LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ clauum()

subroutine clauum ( character  UPLO,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
integer  INFO 
)

CLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

Download CLAUUM + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CLAUUM computes the product U * U**H or L**H * L, where the triangular
 factor U or L is stored in the upper or lower triangular part of
 the array A.

 If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
 overwriting the factor U in A.
 If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
 overwriting the factor L in A.

 This is the blocked form of the algorithm, calling Level 3 BLAS.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the triangular factor stored in the array A
          is upper or lower triangular:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The order of the triangular factor U or L.  N >= 0.
[in,out]A
          A is COMPLEX array, dimension (LDA,N)
          On entry, the triangular factor U or L.
          On exit, if UPLO = 'U', the upper triangle of A is
          overwritten with the upper triangle of the product U * U**H;
          if UPLO = 'L', the lower triangle of A is overwritten with
          the lower triangle of the product L**H * L.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 101 of file clauum.f.

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 COMPLEX A( LDA, * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 REAL ONE
119 parameter( one = 1.0e+0 )
120 COMPLEX CONE
121 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
122* ..
123* .. Local Scalars ..
124 LOGICAL UPPER
125 INTEGER I, IB, NB
126* ..
127* .. External Functions ..
128 LOGICAL LSAME
129 INTEGER ILAENV
130 EXTERNAL lsame, ilaenv
131* ..
132* .. External Subroutines ..
133 EXTERNAL cgemm, cherk, clauu2, ctrmm, xerbla
134* ..
135* .. Intrinsic Functions ..
136 INTRINSIC max, min
137* ..
138* .. Executable Statements ..
139*
140* Test the input parameters.
141*
142 info = 0
143 upper = lsame( uplo, 'U' )
144 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
145 info = -1
146 ELSE IF( n.LT.0 ) THEN
147 info = -2
148 ELSE IF( lda.LT.max( 1, n ) ) THEN
149 info = -4
150 END IF
151 IF( info.NE.0 ) THEN
152 CALL xerbla( 'CLAUUM', -info )
153 RETURN
154 END IF
155*
156* Quick return if possible
157*
158 IF( n.EQ.0 )
159 $ RETURN
160*
161* Determine the block size for this environment.
162*
163 nb = ilaenv( 1, 'CLAUUM', uplo, n, -1, -1, -1 )
164*
165 IF( nb.LE.1 .OR. nb.GE.n ) THEN
166*
167* Use unblocked code
168*
169 CALL clauu2( uplo, n, a, lda, info )
170 ELSE
171*
172* Use blocked code
173*
174 IF( upper ) THEN
175*
176* Compute the product U * U**H.
177*
178 DO 10 i = 1, n, nb
179 ib = min( nb, n-i+1 )
180 CALL ctrmm( 'Right', 'Upper', 'Conjugate transpose',
181 $ 'Non-unit', i-1, ib, cone, a( i, i ), lda,
182 $ a( 1, i ), lda )
183 CALL clauu2( 'