 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cpbcon()

 subroutine cpbcon ( character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real ANORM, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CPBCON

Purpose:
``` CPBCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite band matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed by
CPBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.``` [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 sub-diagonals if UPLO = 'L'. KD >= 0.``` [in] AB ``` AB is COMPLEX array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [in] ANORM ``` ANORM is REAL The 1-norm (or infinity-norm) of the Hermitian band matrix A.``` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 131 of file cpbcon.f.

133 *
134 * -- LAPACK computational routine --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 *
138 * .. Scalar Arguments ..
139  CHARACTER UPLO
140  INTEGER INFO, KD, LDAB, N
141  REAL ANORM, RCOND
142 * ..
143 * .. Array Arguments ..
144  REAL RWORK( * )
145  COMPLEX AB( LDAB, * ), WORK( * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  REAL ONE, ZERO
152  parameter( one = 1.0e+0, zero = 0.0e+0 )
153 * ..
154 * .. Local Scalars ..
155  LOGICAL UPPER
156  CHARACTER NORMIN
157  INTEGER IX, KASE
158  REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
159  COMPLEX ZDUM
160 * ..
161 * .. Local Arrays ..
162  INTEGER ISAVE( 3 )
163 * ..
164 * .. External Functions ..
165  LOGICAL LSAME
166  INTEGER ICAMAX
167  REAL SLAMCH
168  EXTERNAL lsame, icamax, slamch
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL clacn2, clatbs, csrscl, xerbla
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC abs, aimag, real
175 * ..
176 * .. Statement Functions ..
177  REAL CABS1
178 * ..
179 * .. Statement Function definitions ..
180  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187  upper = lsame( uplo, 'U' )
188  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
189  info = -1
190  ELSE IF( n.LT.0 ) THEN
191  info = -2
192  ELSE IF( kd.LT.0 ) THEN
193  info = -3
194  ELSE IF( ldab.LT.kd+1 ) THEN
195  info = -5
196  ELSE IF( anorm.LT.zero ) THEN
197  info = -6
198  END IF
199  IF( info.NE.0 ) THEN
200  CALL xerbla( 'CPBCON', -info )
201  RETURN
202  END IF
203 *
204 * Quick return if possible
205 *
206  rcond = zero
207  IF( n.EQ.0 ) THEN
208  rcond = one
209  RETURN
210  ELSE IF( anorm.EQ.zero ) THEN
211  RETURN
212  END IF
213 *
214  smlnum = slamch( 'Safe minimum' )
215 *
216 * Estimate the 1-norm of the inverse.
217 *
218  kase = 0
219  normin = 'N'
220  10 CONTINUE
221  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
222  IF( kase.NE.0 ) THEN
223  IF( upper ) THEN
224 *
225 * Multiply by inv(U**H).
226 *
227  CALL clatbs( 'Upper', 'Conjugate transpose', 'Non-unit',
228  \$ normin, n, kd, ab, ldab, work, scalel, rwork,
229  \$ info )
230  normin = 'Y'
231 *
232 * Multiply by inv(U).
233 *
234  CALL clatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
235  \$ kd, ab, ldab, work, scaleu, rwork, info )
236  ELSE
237 *
238 * Multiply by inv(L).
239 *
240  CALL clatbs( 'Lower', 'No transpose', 'Non-unit', normin, n,
241  \$ kd, ab, ldab, work, scalel, rwork, info )
242  normin = 'Y'
243 *
244 * Multiply by inv(L**H).
245 *
246  CALL clatbs( 'Lower', 'Conjugate transpose', 'Non-unit',
247  \$ normin, n, kd, ab, ldab, work, scaleu, rwork,
248  \$ info )
249  END IF
250 *
251 * Multiply by 1/SCALE if doing so will not cause overflow.
252 *
253  scale = scalel*scaleu
254  IF( scale.NE.one ) THEN
255  ix = icamax( n, work, 1 )
256  IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
257  \$ GO TO 20
258  CALL csrscl( n, scale, work, 1 )
259  END IF
260  GO TO 10
261  END IF
262 *
263 * Compute the estimate of the reciprocal condition number.
264 *
265  IF( ainvnm.NE.zero )
266  \$ rcond = ( one / ainvnm ) / anorm
267 *
268  20 CONTINUE
269 *
270  RETURN
271 *
272 * End of CPBCON
273 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:84
subroutine clatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
CLATBS solves a triangular banded system of equations.
Definition: clatbs.f:243
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:133
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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