LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zpptri()

subroutine zpptri ( character  uplo,
integer  n,
complex*16, dimension( * )  ap,
integer  info 
)

ZPPTRI

Download ZPPTRI + dependencies [TGZ] [ZIP] [TXT]

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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 92 of file zpptri.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*16 AP( * )
104* ..
105*
106* =====================================================================
107*
108* .. Parameters ..
109 DOUBLE PRECISION ONE
110 parameter( one = 1.0d+0 )
111* ..
112* .. Local Scalars ..
113 LOGICAL UPPER
114 INTEGER J, JC, JJ, JJN
115 DOUBLE PRECISION AJJ
116* ..
117* .. External Functions ..
118 LOGICAL LSAME
119 COMPLEX*16 ZDOTC
120 EXTERNAL lsame, zdotc
121* ..
122* .. External Subroutines ..
123 EXTERNAL xerbla, zdscal, zhpr, ztpmv, ztptri
124* ..
125* .. Intrinsic Functions ..
126 INTRINSIC dble
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( 'ZPPTRI', -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 ztptri( 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 zhpr( 'Upper', j-1, one, ap( jc ), 1, ap )
164 ajj = dble( ap( jj ) )
165 CALL zdscal( 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 ) = dble( zdotc( n-j+1, ap( jj ), 1, ap( jj ), 1 ) )
176 IF( j.LT.n )
177 $ CALL ztpmv( '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 ZPPTRI
186*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
complex *16 function zdotc(n, zx, incx, zy, incy)
ZDOTC
Definition zdotc.f:83
subroutine zhpr(uplo, n, alpha, x, incx, ap)
ZHPR
Definition zhpr.f:130
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine zdscal(n, da, zx, incx)
ZDSCAL
Definition zdscal.f:78
subroutine ztpmv(uplo, trans, diag, n, ap, x, incx)
ZTPMV
Definition ztpmv.f:142
subroutine ztptri(uplo, diag, n, ap, info)
ZTPTRI
Definition ztptri.f:117
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