1 SUBROUTINE DPOTRF( 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 * 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**T*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**T.
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
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 * 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**T*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**T.
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