LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
cpptri.f
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1 *> \brief \b CPPTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CPPTRI( UPLO, N, AP, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX AP( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CPPTRI computes the inverse of a complex Hermitian positive definite
38 *> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
39 *> computed by CPPTRF.
40 *> \endverbatim
41 *
42 * Arguments:
43 * ==========
44 *
45 *> \param[in] UPLO
46 *> \verbatim
47 *> UPLO is CHARACTER*1
48 *> = 'U': Upper triangular factor is stored in AP;
49 *> = 'L': Lower triangular factor is stored in AP.
50 *> \endverbatim
51 *>
52 *> \param[in] N
53 *> \verbatim
54 *> N is INTEGER
55 *> The order of the matrix A. N >= 0.
56 *> \endverbatim
57 *>
58 *> \param[in,out] AP
59 *> \verbatim
60 *> AP is COMPLEX array, dimension (N*(N+1)/2)
61 *> On entry, the triangular factor U or L from the Cholesky
62 *> factorization A = U**H*U or A = L*L**H, packed columnwise as
63 *> a linear array. The j-th column of U or L is stored in the
64 *> array AP as follows:
65 *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
66 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
67 *>
68 *> On exit, the upper or lower triangle of the (Hermitian)
69 *> inverse of A, overwriting the input factor U or L.
70 *> \endverbatim
71 *>
72 *> \param[out] INFO
73 *> \verbatim
74 *> INFO is INTEGER
75 *> = 0: successful exit
76 *> < 0: if INFO = -i, the i-th argument had an illegal value
77 *> > 0: if INFO = i, the (i,i) element of the factor U or L is
78 *> zero, and the inverse could not be computed.
79 *> \endverbatim
80 *
81 * Authors:
82 * ========
83 *
84 *> \author Univ. of Tennessee
85 *> \author Univ. of California Berkeley
86 *> \author Univ. of Colorado Denver
87 *> \author NAG Ltd.
88 *
89 *> \ingroup complexOTHERcomputational
90 *
91 * =====================================================================
92  SUBROUTINE cpptri( UPLO, N, AP, INFO )
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 *
187  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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
subroutine cpptri(UPLO, N, AP, INFO)
CPPTRI
Definition: cpptri.f:93