LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dtptri ( character UPLO, character DIAG, integer N, double precision, dimension( * ) AP, integer INFO )

DTPTRI

Purpose:
``` DTPTRI computes the inverse of a real 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 DOUBLE PRECISION 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 dtptri.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  DOUBLE PRECISION ap( * )
131 * ..
132 *
133 * =====================================================================
134 *
135 * .. Parameters ..
136  DOUBLE PRECISION one, zero
137  parameter ( one = 1.0d+0, zero = 0.0d+0 )
138 * ..
139 * .. Local Scalars ..
140  LOGICAL nounit, upper
141  INTEGER j, jc, jclast, jj
142  DOUBLE PRECISION ajj
143 * ..
144 * .. External Functions ..
145  LOGICAL lsame
146  EXTERNAL lsame
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL dscal, dtpmv, xerbla
150 * ..
151 * .. Executable Statements ..
152 *
153 * Test the input parameters.
154 *
155  info = 0
156  upper = lsame( uplo, 'U' )
157  nounit = lsame( diag, 'N' )
158  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
159  info = -1
160  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
161  info = -2
162  ELSE IF( n.LT.0 ) THEN
163  info = -3
164  END IF
165  IF( info.NE.0 ) THEN
166  CALL xerbla( 'DTPTRI', -info )
167  RETURN
168  END IF
169 *
170 * Check for singularity if non-unit.
171 *
172  IF( nounit ) THEN
173  IF( upper ) THEN
174  jj = 0
175  DO 10 info = 1, n
176  jj = jj + info
177  IF( ap( jj ).EQ.zero )
178  \$ RETURN
179  10 CONTINUE
180  ELSE
181  jj = 1
182  DO 20 info = 1, n
183  IF( ap( jj ).EQ.zero )
184  \$ RETURN
185  jj = jj + n - info + 1
186  20 CONTINUE
187  END IF
188  info = 0
189  END IF
190 *
191  IF( upper ) THEN
192 *
193 * Compute inverse of upper triangular matrix.
194 *
195  jc = 1
196  DO 30 j = 1, n
197  IF( nounit ) THEN
198  ap( jc+j-1 ) = one / ap( jc+j-1 )
199  ajj = -ap( jc+j-1 )
200  ELSE
201  ajj = -one
202  END IF
203 *
204 * Compute elements 1:j-1 of j-th column.
205 *
206  CALL dtpmv( 'Upper', 'No transpose', diag, j-1, ap,
207  \$ ap( jc ), 1 )
208  CALL dscal( j-1, ajj, ap( jc ), 1 )
209  jc = jc + j
210  30 CONTINUE
211 *
212  ELSE
213 *
214 * Compute inverse of lower triangular matrix.
215 *
216  jc = n*( n+1 ) / 2
217  DO 40 j = n, 1, -1
218  IF( nounit ) THEN
219  ap( jc ) = one / ap( jc )
220  ajj = -ap( jc )
221  ELSE
222  ajj = -one
223  END IF
224  IF( j.LT.n ) THEN
225 *
226 * Compute elements j+1:n of j-th column.
227 *
228  CALL dtpmv( 'Lower', 'No transpose', diag, n-j,
229  \$ ap( jclast ), ap( jc+1 ), 1 )
230  CALL dscal( n-j, ajj, ap( jc+1 ), 1 )
231  END IF
232  jclast = jc
233  jc = jc - n + j - 2
234  40 CONTINUE
235  END IF
236 *
237  RETURN
238 *
239 * End of DTPTRI
240 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:55
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:144
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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