Annotation of rpl/lapack/lapack/dpptri.f, revision 1.12
1.9 bertrand 1: *> \brief \b DPPTRI
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DPPTRI + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptri.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptri.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptri.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPPTRI( UPLO, N, AP, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPPTRI computes the inverse of a real symmetric positive definite
38: *> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
39: *> computed by DPPTRF.
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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
61: *> On entry, the triangular factor U or L from the Cholesky
62: *> factorization A = U**T*U or A = L*L**T, 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 (symmetric)
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 doubleOTHERcomputational
92: *
93: * =====================================================================
1.1 bertrand 94: SUBROUTINE DPPTRI( 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: DOUBLE PRECISION 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: DOUBLE PRECISION DDOT
123: EXTERNAL LSAME, DDOT
124: * ..
125: * .. External Subroutines ..
126: EXTERNAL DSCAL, DSPR, DTPMV, DTPTRI, XERBLA
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( 'DPPTRI', -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 DTPTRI( UPLO, 'Non-unit', N, AP, INFO )
152: IF( INFO.GT.0 )
153: $ RETURN
154: *
155: IF( UPPER ) THEN
156: *
1.8 bertrand 157: * Compute the product inv(U) * inv(U)**T.
1.1 bertrand 158: *
159: JJ = 0
160: DO 10 J = 1, N
161: JC = JJ + 1
162: JJ = JJ + J
163: IF( J.GT.1 )
164: $ CALL DSPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
165: AJJ = AP( JJ )
166: CALL DSCAL( J, AJJ, AP( JC ), 1 )
167: 10 CONTINUE
168: *
169: ELSE
170: *
1.8 bertrand 171: * Compute the product inv(L)**T * inv(L).
1.1 bertrand 172: *
173: JJ = 1
174: DO 20 J = 1, N
175: JJN = JJ + N - J + 1
176: AP( JJ ) = DDOT( N-J+1, AP( JJ ), 1, AP( JJ ), 1 )
177: IF( J.LT.N )
178: $ CALL DTPMV( 'Lower', 'Transpose', 'Non-unit', N-J,
179: $ AP( JJN ), AP( JJ+1 ), 1 )
180: JJ = JJN
181: 20 CONTINUE
182: END IF
183: *
184: RETURN
185: *
186: * End of DPPTRI
187: *
188: END
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