Annotation of rpl/lapack/lapack/dpotrf.f, revision 1.11
1.9 bertrand 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: *> \date November 2011
104: *
105: *> \ingroup doublePOcomputational
106: *
107: * =====================================================================
1.1 bertrand 108: SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
109: *
1.9 bertrand 110: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 111: * -- LAPACK is a software package provided by Univ. of Tennessee, --
112: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 113: * November 2011
1.1 bertrand 114: *
115: * .. Scalar Arguments ..
116: CHARACTER UPLO
117: INTEGER INFO, LDA, N
118: * ..
119: * .. Array Arguments ..
120: DOUBLE PRECISION A( LDA, * )
121: * ..
122: *
123: * =====================================================================
124: *
125: * .. Parameters ..
126: DOUBLE PRECISION ONE
127: PARAMETER ( ONE = 1.0D+0 )
128: * ..
129: * .. Local Scalars ..
130: LOGICAL UPPER
131: INTEGER J, JB, NB
132: * ..
133: * .. External Functions ..
134: LOGICAL LSAME
135: INTEGER ILAENV
136: EXTERNAL LSAME, ILAENV
137: * ..
138: * .. External Subroutines ..
139: EXTERNAL DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC MAX, MIN
143: * ..
144: * .. Executable Statements ..
145: *
146: * Test the input parameters.
147: *
148: INFO = 0
149: UPPER = LSAME( UPLO, 'U' )
150: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
151: INFO = -1
152: ELSE IF( N.LT.0 ) THEN
153: INFO = -2
154: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
155: INFO = -4
156: END IF
157: IF( INFO.NE.0 ) THEN
158: CALL XERBLA( 'DPOTRF', -INFO )
159: RETURN
160: END IF
161: *
162: * Quick return if possible
163: *
164: IF( N.EQ.0 )
165: $ RETURN
166: *
167: * Determine the block size for this environment.
168: *
169: NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
170: IF( NB.LE.1 .OR. NB.GE.N ) THEN
171: *
172: * Use unblocked code.
173: *
174: CALL DPOTF2( UPLO, N, A, LDA, INFO )
175: ELSE
176: *
177: * Use blocked code.
178: *
179: IF( UPPER ) THEN
180: *
1.8 bertrand 181: * Compute the Cholesky factorization A = U**T*U.
1.1 bertrand 182: *
183: DO 10 J = 1, N, NB
184: *
185: * Update and factorize the current diagonal block and test
186: * for non-positive-definiteness.
187: *
188: JB = MIN( NB, N-J+1 )
189: CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
190: $ A( 1, J ), LDA, ONE, A( J, J ), LDA )
191: CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
192: IF( INFO.NE.0 )
193: $ GO TO 30
194: IF( J+JB.LE.N ) THEN
195: *
196: * Compute the current block row.
197: *
198: CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,
199: $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ),
200: $ LDA, ONE, A( J, J+JB ), LDA )
201: CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
202: $ JB, N-J-JB+1, ONE, A( J, J ), LDA,
203: $ A( J, J+JB ), LDA )
204: END IF
205: 10 CONTINUE
206: *
207: ELSE
208: *
1.8 bertrand 209: * Compute the Cholesky factorization A = L*L**T.
1.1 bertrand 210: *
211: DO 20 J = 1, N, NB
212: *
213: * Update and factorize the current diagonal block and test
214: * for non-positive-definiteness.
215: *
216: JB = MIN( NB, N-J+1 )
217: CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
218: $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
219: CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
220: IF( INFO.NE.0 )
221: $ GO TO 30
222: IF( J+JB.LE.N ) THEN
223: *
224: * Compute the current block column.
225: *
226: CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
227: $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ),
228: $ LDA, ONE, A( J+JB, J ), LDA )
229: CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
230: $ N-J-JB+1, JB, ONE, A( J, J ), LDA,
231: $ A( J+JB, J ), LDA )
232: END IF
233: 20 CONTINUE
234: END IF
235: END IF
236: GO TO 40
237: *
238: 30 CONTINUE
239: INFO = INFO + J - 1
240: *
241: 40 CONTINUE
242: RETURN
243: *
244: * End of DPOTRF
245: *
246: END
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