1 SUBROUTINE CPOTRF( 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 COMPLEX A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CPOTRF computes the Cholesky factorization of a complex Hermitian
20 * positive definite matrix A.
21 *
22 * The factorization has the form
23 * A = U**H * U, if UPLO = 'U', or
24 * A = L * L**H, 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) COMPLEX array, dimension (LDA,N)
40 * On entry, the Hermitian 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**H*U or A = L*L**H.
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 REAL ONE
65 COMPLEX CONE
66 PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ) )
67 * ..
68 * .. Local Scalars ..
69 LOGICAL UPPER
70 INTEGER J, JB, NB
71 * ..
72 * .. External Functions ..
73 LOGICAL LSAME
74 INTEGER ILAENV
75 EXTERNAL LSAME, ILAENV
76 * ..
77 * .. External Subroutines ..
78 EXTERNAL CGEMM, CHERK, CPOTF2, CTRSM, XERBLA
79 * ..
80 * .. Intrinsic Functions ..
81 INTRINSIC MAX, MIN
82 * ..
83 * .. Executable Statements ..
84 *
85 * Test the input parameters.
86 *
87 INFO = 0
88 UPPER = LSAME( UPLO, 'U' )
89 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
90 INFO = -1
91 ELSE IF( N.LT.0 ) THEN
92 INFO = -2
93 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
94 INFO = -4
95 END IF
96 IF( INFO.NE.0 ) THEN
97 CALL XERBLA( 'CPOTRF', -INFO )
98 RETURN
99 END IF
100 *
101 * Quick return if possible
102 *
103 IF( N.EQ.0 )
104 $ RETURN
105 *
106 * Determine the block size for this environment.
107 *
108 NB = ILAENV( 1, 'CPOTRF', UPLO, N, -1, -1, -1 )
109 IF( NB.LE.1 .OR. NB.GE.N ) THEN
110 *
111 * Use unblocked code.
112 *
113 CALL CPOTF2( UPLO, N, A, LDA, INFO )
114 ELSE
115 *
116 * Use blocked code.
117 *
118 IF( UPPER ) THEN
119 *
120 * Compute the Cholesky factorization A = U**H *U.
121 *
122 DO 10 J = 1, N, NB
123 *
124 * Update and factorize the current diagonal block and test
125 * for non-positive-definiteness.
126 *
127 JB = MIN( NB, N-J+1 )
128 CALL CHERK( 'Upper', 'Conjugate transpose', JB, J-1,
129 $ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
130 CALL CPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
131 IF( INFO.NE.0 )
132 $ GO TO 30
133 IF( J+JB.LE.N ) THEN
134 *
135 * Compute the current block row.
136 *
137 CALL CGEMM( 'Conjugate transpose', 'No transpose', JB,
138 $ N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
139 $ A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
140 $ LDA )
141 CALL CTRSM( 'Left', 'Upper', 'Conjugate transpose',
142 $ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
143 $ LDA, A( J, J+JB ), LDA )
144 END IF
145 10 CONTINUE
146 *
147 ELSE
148 *
149 * Compute the Cholesky factorization A = L*L**H.
150 *
151 DO 20 J = 1, N, NB
152 *
153 * Update and factorize the current diagonal block and test
154 * for non-positive-definiteness.
155 *
156 JB = MIN( NB, N-J+1 )
157 CALL CHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
158 $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
159 CALL CPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
160 IF( INFO.NE.0 )
161 $ GO TO 30
162 IF( J+JB.LE.N ) THEN
163 *
164 * Compute the current block column.
165 *
166 CALL CGEMM( 'No transpose', 'Conjugate transpose',
167 $ N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
168 $ LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
169 $ LDA )
170 CALL CTRSM( 'Right', 'Lower', 'Conjugate transpose',
171 $ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
172 $ LDA, A( J+JB, J ), LDA )
173 END IF
174 20 CONTINUE
175 END IF
176 END IF
177 GO TO 40
178 *
179 30 CONTINUE
180 INFO = INFO + J - 1
181 *
182 40 CONTINUE
183 RETURN
184 *
185 * End of CPOTRF
186 *
187 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 COMPLEX A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CPOTRF computes the Cholesky factorization of a complex Hermitian
20 * positive definite matrix A.
