LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cpptri()

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

CPPTRI

Purpose:
``` CPPTRI 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 CPPTRF.```
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 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.```

Definition at line 92 of file cpptri.f.

93*
94* -- LAPACK computational routine --
95* -- LAPACK is a software package provided by Univ. of Tennessee, --
96* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
97*
98* .. Scalar Arguments ..
99 CHARACTER UPLO
100 INTEGER INFO, N
101* ..
102* .. Array Arguments ..
103 COMPLEX AP( * )
104* ..
105*
106* =====================================================================
107*
108* .. Parameters ..
109 REAL ONE
110 parameter( one = 1.0e+0 )
111* ..
112* .. Local Scalars ..
113 LOGICAL UPPER
114 INTEGER J, JC, JJ, JJN
115 REAL AJJ
116* ..
117* .. External Functions ..
118 LOGICAL LSAME
119 COMPLEX CDOTC
120 EXTERNAL lsame, cdotc
121* ..
122* .. External Subroutines ..
123 EXTERNAL chpr, csscal, ctpmv, ctptri, xerbla
124* ..
125* .. Intrinsic Functions ..
126 INTRINSIC real
127* ..
128* .. Executable Statements ..
129*
130* Test the input parameters.
131*
132 info = 0
133 upper = lsame( uplo, 'U' )
134 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
135 info = -1
136 ELSE IF( n.LT.0 ) THEN
137 info = -2
138 END IF
139 IF( info.NE.0 ) THEN
140 CALL xerbla( 'CPPTRI', -info )
141 RETURN
142 END IF
143*
144* Quick return if possible
145*
146 IF( n.EQ.0 )
147 \$ RETURN
148*
149* Invert the triangular Cholesky factor U or L.
150*
151 CALL ctptri( uplo, 'Non-unit', n, ap, info )
152 IF( info.GT.0 )
153 \$ RETURN
154 IF( upper ) THEN
155*
156* Compute the product inv(U) * inv(U)**H.
157*
158 jj = 0
159 DO 10 j = 1, n
160 jc = jj + 1
161 jj = jj + j
162 IF( j.GT.1 )
163 \$ CALL chpr( 'Upper', j-1, one, ap( jc ), 1, ap )
164 ajj = real( ap( jj ) )
165 CALL csscal( j, ajj, ap( jc ), 1 )
166 10 CONTINUE
167*
168 ELSE
169*
170* Compute the product inv(L)**H * inv(L).
171*
172 jj = 1
173 DO 20 j = 1, n
174 jjn = jj + n - j + 1
175 ap( jj ) = real( cdotc( n-j+1, ap( jj ), 1, ap( jj ), 1 ) )
176 IF( j.LT.n )
177 \$ CALL ctpmv( 'Lower', 'Conjugate transpose', 'Non-unit',
178 \$ n-j, ap( jjn ), ap( jj+1 ), 1 )
179 jj = jjn
180 20 CONTINUE
181 END IF
182*
183 RETURN
184*
185* End of CPPTRI
186*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine chpr(UPLO, N, ALPHA, X, INCX, AP)
CHPR
Definition: chpr.f:130
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
subroutine ctptri(UPLO, DIAG, N, AP, INFO)
CTPTRI
Definition: ctptri.f:117
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