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1.1 bertrand 1: SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INFO, LDA, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DPOTRF computes the Cholesky factorization of a real symmetric
20: * positive definite matrix A.
21: *
22: * The factorization has the form
23: * A = U**T * U, if UPLO = 'U', or
24: * A = L * L**T, if UPLO = 'L',
25: * where U is an upper triangular matrix and L is lower triangular.
26: *
27: * This is the block version of the algorithm, calling Level 3 BLAS.
28: *
29: * Arguments
30: * =========
31: *
32: * UPLO (input) CHARACTER*1
33: * = 'U': Upper triangle of A is stored;
34: * = 'L': Lower triangle of A is stored.
35: *
36: * N (input) INTEGER
37: * The order of the matrix A. N >= 0.
38: *
39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
41: * N-by-N upper triangular part of A contains the upper
42: * triangular part of the matrix A, and the strictly lower
43: * triangular part of A is not referenced. If UPLO = 'L', the
44: * leading N-by-N lower triangular part of A contains the lower
45: * triangular part of the matrix A, and the strictly upper
46: * triangular part of A is not referenced.
47: *
48: * On exit, if INFO = 0, the factor U or L from the Cholesky
49: * factorization A = U**T*U or A = L*L**T.
50: *
51: * LDA (input) INTEGER
52: * The leading dimension of the array A. LDA >= max(1,N).
53: *
54: * INFO (output) INTEGER
55: * = 0: successful exit
56: * < 0: if INFO = -i, the i-th argument had an illegal value
57: * > 0: if INFO = i, the leading minor of order i is not
58: * positive definite, and the factorization could not be
59: * completed.
60: *
61: * =====================================================================
62: *
63: * .. Parameters ..
64: DOUBLE PRECISION ONE
65: PARAMETER ( ONE = 1.0D+0 )
66: * ..
67: * .. Local Scalars ..
68: LOGICAL UPPER
69: INTEGER J, JB, NB
70: * ..
71: * .. External Functions ..
72: LOGICAL LSAME
73: INTEGER ILAENV
74: EXTERNAL LSAME, ILAENV
75: * ..
76: * .. External Subroutines ..
77: EXTERNAL DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA
78: * ..
79: * .. Intrinsic Functions ..
80: INTRINSIC MAX, MIN
81: * ..
82: * .. Executable Statements ..
83: *
84: * Test the input parameters.
85: *
86: INFO = 0
87: UPPER = LSAME( UPLO, 'U' )
88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
89: INFO = -1
90: ELSE IF( N.LT.0 ) THEN
91: INFO = -2
92: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
93: INFO = -4
94: END IF
95: IF( INFO.NE.0 ) THEN
96: CALL XERBLA( 'DPOTRF', -INFO )
97: RETURN
98: END IF
99: *
100: * Quick return if possible
101: *
102: IF( N.EQ.0 )
103: $ RETURN
104: *
105: * Determine the block size for this environment.
106: *
107: NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
108: IF( NB.LE.1 .OR. NB.GE.N ) THEN
109: *
110: * Use unblocked code.
111: *
112: CALL DPOTF2( UPLO, N, A, LDA, INFO )
113: ELSE
114: *
115: * Use blocked code.
116: *
117: IF( UPPER ) THEN
118: *
119: * Compute the Cholesky factorization A = U'*U.
120: *
121: DO 10 J = 1, N, NB
122: *
123: * Update and factorize the current diagonal block and test
124: * for non-positive-definiteness.
125: *
126: JB = MIN( NB, N-J+1 )
127: CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
128: $ A( 1, J ), LDA, ONE, A( J, J ), LDA )
129: CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
130: IF( INFO.NE.0 )
131: $ GO TO 30
132: IF( J+JB.LE.N ) THEN
133: *
134: * Compute the current block row.
135: *
136: CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,
137: $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ),
138: $ LDA, ONE, A( J, J+JB ), LDA )
139: CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
140: $ JB, N-J-JB+1, ONE, A( J, J ), LDA,
141: $ A( J, J+JB ), LDA )
142: END IF
143: 10 CONTINUE
144: *
145: ELSE
146: *
147: * Compute the Cholesky factorization A = L*L'.
148: *
149: DO 20 J = 1, N, NB
150: *
151: * Update and factorize the current diagonal block and test
152: * for non-positive-definiteness.
153: *
154: JB = MIN( NB, N-J+1 )
155: CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
156: $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
157: CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
158: IF( INFO.NE.0 )
159: $ GO TO 30
160: IF( J+JB.LE.N ) THEN
161: *
162: * Compute the current block column.
163: *
164: CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
165: $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ),
166: $ LDA, ONE, A( J+JB, J ), LDA )
167: CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
168: $ N-J-JB+1, JB, ONE, A( J, J ), LDA,
169: $ A( J+JB, J ), LDA )
170: END IF
171: 20 CONTINUE
172: END IF
173: END IF
174: GO TO 40
175: *
176: 30 CONTINUE
177: INFO = INFO + J - 1
178: *
179: 40 CONTINUE
180: RETURN
181: *
182: * End of DPOTRF
183: *
184: END