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1.1 bertrand 1: SUBROUTINE DPPTRF( UPLO, N, AP, 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, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION AP( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DPPTRF computes the Cholesky factorization of a real symmetric
20: * positive definite matrix A stored in packed format.
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: * Arguments
28: * =========
29: *
30: * UPLO (input) CHARACTER*1
31: * = 'U': Upper triangle of A is stored;
32: * = 'L': Lower triangle of A is stored.
33: *
34: * N (input) INTEGER
35: * The order of the matrix A. N >= 0.
36: *
37: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
38: * On entry, the upper or lower triangle of the symmetric matrix
39: * A, packed columnwise in a linear array. The j-th column of A
40: * is stored in the array AP as follows:
41: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
42: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
43: * See below for further details.
44: *
45: * On exit, if INFO = 0, the triangular factor U or L from the
46: * Cholesky factorization A = U**T*U or A = L*L**T, in the same
47: * storage format as A.
48: *
49: * INFO (output) INTEGER
50: * = 0: successful exit
51: * < 0: if INFO = -i, the i-th argument had an illegal value
52: * > 0: if INFO = i, the leading minor of order i is not
53: * positive definite, and the factorization could not be
54: * completed.
55: *
56: * Further Details
57: * ======= =======
58: *
59: * The packed storage scheme is illustrated by the following example
60: * when N = 4, UPLO = 'U':
61: *
62: * Two-dimensional storage of the symmetric matrix A:
63: *
64: * a11 a12 a13 a14
65: * a22 a23 a24
66: * a33 a34 (aij = aji)
67: * a44
68: *
69: * Packed storage of the upper triangle of A:
70: *
71: * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
72: *
73: * =====================================================================
74: *
75: * .. Parameters ..
76: DOUBLE PRECISION ONE, ZERO
77: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
78: * ..
79: * .. Local Scalars ..
80: LOGICAL UPPER
81: INTEGER J, JC, JJ
82: DOUBLE PRECISION AJJ
83: * ..
84: * .. External Functions ..
85: LOGICAL LSAME
86: DOUBLE PRECISION DDOT
87: EXTERNAL LSAME, DDOT
88: * ..
89: * .. External Subroutines ..
90: EXTERNAL DSCAL, DSPR, DTPSV, XERBLA
91: * ..
92: * .. Intrinsic Functions ..
93: INTRINSIC SQRT
94: * ..
95: * .. Executable Statements ..
96: *
97: * Test the input parameters.
98: *
99: INFO = 0
100: UPPER = LSAME( UPLO, 'U' )
101: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
102: INFO = -1
103: ELSE IF( N.LT.0 ) THEN
104: INFO = -2
105: END IF
106: IF( INFO.NE.0 ) THEN
107: CALL XERBLA( 'DPPTRF', -INFO )
108: RETURN
109: END IF
110: *
111: * Quick return if possible
112: *
113: IF( N.EQ.0 )
114: $ RETURN
115: *
116: IF( UPPER ) THEN
117: *
118: * Compute the Cholesky factorization A = U'*U.
119: *
120: JJ = 0
121: DO 10 J = 1, N
122: JC = JJ + 1
123: JJ = JJ + J
124: *
125: * Compute elements 1:J-1 of column J.
126: *
127: IF( J.GT.1 )
128: $ CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP,
129: $ AP( JC ), 1 )
130: *
131: * Compute U(J,J) and test for non-positive-definiteness.
132: *
133: AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
134: IF( AJJ.LE.ZERO ) THEN
135: AP( JJ ) = AJJ
136: GO TO 30
137: END IF
138: AP( JJ ) = SQRT( AJJ )
139: 10 CONTINUE
140: ELSE
141: *
142: * Compute the Cholesky factorization A = L*L'.
143: *
144: JJ = 1
145: DO 20 J = 1, N
146: *
147: * Compute L(J,J) and test for non-positive-definiteness.
148: *
149: AJJ = AP( JJ )
150: IF( AJJ.LE.ZERO ) THEN
151: AP( JJ ) = AJJ
152: GO TO 30
153: END IF
154: AJJ = SQRT( AJJ )
155: AP( JJ ) = AJJ
156: *
157: * Compute elements J+1:N of column J and update the trailing
158: * submatrix.
159: *
160: IF( J.LT.N ) THEN
161: CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
162: CALL DSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
163: $ AP( JJ+N-J+1 ) )
164: JJ = JJ + N - J + 1
165: END IF
166: 20 CONTINUE
167: END IF
168: GO TO 40
169: *
170: 30 CONTINUE
171: INFO = J
172: *
173: 40 CONTINUE
174: RETURN
175: *
176: * End of DPPTRF
177: *
178: END