LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine ctptri ( character UPLO, character DIAG, integer N, complex, dimension( * ) AP, integer INFO )

CTPTRI

Purpose:
``` CTPTRI computes the inverse of a complex upper or lower triangular
matrix A stored in packed format.```
Parameters
 [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,out] AP ``` AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored 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)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.```
Date
November 2011
Further Details:
```  A triangular matrix A can be transferred to packed storage using one
of the following program segments:

UPLO = 'U':                      UPLO = 'L':

JC = 1                           JC = 1
DO 2 J = 1, N                    DO 2 J = 1, N
DO 1 I = 1, J                    DO 1 I = J, N
AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
1    CONTINUE                    1    CONTINUE
JC = JC + J                      JC = JC + N - J + 1
2 CONTINUE                       2 CONTINUE```

Definition at line 119 of file ctptri.f.

119 *
120 * -- LAPACK computational routine (version 3.4.0) --
121 * -- LAPACK is a software package provided by Univ. of Tennessee, --
122 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123 * November 2011
124 *
125 * .. Scalar Arguments ..
126  CHARACTER diag, uplo
127  INTEGER info, n
128 * ..
129 * .. Array Arguments ..
130  COMPLEX ap( * )
131 * ..
132 *
133 * =====================================================================
134 *
135 * .. Parameters ..
136  COMPLEX one, zero
137  parameter ( one = ( 1.0e+0, 0.0e+0 ),
138  \$ zero = ( 0.0e+0, 0.0e+0 ) )
139 * ..
140 * .. Local Scalars ..
141  LOGICAL nounit, upper
142  INTEGER j, jc, jclast, jj
143  COMPLEX ajj
144 * ..
145 * .. External Functions ..
146  LOGICAL lsame
147  EXTERNAL lsame
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL cscal, ctpmv, xerbla
151 * ..
152 * .. Executable Statements ..
153 *
154 * Test the input parameters.
155 *
156  info = 0
157  upper = lsame( uplo, 'U' )
158  nounit = lsame( diag, 'N' )
159  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
160  info = -1
161  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
162  info = -2
163  ELSE IF( n.LT.0 ) THEN
164  info = -3
165  END IF
166  IF( info.NE.0 ) THEN
167  CALL xerbla( 'CTPTRI', -info )
168  RETURN
169  END IF
170 *
171 * Check for singularity if non-unit.
172 *
173  IF( nounit ) THEN
174  IF( upper ) THEN
175  jj = 0
176  DO 10 info = 1, n
177  jj = jj + info
178  IF( ap( jj ).EQ.zero )
179  \$ RETURN
180  10 CONTINUE
181  ELSE
182  jj = 1
183  DO 20 info = 1, n
184  IF( ap( jj ).EQ.zero )
185  \$ RETURN
186  jj = jj + n - info + 1
187  20 CONTINUE
188  END IF
189  info = 0
190  END IF
191 *
192  IF( upper ) THEN
193 *
194 * Compute inverse of upper triangular matrix.
195 *
196  jc = 1
197  DO 30 j = 1, n
198  IF( nounit ) THEN
199  ap( jc+j-1 ) = one / ap( jc+j-1 )
200  ajj = -ap( jc+j-1 )
201  ELSE
202  ajj = -one
203  END IF
204 *
205 * Compute elements 1:j-1 of j-th column.
206 *
207  CALL ctpmv( 'Upper', 'No transpose', diag, j-1, ap,
208  \$ ap( jc ), 1 )
209  CALL cscal( j-1, ajj, ap( jc ), 1 )
210  jc = jc + j
211  30 CONTINUE
212 *
213  ELSE
214 *
215 * Compute inverse of lower triangular matrix.
216 *
217  jc = n*( n+1 ) / 2
218  DO 40 j = n, 1, -1
219  IF( nounit ) THEN
220  ap( jc ) = one / ap( jc )
221  ajj = -ap( jc )
222  ELSE
223  ajj = -one
224  END IF
225  IF( j.LT.n ) THEN
226 *
227 * Compute elements j+1:n of j-th column.
228 *
229  CALL ctpmv( 'Lower', 'No transpose', diag, n-j,
230  \$ ap( jclast ), ap( jc+1 ), 1 )
231  CALL cscal( n-j, ajj, ap( jc+1 ), 1 )
232  END IF
233  jclast = jc
234  jc = jc - n + j - 2
235  40 CONTINUE
236  END IF
237 *
238  RETURN
239 *
240 * End of CTPTRI
241 *
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:144
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:54
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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