21 *
22 * The factorization has the form
23 * A = U**H * U, if UPLO = 'U', or
24 * A = L * L**H, 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) COMPLEX array, dimension (LDA,N)
40 * On entry, the Hermitian 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**H*U or A = L*L**H.
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 REAL ONE
65 COMPLEX CONE
66 PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ) )
67 * ..
68 * .. Local Scalars ..
69 LOGICAL UPPER
70 INTEGER J, JB, NB
71 * ..
72 * .. External Functions ..
73 LOGICAL LSAME
74 INTEGER ILAENV
75 EXTERNAL LSAME, ILAENV
76 * ..
77 * .. External Subroutines ..
78 EXTERNAL CGEMM, CHERK, CPOTF2, CTRSM, XERBLA
79 * ..
80 * .. Intrinsic Functions ..
81 INTRINSIC MAX, MIN
82 * ..
83 * .. Executable Statements ..
84 *
85 * Test the input parameters.
86 *
87 INFO = 0
88 UPPER = LSAME( UPLO, 'U' )
89 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
90 INFO = -1
91 ELSE IF( N.LT.0 ) THEN
92 INFO = -2
93 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
94 INFO = -4
95 END IF
96 IF( INFO.NE.0 ) THEN
97 CALL XERBLA( 'CPOTRF', -INFO )
98 RETURN
99 END IF
100 *
101 * Quick return if possible
102 *
103 IF( N.EQ.0 )
104 $ RETURN
105 *
106 * Determine the block size for this environment.
107 *
108 NB = ILAENV( 1, 'CPOTRF', UPLO, N, -1, -1, -1 )
109 IF( NB.LE.1 .OR. NB.GE.N ) THEN
110 *
111 * Use unblocked code.
112 *
113 CALL CPOTF2( UPLO, N, A, LDA, INFO )
114 ELSE
115 *
116 * Use blocked code.
117 *
118 IF( UPPER ) THEN
119 *
120 * Compute the Cholesky factorization A = U**H *U.
121 *
122 DO 10 J = 1, N, NB
123 *
124 * Update and factorize the current diagonal block and test
125 * for non-positive-definiteness.
126 *
127 JB = MIN( NB, N-J+1 )
128 CALL CHERK( 'Upper', 'Conjugate transpose', JB, J-1,
129 $ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
130 CALL CPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
131 IF( INFO.NE.0 )
132 $ GO TO 30
133 IF( J+JB.LE.N ) THEN
134 *
135 * Compute the current block row.
136 *
137 CALL CGEMM( 'Conjugate transpose', 'No transpose', JB,
138 $ N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
139 $ A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
140 $ LDA )
141 CALL CTRSM( 'Left', 'Upper', 'Conjugate transpose',
142 $ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
143 $ LDA, A( J, J+JB ), LDA )
144 END IF
145 10 CONTINUE
146 *
147 ELSE
148 *
149 * Compute the Cholesky factorization A = L*L**H.
150 *
151 DO 20 J = 1, N, NB
152 *
153 * Update and factorize the current diagonal block and test
154 * for non-positive-definiteness.
155 *
156 JB = MIN( NB, N-J+1 )
157 CALL CHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
158 $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
159 CALL CPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
160 IF( INFO.NE.0 )
161 $ GO TO 30
162 IF( J+JB.LE.N ) THEN
163 *
164 * Compute the current block column.
165 *
166 CALL CGEMM( 'No transpose', 'Conjugate transpose',
167 $ N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
168 $ LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
169 $ LDA )
170 CALL CTRSM( 'Right', 'Lower', 'Conjugate transpose',
171 $ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
172 $ LDA, A( J+JB, J ), LDA )
173 END IF
174 20 CONTINUE
175 END IF
176 END IF
177 GO TO 40
178 *
179 30 CONTINUE
180 INFO = INFO + J - 1
181 *
182 40 CONTINUE
183 RETURN
184 *
185 * End of CPOTRF
186 *
187 END