1: SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
2: *
3: * -- LAPACK routine (version 3.3.1) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * -- April 2011 --
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: * DPOTF2 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 unblocked version of the algorithm, calling Level 2 BLAS.
28: *
29: * Arguments
30: * =========
31: *
32: * UPLO (input) CHARACTER*1
33: * Specifies whether the upper or lower triangular part of the
34: * symmetric matrix A is stored.
35: * = 'U': Upper triangular
36: * = 'L': Lower triangular
37: *
38: * N (input) INTEGER
39: * The order of the matrix A. N >= 0.
40: *
41: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
42: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
43: * n by n upper triangular part of A contains the upper
44: * triangular part of the matrix A, and the strictly lower
45: * triangular part of A is not referenced. If UPLO = 'L', the
46: * leading n by n lower triangular part of A contains the lower
47: * triangular part of the matrix A, and the strictly upper
48: * triangular part of A is not referenced.
49: *
50: * On exit, if INFO = 0, the factor U or L from the Cholesky
51: * factorization A = U**T *U or A = L*L**T.
52: *
53: * LDA (input) INTEGER
54: * The leading dimension of the array A. LDA >= max(1,N).
55: *
56: * INFO (output) INTEGER
57: * = 0: successful exit
58: * < 0: if INFO = -k, the k-th argument had an illegal value
59: * > 0: if INFO = k, the leading minor of order k is not
60: * positive definite, and the factorization could not be
61: * completed.
62: *
63: * =====================================================================
64: *
65: * .. Parameters ..
66: DOUBLE PRECISION ONE, ZERO
67: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
68: * ..
69: * .. Local Scalars ..
70: LOGICAL UPPER
71: INTEGER J
72: DOUBLE PRECISION AJJ
73: * ..
74: * .. External Functions ..
75: LOGICAL LSAME, DISNAN
76: DOUBLE PRECISION DDOT
77: EXTERNAL LSAME, DDOT, DISNAN
78: * ..
79: * .. External Subroutines ..
80: EXTERNAL DGEMV, DSCAL, XERBLA
81: * ..
82: * .. Intrinsic Functions ..
83: INTRINSIC MAX, SQRT
84: * ..
85: * .. Executable Statements ..
86: *
87: * Test the input parameters.
88: *
89: INFO = 0
90: UPPER = LSAME( UPLO, 'U' )
91: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
92: INFO = -1
93: ELSE IF( N.LT.0 ) THEN
94: INFO = -2
95: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
96: INFO = -4
97: END IF
98: IF( INFO.NE.0 ) THEN
99: CALL XERBLA( 'DPOTF2', -INFO )
100: RETURN
101: END IF
102: *
103: * Quick return if possible
104: *
105: IF( N.EQ.0 )
106: $ RETURN
107: *
108: IF( UPPER ) THEN
109: *
110: * Compute the Cholesky factorization A = U**T *U.
111: *
112: DO 10 J = 1, N
113: *
114: * Compute U(J,J) and test for non-positive-definiteness.
115: *
116: AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
117: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
118: A( J, J ) = AJJ
119: GO TO 30
120: END IF
121: AJJ = SQRT( AJJ )
122: A( J, J ) = AJJ
123: *
124: * Compute elements J+1:N of row J.
125: *
126: IF( J.LT.N ) THEN
127: CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
128: $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
129: CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
130: END IF
131: 10 CONTINUE
132: ELSE
133: *
134: * Compute the Cholesky factorization A = L*L**T.
135: *
136: DO 20 J = 1, N
137: *
138: * Compute L(J,J) and test for non-positive-definiteness.
139: *
140: AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
141: $ LDA )
142: IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
143: A( J, J ) = AJJ
144: GO TO 30
145: END IF
146: AJJ = SQRT( AJJ )
147: A( J, J ) = AJJ
148: *
149: * Compute elements J+1:N of column J.
150: *
151: IF( J.LT.N ) THEN
152: CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
153: $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
154: CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
155: END IF
156: 20 CONTINUE
157: END IF
158: GO TO 40
159: *
160: 30 CONTINUE
161: INFO = J
162: *
163: 40 CONTINUE
164: RETURN
165: *
166: * End of DPOTF2
167: *
168: END
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