Annotation of rpl/lapack/lapack/dlauum.f, revision 1.17
1.12 bertrand 1: *> \brief \b DLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download DLAUUM + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlauum.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlauum.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlauum.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
1.16 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( LDA, * )
29: * ..
1.16 bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DLAUUM computes the product U * U**T or L**T * L, where the triangular
38: *> factor U or L is stored in the upper or lower triangular part of
39: *> the array A.
40: *>
41: *> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
42: *> overwriting the factor U in A.
43: *> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
44: *> overwriting the factor L in A.
45: *>
46: *> This is the blocked form of the algorithm, calling Level 3 BLAS.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] UPLO
53: *> \verbatim
54: *> UPLO is CHARACTER*1
55: *> Specifies whether the triangular factor stored in the array A
56: *> is upper or lower triangular:
57: *> = 'U': Upper triangular
58: *> = 'L': Lower triangular
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> The order of the triangular factor U or L. N >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] A
68: *> \verbatim
69: *> A is DOUBLE PRECISION array, dimension (LDA,N)
70: *> On entry, the triangular factor U or L.
71: *> On exit, if UPLO = 'U', the upper triangle of A is
72: *> overwritten with the upper triangle of the product U * U**T;
73: *> if UPLO = 'L', the lower triangle of A is overwritten with
74: *> the lower triangle of the product L**T * L.
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The leading dimension of the array A. LDA >= max(1,N).
81: *> \endverbatim
82: *>
83: *> \param[out] INFO
84: *> \verbatim
85: *> INFO is INTEGER
86: *> = 0: successful exit
87: *> < 0: if INFO = -k, the k-th argument had an illegal value
88: *> \endverbatim
89: *
90: * Authors:
91: * ========
92: *
1.16 bertrand 93: *> \author Univ. of Tennessee
94: *> \author Univ. of California Berkeley
95: *> \author Univ. of Colorado Denver
96: *> \author NAG Ltd.
1.9 bertrand 97: *
1.16 bertrand 98: *> \date December 2016
1.9 bertrand 99: *
100: *> \ingroup doubleOTHERauxiliary
101: *
102: * =====================================================================
1.1 bertrand 103: SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
104: *
1.16 bertrand 105: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 106: * -- LAPACK is a software package provided by Univ. of Tennessee, --
107: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.16 bertrand 108: * December 2016
1.1 bertrand 109: *
110: * .. Scalar Arguments ..
111: CHARACTER UPLO
112: INTEGER INFO, LDA, N
113: * ..
114: * .. Array Arguments ..
115: DOUBLE PRECISION A( LDA, * )
116: * ..
117: *
118: * =====================================================================
119: *
120: * .. Parameters ..
121: DOUBLE PRECISION ONE
122: PARAMETER ( ONE = 1.0D+0 )
123: * ..
124: * .. Local Scalars ..
125: LOGICAL UPPER
126: INTEGER I, IB, NB
127: * ..
128: * .. External Functions ..
129: LOGICAL LSAME
130: INTEGER ILAENV
131: EXTERNAL LSAME, ILAENV
132: * ..
133: * .. External Subroutines ..
134: EXTERNAL DGEMM, DLAUU2, DSYRK, DTRMM, XERBLA
135: * ..
136: * .. Intrinsic Functions ..
137: INTRINSIC MAX, MIN
138: * ..
139: * .. Executable Statements ..
140: *
141: * Test the input parameters.
142: *
143: INFO = 0
144: UPPER = LSAME( UPLO, 'U' )
145: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
146: INFO = -1
147: ELSE IF( N.LT.0 ) THEN
148: INFO = -2
149: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
150: INFO = -4
151: END IF
152: IF( INFO.NE.0 ) THEN
153: CALL XERBLA( 'DLAUUM', -INFO )
154: RETURN
155: END IF
156: *
157: * Quick return if possible
158: *
159: IF( N.EQ.0 )
160: $ RETURN
161: *
162: * Determine the block size for this environment.
163: *
164: NB = ILAENV( 1, 'DLAUUM', UPLO, N, -1, -1, -1 )
165: *
166: IF( NB.LE.1 .OR. NB.GE.N ) THEN
167: *
168: * Use unblocked code
169: *
170: CALL DLAUU2( UPLO, N, A, LDA, INFO )
171: ELSE
172: *
173: * Use blocked code
174: *
175: IF( UPPER ) THEN
176: *
1.8 bertrand 177: * Compute the product U * U**T.
1.1 bertrand 178: *
179: DO 10 I = 1, N, NB
180: IB = MIN( NB, N-I+1 )
181: CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Non-unit',
182: $ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
183: $ LDA )
184: CALL DLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
185: IF( I+IB.LE.N ) THEN
186: CALL DGEMM( 'No transpose', 'Transpose', I-1, IB,
187: $ N-I-IB+1, ONE, A( 1, I+IB ), LDA,
188: $ A( I, I+IB ), LDA, ONE, A( 1, I ), LDA )
189: CALL DSYRK( 'Upper', 'No transpose', IB, N-I-IB+1,
190: $ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
191: $ LDA )
192: END IF
193: 10 CONTINUE
194: ELSE
195: *
1.8 bertrand 196: * Compute the product L**T * L.
1.1 bertrand 197: *
198: DO 20 I = 1, N, NB
199: IB = MIN( NB, N-I+1 )
200: CALL DTRMM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB,
201: $ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
202: CALL DLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
203: IF( I+IB.LE.N ) THEN
204: CALL DGEMM( 'Transpose', 'No transpose', IB, I-1,
205: $ N-I-IB+1, ONE, A( I+IB, I ), LDA,
206: $ A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA )
207: CALL DSYRK( 'Lower', 'Transpose', IB, N-I-IB+1, ONE,
208: $ A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
209: END IF
210: 20 CONTINUE
211: END IF
212: END IF
213: *
214: RETURN
215: *
216: * End of DLAUUM
217: *
218: END
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