LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zpptri()

 subroutine zpptri ( character UPLO, integer N, complex*16, dimension( * ) AP, integer INFO )

ZPPTRI

Purpose:
``` ZPPTRI computes the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
computed by ZPPTRF.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular factor is stored in AP; = 'L': Lower triangular factor is stored in AP.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise as a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. On exit, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed.```
Date
December 2016

Definition at line 95 of file zpptri.f.

95 *
96 * -- LAPACK computational routine (version 3.7.0) --
97 * -- LAPACK is a software package provided by Univ. of Tennessee, --
98 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99 * December 2016
100 *
101 * .. Scalar Arguments ..
102  CHARACTER uplo
103  INTEGER info, n
104 * ..
105 * .. Array Arguments ..
106  COMPLEX*16 ap( * )
107 * ..
108 *
109 * =====================================================================
110 *
111 * .. Parameters ..
112  DOUBLE PRECISION one
113  parameter( one = 1.0d+0 )
114 * ..
115 * .. Local Scalars ..
116  LOGICAL upper
117  INTEGER j, jc, jj, jjn
118  DOUBLE PRECISION ajj
119 * ..
120 * .. External Functions ..
121  LOGICAL lsame
122  COMPLEX*16 zdotc
123  EXTERNAL lsame, zdotc
124 * ..
125 * .. External Subroutines ..
126  EXTERNAL xerbla, zdscal, zhpr, ztpmv, ztptri
127 * ..
128 * .. Intrinsic Functions ..
129  INTRINSIC dble
130 * ..
131 * .. Executable Statements ..
132 *
133 * Test the input parameters.
134 *
135  info = 0
136  upper = lsame( uplo, 'U' )
137  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
138  info = -1
139  ELSE IF( n.LT.0 ) THEN
140  info = -2
141  END IF
142  IF( info.NE.0 ) THEN
143  CALL xerbla( 'ZPPTRI', -info )
144  RETURN
145  END IF
146 *
147 * Quick return if possible
148 *
149  IF( n.EQ.0 )
150  \$ RETURN
151 *
152 * Invert the triangular Cholesky factor U or L.
153 *
154  CALL ztptri( uplo, 'Non-unit', n, ap, info )
155  IF( info.GT.0 )
156  \$ RETURN
157  IF( upper ) THEN
158 *
159 * Compute the product inv(U) * inv(U)**H.
160 *
161  jj = 0
162  DO 10 j = 1, n
163  jc = jj + 1
164  jj = jj + j
165  IF( j.GT.1 )
166  \$ CALL zhpr( 'Upper', j-1, one, ap( jc ), 1, ap )
167  ajj = ap( jj )
168  CALL zdscal( j, ajj, ap( jc ), 1 )
169  10 CONTINUE
170 *
171  ELSE
172 *
173 * Compute the product inv(L)**H * inv(L).
174 *
175  jj = 1
176  DO 20 j = 1, n
177  jjn = jj + n - j + 1
178  ap( jj ) = dble( zdotc( n-j+1, ap( jj ), 1, ap( jj ), 1 ) )
179  IF( j.LT.n )
180  \$ CALL ztpmv( 'Lower', 'Conjugate transpose', 'Non-unit',
181  \$ n-j, ap( jjn ), ap( jj+1 ), 1 )
182  jj = jjn
183  20 CONTINUE
184  END IF
185 *
186  RETURN
187 *
188 * End of ZPPTRI
189 *
subroutine ztptri(UPLO, DIAG, N, AP, INFO)
ZTPTRI
Definition: ztptri.f:119
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:85
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:144
subroutine zhpr(UPLO, N, ALPHA, X, INCX, AP)
ZHPR
Definition: zhpr.f:132
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:80
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