Annotation of rpl/lapack/lapack/dpptrf.f, revision 1.18
1.9 bertrand 1: *> \brief \b DPPTRF
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download DPPTRF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrf.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
1.15 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( * )
29: * ..
1.15 bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPPTRF computes the Cholesky factorization of a real symmetric
38: *> positive definite matrix A stored in packed format.
39: *>
40: *> The factorization has the form
41: *> A = U**T * U, if UPLO = 'U', or
42: *> A = L * L**T, if UPLO = 'L',
43: *> where U is an upper triangular matrix and L is lower triangular.
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] UPLO
50: *> \verbatim
51: *> UPLO is CHARACTER*1
52: *> = 'U': Upper triangle of A is stored;
53: *> = 'L': Lower triangle of A is stored.
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The order of the matrix A. N >= 0.
60: *> \endverbatim
61: *>
62: *> \param[in,out] AP
63: *> \verbatim
64: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
65: *> On entry, the upper or lower triangle of the symmetric matrix
66: *> A, packed columnwise in a linear array. The j-th column of A
67: *> is stored in the array AP as follows:
68: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
69: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
70: *> See below for further details.
71: *>
72: *> On exit, if INFO = 0, the triangular factor U or L from the
73: *> Cholesky factorization A = U**T*U or A = L*L**T, in the same
74: *> storage format as A.
75: *> \endverbatim
76: *>
77: *> \param[out] INFO
78: *> \verbatim
79: *> INFO is INTEGER
80: *> = 0: successful exit
81: *> < 0: if INFO = -i, the i-th argument had an illegal value
82: *> > 0: if INFO = i, the leading minor of order i is not
83: *> positive definite, and the factorization could not be
84: *> completed.
85: *> \endverbatim
86: *
87: * Authors:
88: * ========
89: *
1.15 bertrand 90: *> \author Univ. of Tennessee
91: *> \author Univ. of California Berkeley
92: *> \author Univ. of Colorado Denver
93: *> \author NAG Ltd.
1.9 bertrand 94: *
95: *> \ingroup doubleOTHERcomputational
96: *
97: *> \par Further Details:
98: * =====================
99: *>
100: *> \verbatim
101: *>
102: *> The packed storage scheme is illustrated by the following example
103: *> when N = 4, UPLO = 'U':
104: *>
105: *> Two-dimensional storage of the symmetric matrix A:
106: *>
107: *> a11 a12 a13 a14
108: *> a22 a23 a24
109: *> a33 a34 (aij = aji)
110: *> a44
111: *>
112: *> Packed storage of the upper triangle of A:
113: *>
114: *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
115: *> \endverbatim
116: *>
117: * =====================================================================
1.1 bertrand 118: SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
119: *
1.18 ! bertrand 120: * -- LAPACK computational routine --
1.1 bertrand 121: * -- LAPACK is a software package provided by Univ. of Tennessee, --
122: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123: *
124: * .. Scalar Arguments ..
125: CHARACTER UPLO
126: INTEGER INFO, N
127: * ..
128: * .. Array Arguments ..
129: DOUBLE PRECISION AP( * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ONE, ZERO
136: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
137: * ..
138: * .. Local Scalars ..
139: LOGICAL UPPER
140: INTEGER J, JC, JJ
141: DOUBLE PRECISION AJJ
142: * ..
143: * .. External Functions ..
144: LOGICAL LSAME
145: DOUBLE PRECISION DDOT
146: EXTERNAL LSAME, DDOT
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL DSCAL, DSPR, DTPSV, XERBLA
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC SQRT
153: * ..
154: * .. Executable Statements ..
155: *
156: * Test the input parameters.
157: *
158: INFO = 0
159: UPPER = LSAME( UPLO, 'U' )
160: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
161: INFO = -1
162: ELSE IF( N.LT.0 ) THEN
163: INFO = -2
164: END IF
165: IF( INFO.NE.0 ) THEN
166: CALL XERBLA( 'DPPTRF', -INFO )
167: RETURN
168: END IF
169: *
170: * Quick return if possible
171: *
172: IF( N.EQ.0 )
173: $ RETURN
174: *
175: IF( UPPER ) THEN
176: *
1.8 bertrand 177: * Compute the Cholesky factorization A = U**T*U.
1.1 bertrand 178: *
179: JJ = 0
180: DO 10 J = 1, N
181: JC = JJ + 1
182: JJ = JJ + J
183: *
184: * Compute elements 1:J-1 of column J.
185: *
186: IF( J.GT.1 )
187: $ CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP,
188: $ AP( JC ), 1 )
189: *
190: * Compute U(J,J) and test for non-positive-definiteness.
191: *
192: AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
193: IF( AJJ.LE.ZERO ) THEN
194: AP( JJ ) = AJJ
195: GO TO 30
196: END IF
197: AP( JJ ) = SQRT( AJJ )
198: 10 CONTINUE
199: ELSE
200: *
1.8 bertrand 201: * Compute the Cholesky factorization A = L*L**T.
1.1 bertrand 202: *
203: JJ = 1
204: DO 20 J = 1, N
205: *
206: * Compute L(J,J) and test for non-positive-definiteness.
207: *
208: AJJ = AP( JJ )
209: IF( AJJ.LE.ZERO ) THEN
210: AP( JJ ) = AJJ
211: GO TO 30
212: END IF
213: AJJ = SQRT( AJJ )
214: AP( JJ ) = AJJ
215: *
216: * Compute elements J+1:N of column J and update the trailing
217: * submatrix.
218: *
219: IF( J.LT.N ) THEN
220: CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
221: CALL DSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
222: $ AP( JJ+N-J+1 ) )
223: JJ = JJ + N - J + 1
224: END IF
225: 20 CONTINUE
226: END IF
227: GO TO 40
228: *
229: 30 CONTINUE
230: INFO = J
231: *
232: 40 CONTINUE
233: RETURN
234: *
235: * End of DPPTRF
236: *
237: END
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