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
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