Annotation of rpl/lapack/lapack/zpptri.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZPPTRI
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZPPTRI + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptri.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptri.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptri.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZPPTRI( UPLO, N, AP, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 AP( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZPPTRI 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 ZPPTRF.
! 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*16 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: *> \date November 2011
! 90: *
! 91: *> \ingroup complex16OTHERcomputational
! 92: *
! 93: * =====================================================================
1.1 bertrand 94: SUBROUTINE ZPPTRI( UPLO, N, AP, INFO )
95: *
1.9 ! bertrand 96: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 97: * -- LAPACK is a software package provided by Univ. of Tennessee, --
98: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 99: * November 2011
1.1 bertrand 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: *
1.8 bertrand 159: * Compute the product inv(U) * inv(U)**H.
1.1 bertrand 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: *
1.8 bertrand 173: * Compute the product inv(L)**H * inv(L).
1.1 bertrand 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: *
190: END
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