LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
slauum.f
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1 *> \brief \b SLAUUM 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 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLAUUM( UPLO, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * REAL A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> SLAUUM 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 REAL 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 realOTHERauxiliary
99 *
100 * =====================================================================
101  SUBROUTINE slauum( 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  REAL A( LDA, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Parameters ..
118  REAL ONE
119  parameter( one = 1.0e+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 sgemm, slauu2, ssyrk, strmm, 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( 'SLAUUM', -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, 'SLAUUM', uplo, n, -1, -1, -1 )
162 *
163  IF( nb.LE.1 .OR. nb.GE.n ) THEN
164 *
165 * Use unblocked code
166 *
167  CALL slauu2( 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 strmm( 'Right', 'Upper', 'Transpose', 'Non-unit',
179  $ i-1, ib, one, a( i, i ), lda, a( 1, i ),
180  $ lda )
181  CALL slauu2( 'Upper', ib, a( i, i ), lda, info )
182  IF( i+ib.LE.n ) THEN
183  CALL sgemm( '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 ssyrk( '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 strmm( 'Left', 'Lower', 'Transpose', 'Non-unit', ib,
198  $ i-1, one, a( i, i ), lda, a( i, 1 ), lda )
199  CALL slauu2( 'Lower', ib, a( i, i ), lda, info )
200  IF( i+ib.LE.n ) THEN
201  CALL sgemm( '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 ssyrk( '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 SLAUUM
214 *
215  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slauu2(UPLO, N, A, LDA, INFO)
SLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblock...
Definition: slauu2.f:102
subroutine slauum(UPLO, N, A, LDA, INFO)
SLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked...
Definition: slauum.f:102
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
Definition: strmm.f:177
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187