LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dlauum.f
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1*> \brief \b DLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INFO, LDA, N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION A( LDA, * )
29* ..
30*
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*
93*> \author Univ. of Tennessee
94*> \author Univ. of California Berkeley
95*> \author Univ. of Colorado Denver
96*> \author NAG Ltd.
97*
98*> \ingroup doubleOTHERauxiliary
99*
100* =====================================================================
101 SUBROUTINE dlauum( UPLO, N, A, LDA, INFO )
102*
103* -- LAPACK auxiliary routine --
104* -- LAPACK is a software package provided by Univ. of Tennessee, --
105* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106*
107* .. Scalar Arguments ..
108 CHARACTER UPLO
109 INTEGER INFO, LDA, N
110* ..
111* .. Array Arguments ..
112 DOUBLE PRECISION A( LDA, * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 DOUBLE PRECISION ONE
119 parameter( one = 1.0d+0 )
120* ..
121* .. Local Scalars ..
122 LOGICAL UPPER
123 INTEGER I, IB, NB
124* ..
125* .. External Functions ..
126 LOGICAL LSAME
127 INTEGER ILAENV
128 EXTERNAL lsame, ilaenv
129* ..
130* .. External Subroutines ..
131 EXTERNAL dgemm, dlauu2, dsyrk, dtrmm, xerbla
132* ..
133* .. Intrinsic Functions ..
134 INTRINSIC max, min
135* ..
136* .. Executable Statements ..
137*
138* Test the input parameters.
139*
140 info = 0
141 upper = lsame( uplo, 'U' )
142 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
143 info = -1
144 ELSE IF( n.LT.0 ) THEN
145 info = -2
146 ELSE IF( lda.LT.max( 1, n ) ) THEN
147 info = -4
148 END IF
149 IF( info.NE.0 ) THEN
150 CALL xerbla( 'DLAUUM', -info )
151 RETURN
152 END IF
153*
154* Quick return if possible
155*
156 IF( n.EQ.0 )
157 \$ RETURN
158*
159* Determine the block size for this environment.
160*
161 nb = ilaenv( 1, 'DLAUUM', uplo, n, -1, -1, -1 )
162*
163 IF( nb.LE.1 .OR. nb.GE.n ) THEN
164*
165* Use unblocked code
166*
167 CALL dlauu2( uplo, n, a, lda, info )
168 ELSE
169*
170* Use blocked code
171*
172 IF( upper ) THEN
173*
174* Compute the product U * U**T.
175*
176 DO 10 i = 1, n, nb
177 ib = min( nb, n-i+1 )
178 CALL dtrmm( 'Right', 'Upper', 'Transpose', 'Non-unit',
179 \$ i-1, ib, one, a( i, i ), lda, a( 1, i ),
180 \$ lda )
181 CALL dlauu2( 'Upper', ib, a( i, i ), lda, info )
182 IF( i+ib.LE.n ) THEN
183 CALL dgemm( 'No transpose', 'Transpose', i-1, ib,
184 \$ n-i-ib+1, one, a( 1, i+ib ), lda,
185 \$ a( i, i+ib ), lda, one, a( 1, i ), lda )
186 CALL dsyrk( 'Upper', 'No transpose', ib, n-i-ib+1,
187 \$ one, a( i, i+ib ), lda, one, a( i, i ),
188 \$ lda )
189 END IF
190 10 CONTINUE
191 ELSE
192*
193* Compute the product L**T * L.
194*
195 DO 20 i = 1, n, nb
196 ib = min( nb, n-i+1 )
197 CALL dtrmm( 'Left', 'Lower', 'Transpose', 'Non-unit', ib,
198 \$ i-1, one, a( i, i ), lda, a( i, 1 ), lda )
199 CALL dlauu2( 'Lower', ib, a( i, i ), lda, info )
200 IF( i+ib.LE.n ) THEN
201 CALL dgemm( 'Transpose', 'No transpose', ib, i-1,
202 \$ n-i-ib+1, one, a( i+ib, i ), lda,
203 \$ a( i+ib, 1 ), lda, one, a( i, 1 ), lda )
204 CALL dsyrk( 'Lower', 'Transpose', ib, n-i-ib+1, one,
205 \$ a( i+ib, i ), lda, one, a( i, i ), lda )
206 END IF
207 20 CONTINUE
208 END IF
209 END IF
210*
211 RETURN
212*
213* End of DLAUUM
214*
215 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:177
subroutine dlauum(UPLO, N, A, LDA, INFO)
DLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked...
Definition: dlauum.f:102
subroutine dlauu2(UPLO, N, A, LDA, INFO)
DLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblock...
Definition: dlauu2.f:102