond
142 * ..
143 * .. Array Arguments ..
144  REAL s( * )
145  COMPLEX ab( ldab, * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  REAL zero, one
152  parameter( zero = 0.0e+0, one = 1.0e+0 )
153 * ..
154 * .. Local Scalars ..
155  LOGICAL upper
156  INTEGER i, j
157  REAL smin
158 * ..
159 * .. External Functions ..
160  LOGICAL lsame
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC max, min, REAL, sqrt
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173  info = 0
174  upper = lsame( uplo, 'U' )
175  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
176  info = -1
177  ELSE IF( n.LT.0 ) THEN
178  info = -2
179  ELSE IF( kd.LT.0 ) THEN
180  info = -3
181  ELSE IF( ldab.LT.kd+1 ) THEN
182  info = -5
183  END IF
184  IF( info.NE.0 ) THEN
185  CALL xerbla( 'CPBEQU', -info )
186  RETURN
187  END IF
188 *
189 * Quick return if possible
190 *
191  IF( n.EQ.0 ) THEN
192  scond = one
193  amax = zero
194  RETURN
195  END IF
196 *
197  IF( upper ) THEN
198  j = kd + 1
199  ELSE
200  j = 1
201  END IF
202 *
203 * Initialize SMIN and AMAX.
204 *
205  s( 1 ) = REAL( AB( J, 1 ) )
206  smin = s( 1 )
207  amax = s( 1 )
208 *
209 * Find the minimum and maximum diagonal elements.
210 *
211  DO 10 i = 2, n
212  s( i ) = REAL( AB( J, I ) )
213  smin = min( smin, s( i ) )
214  amax = max( amax, s( i ) )
215  10 CONTINUE
216 *
217  IF( smin.LE.zero ) THEN
218 *
219 * Find the first non-positive diagonal element and return.
220 *
221  DO 20 i = 1, n
222  IF( s( i ).LE.zero ) THEN
223  info = i
224  RETURN
225  END IF
226  20 CONTINUE
227  ELSE
228 *
229 * Set the scale factors to the reciprocals
230 * of the diagonal elements.
231 *
232  DO 30 i = 1, n
233  s( i ) = one / sqrt( s( i ) )
234  30 CONTINUE
235 *
236 * Compute SCOND = min(S(I)) / max(S(I))
237 *
238  scond = sqrt( smin ) / sqrt( amax )
239  END IF
240  RETURN
241 *
242 * End of CPBEQU
243 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
Here is the call graph for this function:
Here is the caller graph for this function: