Annotation of rpl/lapack/lapack/zpotf2.f, revision 1.15
1.12 bertrand 1: *> \brief \b ZPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZPOTF2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpotf2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpotf2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpotf2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 A( LDA, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZPOTF2 computes the Cholesky factorization of a complex Hermitian
38: *> positive definite matrix A.
39: *>
40: *> The factorization has the form
41: *> A = U**H * U , if UPLO = 'U', or
42: *> A = L * L**H, 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: *> Hermitian 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 COMPLEX*16 array, dimension (LDA,N)
69: *> On entry, the Hermitian 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**H *U or A = L*L**H.
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: *
100: *> \author Univ. of Tennessee
101: *> \author Univ. of California Berkeley
102: *> \author Univ. of Colorado Denver
103: *> \author NAG Ltd.
104: *
1.12 bertrand 105: *> \date September 2012
1.9 bertrand 106: *
107: *> \ingroup complex16POcomputational
108: *
109: * =====================================================================
1.1 bertrand 110: SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
111: *
1.12 bertrand 112: * -- LAPACK computational routine (version 3.4.2) --
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..--
1.12 bertrand 115: * September 2012
1.1 bertrand 116: *
117: * .. Scalar Arguments ..
118: CHARACTER UPLO
119: INTEGER INFO, LDA, N
120: * ..
121: * .. Array Arguments ..
122: COMPLEX*16 A( LDA, * )
123: * ..
124: *
125: * =====================================================================
126: *
127: * .. Parameters ..
128: DOUBLE PRECISION ONE, ZERO
129: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
130: COMPLEX*16 CONE
131: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
132: * ..
133: * .. Local Scalars ..
134: LOGICAL UPPER
135: INTEGER J
136: DOUBLE PRECISION AJJ
137: * ..
138: * .. External Functions ..
139: LOGICAL LSAME, DISNAN
140: COMPLEX*16 ZDOTC
141: EXTERNAL LSAME, ZDOTC, DISNAN
142: * ..
143: * .. External Subroutines ..
144: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZLACGV
145: * ..
146: * .. Intrinsic Functions ..
147: INTRINSIC DBLE, MAX, SQRT
148: * ..
149: * .. Executable Statements ..
150: *
151: * Test the input parameters.
152: *
153: INFO = 0
154: UPPER = LSAME( UPLO, 'U' )
155: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
156: INFO = -1
157: ELSE IF( N.LT.0 ) THEN
158: INFO = -2
159: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
160: INFO = -4
161: END IF
162: IF( INFO.NE.0 ) THEN
163: CALL XERBLA( 'ZPOTF2', -INFO )
164: RETURN
165: END IF
166: *
167: * Quick return if possible
168: *
169: IF( N.EQ.0 )
170: $ RETURN
171: *
172: IF( UPPER ) THEN
173: *
1.8 bertrand 174: * Compute the Cholesky factorization A = U**H *U.
1.1 bertrand 175: *
176: DO 10 J = 1, N
177: *
178: * Compute U(J,J) and test for non-positive-definiteness.
179: *
180: AJJ = DBLE( A( J, J ) ) - ZDOTC( J-1, A( 1, J ), 1,
181: $ A( 1, J ), 1 )
182: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
183: A( J, J ) = AJJ
184: GO TO 30
185: END IF
186: AJJ = SQRT( AJJ )
187: A( J, J ) = AJJ
188: *
189: * Compute elements J+1:N of row J.
190: *
191: IF( J.LT.N ) THEN
192: CALL ZLACGV( J-1, A( 1, J ), 1 )
193: CALL ZGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ),
194: $ LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA )
195: CALL ZLACGV( J-1, A( 1, J ), 1 )
196: CALL ZDSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
197: END IF
198: 10 CONTINUE
199: ELSE
200: *
1.8 bertrand 201: * Compute the Cholesky factorization A = L*L**H.
1.1 bertrand 202: *
203: DO 20 J = 1, N
204: *
205: * Compute L(J,J) and test for non-positive-definiteness.
206: *
207: AJJ = DBLE( A( J, J ) ) - ZDOTC( J-1, A( J, 1 ), LDA,
208: $ A( J, 1 ), LDA )
209: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
210: A( J, J ) = AJJ
211: GO TO 30
212: END IF
213: AJJ = SQRT( AJJ )
214: A( J, J ) = AJJ
215: *
216: * Compute elements J+1:N of column J.
217: *
218: IF( J.LT.N ) THEN
219: CALL ZLACGV( J-1, A( J, 1 ), LDA )
220: CALL ZGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ),
221: $ LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 )
222: CALL ZLACGV( J-1, A( J, 1 ), LDA )
223: CALL ZDSCAL( N-J, ONE / AJJ, A( J+1, 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 ZPOTF2
236: *
237: END
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