1: *> \brief \b DPOTRF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DPOTRF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotrf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotrf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotrf.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( LDA, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPOTRF 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 block version of the algorithm, calling Level 3 BLAS.
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in,out] A
65: *> \verbatim
66: *> A is DOUBLE PRECISION array, dimension (LDA,N)
67: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
68: *> N-by-N upper triangular part of A contains the upper
69: *> triangular part of the matrix A, and the strictly lower
70: *> triangular part of A is not referenced. If UPLO = 'L', the
71: *> leading N-by-N lower triangular part of A contains the lower
72: *> triangular part of the matrix A, and the strictly upper
73: *> triangular part of A is not referenced.
74: *>
75: *> On exit, if INFO = 0, the factor U or L from the Cholesky
76: *> factorization A = U**T*U or A = L*L**T.
77: *> \endverbatim
78: *>
79: *> \param[in] LDA
80: *> \verbatim
81: *> LDA is INTEGER
82: *> The leading dimension of the array A. LDA >= max(1,N).
83: *> \endverbatim
84: *>
85: *> \param[out] INFO
86: *> \verbatim
87: *> INFO is INTEGER
88: *> = 0: successful exit
89: *> < 0: if INFO = -i, the i-th argument had an illegal value
90: *> > 0: if INFO = i, the leading minor of order i is not
91: *> positive definite, and the factorization could not be
92: *> completed.
93: *> \endverbatim
94: *
95: * Authors:
96: * ========
97: *
98: *> \author Univ. of Tennessee
99: *> \author Univ. of California Berkeley
100: *> \author Univ. of Colorado Denver
101: *> \author NAG Ltd.
102: *
103: *> \ingroup doublePOcomputational
104: *
105: * =====================================================================
106: SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
107: *
108: * -- LAPACK computational routine --
109: * -- LAPACK is a software package provided by Univ. of Tennessee, --
110: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111: *
112: * .. Scalar Arguments ..
113: CHARACTER UPLO
114: INTEGER INFO, LDA, N
115: * ..
116: * .. Array Arguments ..
117: DOUBLE PRECISION A( LDA, * )
118: * ..
119: *
120: * =====================================================================
121: *
122: * .. Parameters ..
123: DOUBLE PRECISION ONE
124: PARAMETER ( ONE = 1.0D+0 )
125: * ..
126: * .. Local Scalars ..
127: LOGICAL UPPER
128: INTEGER J, JB, NB
129: * ..
130: * .. External Functions ..
131: LOGICAL LSAME
132: INTEGER ILAENV
133: EXTERNAL LSAME, ILAENV
134: * ..
135: * .. External Subroutines ..
136: EXTERNAL DGEMM, DPOTRF2, DSYRK, DTRSM, XERBLA
137: * ..
138: * .. Intrinsic Functions ..
139: INTRINSIC MAX, MIN
140: * ..
141: * .. Executable Statements ..
142: *
143: * Test the input parameters.
144: *
145: INFO = 0
146: UPPER = LSAME( UPLO, 'U' )
147: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
148: INFO = -1
149: ELSE IF( N.LT.0 ) THEN
150: INFO = -2
151: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
152: INFO = -4
153: END IF
154: IF( INFO.NE.0 ) THEN
155: CALL XERBLA( 'DPOTRF', -INFO )
156: RETURN
157: END IF
158: *
159: * Quick return if possible
160: *
161: IF( N.EQ.0 )
162: $ RETURN
163: *
164: * Determine the block size for this environment.
165: *
166: NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
167: IF( NB.LE.1 .OR. NB.GE.N ) THEN
168: *
169: * Use unblocked code.
170: *
171: CALL DPOTRF2( UPLO, N, A, LDA, INFO )
172: ELSE
173: *
174: * Use blocked code.
175: *
176: IF( UPPER ) THEN
177: *
178: * Compute the Cholesky factorization A = U**T*U.
179: *
180: DO 10 J = 1, N, NB
181: *
182: * Update and factorize the current diagonal block and test
183: * for non-positive-definiteness.
184: *
185: JB = MIN( NB, N-J+1 )
186: CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
187: $ A( 1, J ), LDA, ONE, A( J, J ), LDA )
188: CALL DPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
189: IF( INFO.NE.0 )
190: $ GO TO 30
191: IF( J+JB.LE.N ) THEN
192: *
193: * Compute the current block row.
194: *
195: CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,
196: $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ),
197: $ LDA, ONE, A( J, J+JB ), LDA )
198: CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
199: $ JB, N-J-JB+1, ONE, A( J, J ), LDA,
200: $ A( J, J+JB ), LDA )
201: END IF
202: 10 CONTINUE
203: *
204: ELSE
205: *
206: * Compute the Cholesky factorization A = L*L**T.
207: *
208: DO 20 J = 1, N, NB
209: *
210: * Update and factorize the current diagonal block and test
211: * for non-positive-definiteness.
212: *
213: JB = MIN( NB, N-J+1 )
214: CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
215: $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
216: CALL DPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
217: IF( INFO.NE.0 )
218: $ GO TO 30
219: IF( J+JB.LE.N ) THEN
220: *
221: * Compute the current block column.
222: *
223: CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
224: $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ),
225: $ LDA, ONE, A( J+JB, J ), LDA )
226: CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
227: $ N-J-JB+1, JB, ONE, A( J, J ), LDA,
228: $ A( J+JB, J ), LDA )
229: END IF
230: 20 CONTINUE
231: END IF
232: END IF
233: GO TO 40
234: *
235: 30 CONTINUE
236: INFO = INFO + J - 1
237: *
238: 40 CONTINUE
239: RETURN
240: *
241: * End of DPOTRF
242: *
243: END
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