1 SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
2 *
3 * -- LAPACK auxiliary 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 * DLAUUM computes the product U * U**T or L**T * L, where the triangular
20 * factor U or L is stored in the upper or lower triangular part of
21 * the array A.
22 *
23 * If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
24 * overwriting the factor U in A.
25 * If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
26 * overwriting the factor L in A.
27 *
28 * This is the blocked form of the algorithm, calling Level 3 BLAS.
29 *
30 * Arguments
31 * =========
32 *
33 * UPLO (input) CHARACTER*1
34 * Specifies whether the triangular factor stored in the array A
35 * is upper or lower triangular:
36 * = 'U': Upper triangular
37 * = 'L': Lower triangular
38 *
39 * N (input) INTEGER
40 * The order of the triangular factor U or L. N >= 0.
41 *
42 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
43 * On entry, the triangular factor U or L.
44 * On exit, if UPLO = 'U', the upper triangle of A is
45 * overwritten with the upper triangle of the product U * U**T;
46 * if UPLO = 'L', the lower triangle of A is overwritten with
47 * the lower triangle of the product L**T * L.
48 *
49 * LDA (input) INTEGER
50 * The leading dimension of the array A. LDA >= max(1,N).
51 *
52 * INFO (output) INTEGER
53 * = 0: successful exit
54 * < 0: if INFO = -k, the k-th argument had an illegal value
55 *
56 * =====================================================================
57 *
58 * .. Parameters ..
59 DOUBLE PRECISION ONE
60 PARAMETER ( ONE = 1.0D+0 )
61 * ..
62 * .. Local Scalars ..
63 LOGICAL UPPER
64 INTEGER I, IB, NB
65 * ..
66 * .. External Functions ..
67 LOGICAL LSAME
68 INTEGER ILAENV
69 EXTERNAL LSAME, ILAENV
70 * ..
71 * .. External Subroutines ..
72 EXTERNAL DGEMM, DLAUU2, DSYRK, DTRMM, XERBLA
73 * ..
74 * .. Intrinsic Functions ..
75 INTRINSIC MAX, MIN
76 * ..
77 * .. Executable Statements ..
78 *
79 * Test the input parameters.
80 *
81 INFO = 0
82 UPPER = LSAME( UPLO, 'U' )
83 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
84 INFO = -1
85 ELSE IF( N.LT.0 ) THEN
86 INFO = -2
87 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
88 INFO = -4
89 END IF
90 IF( INFO.NE.0 ) THEN
91 CALL XERBLA( 'DLAUUM', -INFO )
92 RETURN
93 END IF
94 *
95 * Quick return if possible
96 *
97 IF( N.EQ.0 )
98 $ RETURN
99 *
100 * Determine the block size for this environment.
101 *
102 NB = ILAENV( 1, 'DLAUUM', UPLO, N, -1, -1, -1 )
103 *
104 IF( NB.LE.1 .OR. NB.GE.N ) THEN
105 *
106 * Use unblocked code
107 *
108 CALL DLAUU2( UPLO, N, A, LDA, INFO )
109 ELSE
110 *
111 * Use blocked code
112 *
113 IF( UPPER ) THEN
114 *
115 * Compute the product U * U**T.
116 *
117 DO 10 I = 1, N, NB
118 IB = MIN( NB, N-I+1 )
119 CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Non-unit',
120 $ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
121 $ LDA )
122 CALL DLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
123 IF( I+IB.LE.N ) THEN
124 CALL DGEMM( 'No transpose', 'Transpose', I-1, IB,
125 $ N-I-IB+1, ONE, A( 1, I+IB ), LDA,
126 $ A( I, I+IB ), LDA, ONE, A( 1, I ), LDA )
127 CALL DSYRK( 'Upper', 'No transpose', IB, N-I-IB+1,
128 $ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
129 $ LDA )
130 END IF
131 10 CONTINUE
132 ELSE
133 *
134 * Compute the product L**T * L.
135 *
136 DO 20 I = 1, N, NB
137 IB = MIN( NB, N-I+1 )
138 CALL DTRMM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB,
139 $ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
140 CALL DLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
141 IF( I+IB.LE.N ) THEN
142 CALL DGEMM( 'Transpose', 'No transpose', IB, I-1,
143 $ N-I-IB+1, ONE, A( I+IB, I ), LDA,
144 $ A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA )
145 CALL DSYRK( 'Lower', 'Transpose', IB, N-I-IB+1, ONE,
146 $ A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
147 END IF
148 20 CONTINUE
149 END IF
150 END IF
151 *
152 RETURN
153 *
154 * End of DLAUUM
155 *
156 END
2 *
3 * -- LAPACK auxiliary 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 * DLAUUM computes the product U * U**T or L**T * L, where the triangular
20 * factor U or L is stored in the upper or lower triangular part of
21 * the array A.
