Annotation of rpl/lapack/lapack/zpotrf.f, revision 1.18
1.9 bertrand 1: *> \brief \b ZPOTRF
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.18 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.18 ! bertrand 9: *> Download ZPOTRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpotrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpotrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpotrf.f">
1.9 bertrand 15: *> [TXT]</a>
1.18 ! bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO )
1.18 ! bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 A( LDA, * )
29: * ..
1.18 ! bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZPOTRF 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 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 COMPLEX*16 array, dimension (LDA,N)
67: *> On entry, the Hermitian 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**H *U or A = L*L**H.
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: *
1.18 ! bertrand 98: *> \author Univ. of Tennessee
! 99: *> \author Univ. of California Berkeley
! 100: *> \author Univ. of Colorado Denver
! 101: *> \author NAG Ltd.
1.9 bertrand 102: *
1.18 ! bertrand 103: *> \date December 2016
1.9 bertrand 104: *
105: *> \ingroup complex16POcomputational
106: *
107: * =====================================================================
1.1 bertrand 108: SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO )
109: *
1.18 ! bertrand 110: * -- LAPACK computational routine (version 3.7.0) --
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..--
1.18 ! bertrand 113: * December 2016
1.1 bertrand 114: *
115: * .. Scalar Arguments ..
116: CHARACTER UPLO
117: INTEGER INFO, LDA, N
118: * ..
119: * .. Array Arguments ..
120: COMPLEX*16 A( LDA, * )
121: * ..
122: *
123: * =====================================================================
124: *
125: * .. Parameters ..
126: DOUBLE PRECISION ONE
127: COMPLEX*16 CONE
128: PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) )
129: * ..
130: * .. Local Scalars ..
131: LOGICAL UPPER
132: INTEGER J, JB, NB
133: * ..
134: * .. External Functions ..
135: LOGICAL LSAME
136: INTEGER ILAENV
137: EXTERNAL LSAME, ILAENV
138: * ..
139: * .. External Subroutines ..
1.14 bertrand 140: EXTERNAL XERBLA, ZGEMM, ZHERK, ZPOTRF2, ZTRSM
1.1 bertrand 141: * ..
142: * .. Intrinsic Functions ..
143: INTRINSIC MAX, MIN
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( 'ZPOTRF', -INFO )
160: RETURN
161: END IF
162: *
163: * Quick return if possible
164: *
165: IF( N.EQ.0 )
166: $ RETURN
167: *
168: * Determine the block size for this environment.
169: *
170: NB = ILAENV( 1, 'ZPOTRF', UPLO, N, -1, -1, -1 )
171: IF( NB.LE.1 .OR. NB.GE.N ) THEN
172: *
173: * Use unblocked code.
174: *
1.14 bertrand 175: CALL ZPOTRF2( UPLO, N, A, LDA, INFO )
1.1 bertrand 176: ELSE
177: *
178: * Use blocked code.
179: *
180: IF( UPPER ) THEN
181: *
1.8 bertrand 182: * Compute the Cholesky factorization A = U**H *U.
1.1 bertrand 183: *
184: DO 10 J = 1, N, NB
185: *
186: * Update and factorize the current diagonal block and test
187: * for non-positive-definiteness.
188: *
189: JB = MIN( NB, N-J+1 )
190: CALL ZHERK( 'Upper', 'Conjugate transpose', JB, J-1,
191: $ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
1.14 bertrand 192: CALL ZPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
1.1 bertrand 193: IF( INFO.NE.0 )
194: $ GO TO 30
195: IF( J+JB.LE.N ) THEN
196: *
197: * Compute the current block row.
198: *
199: CALL ZGEMM( 'Conjugate transpose', 'No transpose', JB,
200: $ N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
201: $ A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
202: $ LDA )
203: CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose',
204: $ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
205: $ LDA, A( J, J+JB ), LDA )
206: END IF
207: 10 CONTINUE
208: *
209: ELSE
210: *
1.8 bertrand 211: * Compute the Cholesky factorization A = L*L**H.
1.1 bertrand 212: *
213: DO 20 J = 1, N, NB
214: *
215: * Update and factorize the current diagonal block and test
216: * for non-positive-definiteness.
217: *
218: JB = MIN( NB, N-J+1 )
219: CALL ZHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
220: $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
1.14 bertrand 221: CALL ZPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
1.1 bertrand 222: IF( INFO.NE.0 )
223: $ GO TO 30
224: IF( J+JB.LE.N ) THEN
225: *
226: * Compute the current block column.
227: *
228: CALL ZGEMM( 'No transpose', 'Conjugate transpose',
229: $ N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
230: $ LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
231: $ LDA )
232: CALL ZTRSM( 'Right', 'Lower', 'Conjugate transpose',
233: $ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
234: $ LDA, A( J+JB, J ), LDA )
235: END IF
236: 20 CONTINUE
237: END IF
238: END IF
239: GO TO 40
240: *
241: 30 CONTINUE
242: INFO = INFO + J - 1
243: *
244: 40 CONTINUE
245: RETURN
246: *
247: * End of ZPOTRF
248: *
249: END
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