1 SUBROUTINE ZLAUUM( 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 COMPLEX*16 A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZLAUUM computes the product U * U**H or L**H * 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) COMPLEX*16 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**H;
46 * if UPLO = 'L', the lower triangle of A is overwritten with
47 * the lower triangle of the product L**H * 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 COMPLEX*16 CONE
62 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
63 * ..
64 * .. Local Scalars ..
65 LOGICAL UPPER
66 INTEGER I, IB, NB
67 * ..
68 * .. External Functions ..
69 LOGICAL LSAME
70 INTEGER ILAENV
71 EXTERNAL LSAME, ILAENV
72 * ..
73 * .. External Subroutines ..
74 EXTERNAL XERBLA, ZGEMM, ZHERK, ZLAUU2, ZTRMM
75 * ..
76 * .. Intrinsic Functions ..
77 INTRINSIC MAX, MIN
78 * ..
79 * .. Executable Statements ..
80 *
81 * Test the input parameters.
82 *
83 INFO = 0
84 UPPER = LSAME( UPLO, 'U' )
85 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
86 INFO = -1
87 ELSE IF( N.LT.0 ) THEN
88 INFO = -2
89 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
90 INFO = -4
91 END IF
92 IF( INFO.NE.0 ) THEN
93 CALL XERBLA( 'ZLAUUM', -INFO )
94 RETURN
95 END IF
96 *
97 * Quick return if possible
98 *
99 IF( N.EQ.0 )
100 $ RETURN
101 *
102 * Determine the block size for this environment.
103 *
104 NB = ILAENV( 1, 'ZLAUUM', UPLO, N, -1, -1, -1 )
105 *
106 IF( NB.LE.1 .OR. NB.GE.N ) THEN
107 *
108 * Use unblocked code
109 *
110 CALL ZLAUU2( UPLO, N, A, LDA, INFO )
111 ELSE
112 *
113 * Use blocked code
114 *
115 IF( UPPER ) THEN
116 *
117 * Compute the product U * U**H.
118 *
119 DO 10 I = 1, N, NB
120 IB = MIN( NB, N-I+1 )
121 CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
122 $ 'Non-unit', I-1, IB, CONE, A( I, I ), LDA,
123 $ A( 1, I ), LDA )
124 CALL ZLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
125 IF( I+IB.LE.N ) THEN
126 CALL ZGEMM( 'No transpose', 'Conjugate transpose',
127 $ I-1, IB, N-I-IB+1, CONE, A( 1, I+IB ),
128 $ LDA, A( I, I+IB ), LDA, CONE, A( 1, I ),
129 $ LDA )
130 CALL ZHERK( 'Upper', 'No transpose', IB, N-I-IB+1,
131 $ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
132 $ LDA )
133 END IF
134 10 CONTINUE
135 ELSE
136 *
137 * Compute the product L**H * L.
138 *
139 DO 20 I = 1, N, NB
140 IB = MIN( NB, N-I+1 )
141 CALL ZTRMM( 'Left', 'Lower', 'Conjugate transpose',
142 $ 'Non-unit', IB, I-1, CONE, A( I, I ), LDA,
143 $ A( I, 1 ), LDA )
144 CALL ZLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
145 IF( I+IB.LE.N ) THEN
146 CALL ZGEMM( 'Conjugate transpose', 'No transpose', IB,
147 $ I-1, N-I-IB+1, CONE, A( I+IB, I ), LDA,
148 $ A( I+IB, 1 ), LDA, CONE, A( I, 1 ), LDA )
149 CALL ZHERK( 'Lower', 'Conjugate transpose', IB,
150 $ N-I-IB+1, ONE, A( I+IB, I ), LDA, ONE,
151 $ A( I, I ), LDA )
152 END IF
153 20 CONTINUE
154 END IF
155 END IF
156 *
157 RETURN
158 *
159 * End of ZLAUUM
160 *
161 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 COMPLEX*16 A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZLAUUM computes the product U * U**H or L**H * 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) COMPLEX*16 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**H;
46 * if UPLO = 'L', the lower triangle of A is overwritten with
47 * the lower triangle of the product L**H * 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 COMPLEX*16 CONE
62 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
63 * ..
64 * .. Local Scalars ..
65 LOGICAL UPPER
66 INTEGER I, IB, NB
67 * ..
68 * .. External Functions ..
69 LOGICAL LSAME
70 INTEGER ILAENV
71 EXTERNAL LSAME, ILAENV
72 * ..
73 * .. External Subroutines ..
74 EXTERNAL XERBLA, ZGEMM, ZHERK, ZLAUU2, ZTRMM
75 * ..
76 * .. Intrinsic Functions ..
77 INTRINSIC MAX, MIN
78 * ..
79 * .. Executable Statements ..
80 *
81 * Test the input parameters.
82 *
83 INFO = 0
84 UPPER = LSAME( UPLO, 'U' )
85 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
86 INFO = -1
87 ELSE IF( N.LT.0 ) THEN
88 INFO = -2
89 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
90 INFO = -4
91 END IF
92 IF( INFO.NE.0 ) THEN
93 CALL XERBLA( 'ZLAUUM', -INFO )
94 RETURN
95 END IF
96 *
97 * Quick return if possible
98 *
99 IF( N.EQ.0 )
100 $ RETURN
101 *
102 * Determine the block size for this environment.
103 *
104 NB = ILAENV( 1, 'ZLAUUM', UPLO, N, -1, -1, -1 )
105 *
106 IF( NB.LE.1 .OR. NB.GE.N ) THEN
107 *
108 * Use unblocked code
109 *
110 CALL ZLAUU2( UPLO, N, A, LDA, INFO )
111 ELSE
112 *
113 * Use blocked code
114 *
115 IF( UPPER ) THEN
116 *
117 * Compute the product U * U**H.
118 *
119 DO 10 I = 1, N, NB
120 IB = MIN( NB, N-I+1 )
121 CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
122 $ 'Non-unit', I-1, IB, CONE, A( I, I ), LDA,
123 $ A( 1, I ), LDA )
124 CALL ZLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
125 IF( I+IB.LE.N ) THEN
126 CALL ZGEMM( 'No transpose', 'Conjugate transpose',
127 $ I-1, IB, N-I-IB+1, CONE, A( 1, I+IB ),
128 $ LDA, A( I, I+IB ), LDA, CONE, A( 1, I ),
129 $ LDA )
130 CALL ZHERK( 'Upper', 'No transpose', IB, N-I-IB+1,
131 $ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
132 $ LDA )
133 END IF
134 10 CONTINUE
135 ELSE
136 *
137 * Compute the product L**H * L.
138 *
139 DO 20 I = 1, N, NB
140 IB = MIN( NB, N-I+1 )
141 CALL ZTRMM( 'Left', 'Lower', 'Conjugate transpose',
142 $ 'Non-unit', IB, I-1, CONE, A( I, I ), LDA,
143 $ A( I, 1 ), LDA )
144 CALL ZLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
145 IF( I+IB.LE.N ) THEN
146 CALL ZGEMM( 'Conjugate transpose', 'No transpose', IB,
147 $ I-1, N-I-IB+1, CONE, A( I+IB, I ), LDA,
148 $ A( I+IB, 1 ), LDA, CONE, A( I, 1 ), LDA )
149 CALL ZHERK( 'Lower', 'Conjugate transpose', IB,
150 $ N-I-IB+1, ONE, A( I+IB, I ), LDA, ONE,
151 $ A( I, I ), LDA )
152 END IF
153 20 CONTINUE
154 END IF
155 END IF
156 *
157 RETURN
158 *
159 * End of ZLAUUM
160 *
161 END