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1.1 bertrand 1: SUBROUTINE ZLAUUM( UPLO, N, A, LDA, INFO )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
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' or L' * 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';
46: * if UPLO = 'L', the lower triangle of A is overwritten with
47: * the lower triangle of the product L' * 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'.
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' * 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