 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ ctptri()

 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.```
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 116 of file ctptri.f.

117 *
118 * -- LAPACK computational routine --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 *
122 * .. Scalar Arguments ..
123  CHARACTER DIAG, UPLO
124  INTEGER INFO, N
125 * ..
126 * .. Array Arguments ..
127  COMPLEX AP( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  COMPLEX ONE, ZERO
134  parameter( one = ( 1.0e+0, 0.0e+0 ),
135  \$ zero = ( 0.0e+0, 0.0e+0 ) )
136 * ..
137 * .. Local Scalars ..
138  LOGICAL NOUNIT, UPPER
139  INTEGER J, JC, JCLAST, JJ
140  COMPLEX AJJ
141 * ..
142 * .. External Functions ..
143  LOGICAL LSAME
144  EXTERNAL lsame
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL cscal, ctpmv, xerbla
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input parameters.
152 *
153  info = 0
154  upper = lsame( uplo, 'U' )
155  nounit = lsame( diag, 'N' )
156  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
157  info = -1
158  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
159  info = -2
160  ELSE IF( n.LT.0 ) THEN
161  info = -3
162  END IF
163  IF( info.NE.0 ) THEN
164  CALL xerbla( 'CTPTRI', -info )
165  RETURN
166  END IF
167 *
168 * Check for singularity if non-unit.
169 *
170  IF( nounit ) THEN
171  IF( upper ) THEN
172  jj = 0
173  DO 10 info = 1, n
174  jj = jj + info
175  IF( ap( jj ).EQ.zero )
176  \$ RETURN
177  10 CONTINUE
178  ELSE
179  jj = 1
180  DO 20 info = 1, n
181  IF( ap( jj ).EQ.zero )
182  \$ RETURN
183  jj = jj + n - info + 1
184  20 CONTINUE
185  END IF
186  info = 0
187  END IF
188 *
189  IF( upper ) THEN
190 *
191 * Compute inverse of upper triangular matrix.
192 *
193  jc = 1
194  DO 30 j = 1, n
195  IF( nounit ) THEN
196  ap( jc+j-1 ) = one / ap( jc+j-1 )
197  ajj = -ap( jc+j-1 )
198  ELSE
199  ajj = -one
200  END IF
201 *
202 * Compute elements 1:j-1 of j-th column.
203 *
204  CALL ctpmv( 'Upper', 'No transpose', diag, j-1, ap,
205  \$ ap( jc ), 1 )
206  CALL cscal( j-1, ajj, ap( jc ), 1 )
207  jc = jc + j
208  30 CONTINUE
209 *
210  ELSE
211 *
212 * Compute inverse of lower triangular matrix.
213 *
214  jc = n*( n+1 ) / 2
215  DO 40 j = n, 1, -1
216  IF( nounit ) THEN
217  ap( jc ) = one / ap( jc )
218  ajj = -ap( jc )
219  ELSE
220  ajj = -one
221  END IF
222  IF( j.LT.n ) THEN
223 *
224 * Compute elements j+1:n of j-th column.
225 *
226  CALL ctpmv( 'Lower', 'No transpose', diag, n-j,
227  \$ ap( jclast ), ap( jc+1 ), 1 )
228  CALL cscal( n-j, ajj, ap( jc+1 ), 1 )
229  END IF
230  jclast = jc
231  jc = jc - n + j - 2
232  40 CONTINUE
233  END IF
234 *
235  RETURN
236 *
237 * End of CTPTRI
238 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
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