22 *
23 * If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
24 * overwriting the factor U in A.
25 * If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
26 * overwriting the factor L in A.
27 *
28 * This is the blocked form of the algorithm, calling Level 3 BLAS.
29 *
30 * Arguments
31 * =========
32 *
33 * UPLO (input) CHARACTER*1
34 * Specifies whether the triangular factor stored in the array A
35 * is upper or lower triangular:
36 * = 'U': Upper triangular
37 * = 'L': Lower triangular
38 *
39 * N (input) INTEGER
40 * The order of the triangular factor U or L. N >= 0.
41 *
42 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
43 * On entry, the triangular factor U or L.
44 * On exit, if UPLO = 'U', the upper triangle of A is
45 * overwritten with the upper triangle of the product U * U**T;
46 * if UPLO = 'L', the lower triangle of A is overwritten with
47 * the lower triangle of the product L**T * L.
48 *
49 * LDA (input) INTEGER
50 * The leading dimension of the array A. LDA >= max(1,N).
51 *
52 * INFO (output) INTEGER
53 * = 0: successful exit
54 * < 0: if INFO = -k, the k-th argument had an illegal value
55 *
56 * =====================================================================
57 *
58 * .. Parameters ..
59 DOUBLE PRECISION ONE
60 PARAMETER ( ONE = 1.0D+0 )
61 * ..
62 * .. Local Scalars ..
63 LOGICAL UPPER
64 INTEGER I, IB, NB
65 * ..
66 * .. External Functions ..
67 LOGICAL LSAME
68 INTEGER ILAENV
69 EXTERNAL LSAME, ILAENV
70 * ..
71 * .. External Subroutines ..
72 EXTERNAL DGEMM, DLAUU2, DSYRK, DTRMM, XERBLA
73 * ..
74 * .. Intrinsic Functions ..
75 INTRINSIC MAX, MIN
76 * ..
77 * .. Executable Statements ..
78 *
79 * Test the input parameters.
80 *
81 INFO = 0
82 UPPER = LSAME( UPLO, 'U' )
83 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
84 INFO = -1
85 ELSE IF( N.LT.0 ) THEN
86 INFO = -2
87 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
88 INFO = -4
89 END IF
90 IF( INFO.NE.0 ) THEN
91 CALL XERBLA( 'DLAUUM', -INFO )
92 RETURN
93 END IF
94 *
95 * Quick return if possible
96 *
97 IF( N.EQ.0 )
98 $ RETURN
99 *
100 * Determine the block size for this environment.
101 *
102 NB = ILAENV( 1, 'DLAUUM', UPLO, N, -1, -1, -1 )
103 *
104 IF( NB.LE.1 .OR. NB.GE.N ) THEN
105 *
106 * Use unblocked code
107 *
108 CALL DLAUU2( UPLO, N, A, LDA, INFO )
109 ELSE
110 *
111 * Use blocked code
112 *
113 IF( UPPER ) THEN
114 *
115 * Compute the product U * U**T.
116 *
117 DO 10 I = 1, N, NB
118 IB = MIN( NB, N-I+1 )
119 CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Non-unit',
120 $ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
121 $ LDA )
122 CALL DLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
123 IF( I+IB.LE.N ) THEN
124 CALL DGEMM( 'No transpose', 'Transpose', I-1, IB,
125 $ N-I-IB+1, ONE, A( 1, I+IB ), LDA,
126 $ A( I, I+IB ), LDA, ONE, A( 1, I ), LDA )
127 CALL DSYRK( 'Upper', 'No transpose', IB, N-I-IB+1,
128 $ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
129 $ LDA )
130 END IF
131 10 CONTINUE
132 ELSE
133 *
134 * Compute the product L**T * L.
135 *
136 DO 20 I = 1, N, NB
137 IB = MIN( NB, N-I+1 )
138 CALL DTRMM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB,
139 $ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
140 CALL DLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
141 IF( I+IB.LE.N ) THEN
142 CALL DGEMM( 'Transpose', 'No transpose', IB, I-1,
143 $ N-I-IB+1, ONE, A( I+IB, I ), LDA,
144 $ A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA )
145 CALL DSYRK( 'Lower', 'Transpose', IB, N-I-IB+1, ONE,
146 $ A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
147 END IF
148 20 CONTINUE
149 END IF
150 END IF
151 *
152 RETURN
153 *
154 * End of DLAUUM
155 *
156 END