LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dtpcon()

 subroutine dtpcon ( character NORM, character UPLO, character DIAG, integer N, double precision, dimension( * ) AP, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

DTPCON

Purpose:
``` DTPCON estimates the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).```
Parameters
 [in] NORM ``` NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.``` [in] DIAG ``` DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] AP ``` AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.``` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (3*N)` [out] IWORK ` IWORK is INTEGER 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 128 of file dtpcon.f.

130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER DIAG, NORM, UPLO
137  INTEGER INFO, N
138  DOUBLE PRECISION RCOND
139 * ..
140 * .. Array Arguments ..
141  INTEGER IWORK( * )
142  DOUBLE PRECISION AP( * ), WORK( * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION ONE, ZERO
149  parameter( one = 1.0d+0, zero = 0.0d+0 )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL NOUNIT, ONENRM, UPPER
153  CHARACTER NORMIN
154  INTEGER IX, KASE, KASE1
155  DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
156 * ..
157 * .. Local Arrays ..
158  INTEGER ISAVE( 3 )
159 * ..
160 * .. External Functions ..
161  LOGICAL LSAME
162  INTEGER IDAMAX
163  DOUBLE PRECISION DLAMCH, DLANTP
164  EXTERNAL lsame, idamax, dlamch, dlantp
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL dlacn2, dlatps, drscl, xerbla
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC abs, dble, max
171 * ..
172 * .. Executable Statements ..
173 *
174 * Test the input parameters.
175 *
176  info = 0
177  upper = lsame( uplo, 'U' )
178  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
179  nounit = lsame( diag, 'N' )
180 *
181  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
182  info = -1
183  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
184  info = -2
185  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
186  info = -3
187  ELSE IF( n.LT.0 ) THEN
188  info = -4
189  END IF
190  IF( info.NE.0 ) THEN
191  CALL xerbla( 'DTPCON', -info )
192  RETURN
193  END IF
194 *
195 * Quick return if possible
196 *
197  IF( n.EQ.0 ) THEN
198  rcond = one
199  RETURN
200  END IF
201 *
202  rcond = zero
203  smlnum = dlamch( 'Safe minimum' )*dble( max( 1, n ) )
204 *
205 * Compute the norm of the triangular matrix A.
206 *
207  anorm = dlantp( norm, uplo, diag, n, ap, work )
208 *
209 * Continue only if ANORM > 0.
210 *
211  IF( anorm.GT.zero ) THEN
212 *
213 * Estimate the norm of the inverse of A.
214 *
215  ainvnm = zero
216  normin = 'N'
217  IF( onenrm ) THEN
218  kase1 = 1
219  ELSE
220  kase1 = 2
221  END IF
222  kase = 0
223  10 CONTINUE
224  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
225  IF( kase.NE.0 ) THEN
226  IF( kase.EQ.kase1 ) THEN
227 *
228 * Multiply by inv(A).
229 *
230  CALL dlatps( uplo, 'No transpose', diag, normin, n, ap,
231  \$ work, scale, work( 2*n+1 ), info )
232  ELSE
233 *
234 * Multiply by inv(A**T).
235 *
236  CALL dlatps( uplo, 'Transpose', diag, normin, n, ap,
237  \$ work, scale, work( 2*n+1 ), info )
238  END IF
239  normin = 'Y'
240 *
241 * Multiply by 1/SCALE if doing so will not cause overflow.
242 *
243  IF( scale.NE.one ) THEN
244  ix = idamax( n, work, 1 )
245  xnorm = abs( work( ix ) )
246  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
247  \$ GO TO 20
248  CALL drscl( n, scale, work, 1 )
249  END IF
250  GO TO 10
251  END IF
252 *
253 * Compute the estimate of the reciprocal condition number.
254 *
255  IF( ainvnm.NE.zero )
256  \$ rcond = ( one / anorm ) / ainvnm
257  END IF
258 *
259  20 CONTINUE
260  RETURN
261 *
262 * End of DTPCON
263 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dlantp(NORM, UPLO, DIAG, N, AP, WORK)
DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantp.f:124
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:84
subroutine dlatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
DLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: dlatps.f:229
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
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