Annotation of rpl/lapack/lapack/dpotf2.f, revision 1.18
1.12 bertrand 1: *> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download DPOTF2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotf2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotf2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotf2.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
1.16 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( LDA, * )
29: * ..
1.16 bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPOTF2 computes the Cholesky factorization of a real symmetric
38: *> positive definite matrix A.
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: *>
45: *> This is the unblocked version of the algorithm, calling Level 2 BLAS.
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> Specifies whether the upper or lower triangular part of the
55: *> symmetric matrix A is stored.
56: *> = 'U': Upper triangular
57: *> = 'L': Lower triangular
58: *> \endverbatim
59: *>
60: *> \param[in] N
61: *> \verbatim
62: *> N is INTEGER
63: *> The order of the matrix A. N >= 0.
64: *> \endverbatim
65: *>
66: *> \param[in,out] A
67: *> \verbatim
68: *> A is DOUBLE PRECISION array, dimension (LDA,N)
69: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
70: *> n by n upper triangular part of A contains the upper
71: *> triangular part of the matrix A, and the strictly lower
72: *> triangular part of A is not referenced. If UPLO = 'L', the
73: *> leading n by n lower triangular part of A contains the lower
74: *> triangular part of the matrix A, and the strictly upper
75: *> triangular part of A is not referenced.
76: *>
77: *> On exit, if INFO = 0, the factor U or L from the Cholesky
78: *> factorization A = U**T *U or A = L*L**T.
79: *> \endverbatim
80: *>
81: *> \param[in] LDA
82: *> \verbatim
83: *> LDA is INTEGER
84: *> The leading dimension of the array A. LDA >= max(1,N).
85: *> \endverbatim
86: *>
87: *> \param[out] INFO
88: *> \verbatim
89: *> INFO is INTEGER
90: *> = 0: successful exit
91: *> < 0: if INFO = -k, the k-th argument had an illegal value
92: *> > 0: if INFO = k, the leading minor of order k is not
93: *> positive definite, and the factorization could not be
94: *> completed.
95: *> \endverbatim
96: *
97: * Authors:
98: * ========
99: *
1.16 bertrand 100: *> \author Univ. of Tennessee
101: *> \author Univ. of California Berkeley
102: *> \author Univ. of Colorado Denver
103: *> \author NAG Ltd.
1.9 bertrand 104: *
1.16 bertrand 105: *> \date December 2016
1.9 bertrand 106: *
107: *> \ingroup doublePOcomputational
108: *
109: * =====================================================================
1.1 bertrand 110: SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
111: *
1.16 bertrand 112: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 113: * -- LAPACK is a software package provided by Univ. of Tennessee, --
114: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.16 bertrand 115: * December 2016
1.1 bertrand 116: *
117: * .. Scalar Arguments ..
118: CHARACTER UPLO
119: INTEGER INFO, LDA, N
120: * ..
121: * .. Array Arguments ..
122: DOUBLE PRECISION A( LDA, * )
123: * ..
124: *
125: * =====================================================================
126: *
127: * .. Parameters ..
128: DOUBLE PRECISION ONE, ZERO
129: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
130: * ..
131: * .. Local Scalars ..
132: LOGICAL UPPER
133: INTEGER J
134: DOUBLE PRECISION AJJ
135: * ..
136: * .. External Functions ..
137: LOGICAL LSAME, DISNAN
138: DOUBLE PRECISION DDOT
139: EXTERNAL LSAME, DDOT, DISNAN
140: * ..
141: * .. External Subroutines ..
142: EXTERNAL DGEMV, DSCAL, XERBLA
143: * ..
144: * .. Intrinsic Functions ..
145: INTRINSIC MAX, SQRT
146: * ..
147: * .. Executable Statements ..
148: *
149: * Test the input parameters.
150: *
151: INFO = 0
152: UPPER = LSAME( UPLO, 'U' )
153: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
154: INFO = -1
155: ELSE IF( N.LT.0 ) THEN
156: INFO = -2
157: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
158: INFO = -4
159: END IF
160: IF( INFO.NE.0 ) THEN
161: CALL XERBLA( 'DPOTF2', -INFO )
162: RETURN
163: END IF
164: *
165: * Quick return if possible
166: *
167: IF( N.EQ.0 )
168: $ RETURN
169: *
170: IF( UPPER ) THEN
171: *
1.8 bertrand 172: * Compute the Cholesky factorization A = U**T *U.
1.1 bertrand 173: *
174: DO 10 J = 1, N
175: *
176: * Compute U(J,J) and test for non-positive-definiteness.
177: *
178: AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
179: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
180: A( J, J ) = AJJ
181: GO TO 30
182: END IF
183: AJJ = SQRT( AJJ )
184: A( J, J ) = AJJ
185: *
186: * Compute elements J+1:N of row J.
187: *
188: IF( J.LT.N ) THEN
189: CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
190: $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
191: CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
192: END IF
193: 10 CONTINUE
194: ELSE
195: *
1.8 bertrand 196: * Compute the Cholesky factorization A = L*L**T.
1.1 bertrand 197: *
198: DO 20 J = 1, N
199: *
200: * Compute L(J,J) and test for non-positive-definiteness.
201: *
202: AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
203: $ LDA )
204: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
205: A( J, J ) = AJJ
206: GO TO 30
207: END IF
208: AJJ = SQRT( AJJ )
209: A( J, J ) = AJJ
210: *
211: * Compute elements J+1:N of column J.
212: *
213: IF( J.LT.N ) THEN
214: CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
215: $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
216: CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
217: END IF
218: 20 CONTINUE
219: END IF
220: GO TO 40
221: *
222: 30 CONTINUE
223: INFO = J
224: *
225: 40 CONTINUE
226: RETURN
227: *
228: * End of DPOTF2
229: *
230: END
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