1: SUBROUTINE DLAUUM( 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: DOUBLE PRECISION A( LDA, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DLAUUM 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) 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';
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: * ..
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'.
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' * 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
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