Annotation of rpl/lapack/lapack/zpotrf2.f, revision 1.6
1.1 bertrand 1: *> \brief \b ZPOTRF2
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.3 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
8: * Definition:
9: * ===========
10: *
11: * RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
1.3 bertrand 12: *
1.1 bertrand 13: * .. Scalar Arguments ..
14: * CHARACTER UPLO
15: * INTEGER INFO, LDA, N
16: * ..
17: * .. Array Arguments ..
18: * COMPLEX*16 A( LDA, * )
19: * ..
1.3 bertrand 20: *
1.1 bertrand 21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
1.6 ! bertrand 27: *> ZPOTRF2 computes the Cholesky factorization of a Hermitian
1.1 bertrand 28: *> positive definite matrix A using the recursive algorithm.
29: *>
30: *> The factorization has the form
31: *> A = U**H * U, if UPLO = 'U', or
32: *> A = L * L**H, if UPLO = 'L',
33: *> where U is an upper triangular matrix and L is lower triangular.
34: *>
35: *> This is the recursive version of the algorithm. It divides
36: *> the matrix into four submatrices:
37: *>
38: *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
39: *> A = [ -----|----- ] with n1 = n/2
40: *> [ A21 | A22 ] n2 = n-n1
41: *>
42: *> The subroutine calls itself to factor A11. Update and scale A21
43: *> or A12, update A22 then call itself to factor A22.
1.3 bertrand 44: *>
1.1 bertrand 45: *> \endverbatim
46: *
47: * Arguments:
48: * ==========
49: *
50: *> \param[in] UPLO
51: *> \verbatim
52: *> UPLO is CHARACTER*1
53: *> = 'U': Upper triangle of A is stored;
54: *> = 'L': Lower triangle of A is stored.
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The order of the matrix A. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in,out] A
64: *> \verbatim
65: *> A is COMPLEX*16 array, dimension (LDA,N)
1.6 ! bertrand 66: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
1.1 bertrand 67: *> N-by-N upper triangular part of A contains the upper
68: *> triangular part of the matrix A, and the strictly lower
69: *> triangular part of A is not referenced. If UPLO = 'L', the
70: *> leading N-by-N lower triangular part of A contains the lower
71: *> triangular part of the matrix A, and the strictly upper
72: *> triangular part of A is not referenced.
73: *>
74: *> On exit, if INFO = 0, the factor U or L from the Cholesky
75: *> factorization A = U**H*U or A = L*L**H.
76: *> \endverbatim
77: *>
78: *> \param[in] LDA
79: *> \verbatim
80: *> LDA is INTEGER
81: *> The leading dimension of the array A. LDA >= max(1,N).
82: *> \endverbatim
83: *>
84: *> \param[out] INFO
85: *> \verbatim
86: *> INFO is INTEGER
87: *> = 0: successful exit
88: *> < 0: if INFO = -i, the i-th argument had an illegal value
89: *> > 0: if INFO = i, the leading minor of order i is not
90: *> positive definite, and the factorization could not be
91: *> completed.
92: *> \endverbatim
93: *
94: * Authors:
95: * ========
96: *
1.3 bertrand 97: *> \author Univ. of Tennessee
98: *> \author Univ. of California Berkeley
99: *> \author Univ. of Colorado Denver
100: *> \author NAG Ltd.
1.1 bertrand 101: *
1.3 bertrand 102: *> \date December 2016
1.1 bertrand 103: *
104: *> \ingroup complex16POcomputational
105: *
106: * =====================================================================
107: RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
108: *
1.3 bertrand 109: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 110: * -- LAPACK is a software package provided by Univ. of Tennessee, --
111: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.3 bertrand 112: * December 2016
1.1 bertrand 113: *
114: * .. Scalar Arguments ..
115: CHARACTER UPLO
116: INTEGER INFO, LDA, N
117: * ..
118: * .. Array Arguments ..
119: COMPLEX*16 A( LDA, * )
120: * ..
121: *
122: * =====================================================================
123: *
124: * .. Parameters ..
125: DOUBLE PRECISION ONE, ZERO
126: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
127: COMPLEX*16 CONE
128: PARAMETER ( CONE = (1.0D+0, 0.0D+0) )
129: * ..
130: * .. Local Scalars ..
1.3 bertrand 131: LOGICAL UPPER
1.1 bertrand 132: INTEGER N1, N2, IINFO
133: DOUBLE PRECISION AJJ
134: * ..
135: * .. External Functions ..
136: LOGICAL LSAME, DISNAN
137: EXTERNAL LSAME, DISNAN
138: * ..
139: * .. External Subroutines ..
140: EXTERNAL ZHERK, ZTRSM, XERBLA
141: * ..
142: * .. Intrinsic Functions ..
143: INTRINSIC MAX, DBLE, SQRT
144: * ..
145: * .. Executable Statements ..
146: *
147: * Test the input parameters
148: *
149: INFO = 0
150: UPPER = LSAME( UPLO, 'U' )
151: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
152: INFO = -1
153: ELSE IF( N.LT.0 ) THEN
154: INFO = -2
155: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
156: INFO = -4
157: END IF
158: IF( INFO.NE.0 ) THEN
159: CALL XERBLA( 'ZPOTRF2', -INFO )
160: RETURN
161: END IF
162: *
163: * Quick return if possible
164: *
165: IF( N.EQ.0 )
166: $ RETURN
167: *
168: * N=1 case
169: *
170: IF( N.EQ.1 ) THEN
171: *
172: * Test for non-positive-definiteness
173: *
174: AJJ = DBLE( A( 1, 1 ) )
175: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
176: INFO = 1
177: RETURN
178: END IF
179: *
180: * Factor
181: *
182: A( 1, 1 ) = SQRT( AJJ )
183: *
184: * Use recursive code
185: *
186: ELSE
187: N1 = N/2
188: N2 = N-N1
189: *
190: * Factor A11
191: *
192: CALL ZPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
193: IF ( IINFO.NE.0 ) THEN
194: INFO = IINFO
195: RETURN
1.3 bertrand 196: END IF
1.1 bertrand 197: *
198: * Compute the Cholesky factorization A = U**H*U
199: *
200: IF( UPPER ) THEN
201: *
202: * Update and scale A12
203: *
204: CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE,
205: $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
206: *
207: * Update and factor A22
1.3 bertrand 208: *
1.1 bertrand 209: CALL ZHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA,
210: $ ONE, A( N1+1, N1+1 ), LDA )
211: CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
212: IF ( IINFO.NE.0 ) THEN
213: INFO = IINFO + N1
214: RETURN
215: END IF
216: *
217: * Compute the Cholesky factorization A = L*L**H
218: *
219: ELSE
220: *
221: * Update and scale A21
222: *
223: CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE,
224: $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
225: *
226: * Update and factor A22
227: *
228: CALL ZHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
229: $ ONE, A( N1+1, N1+1 ), LDA )
230: CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
231: IF ( IINFO.NE.0 ) THEN
232: INFO = IINFO + N1
233: RETURN
234: END IF
235: END IF
236: END IF
237: RETURN
238: *
239: * End of ZPOTRF2
240: *
241: END
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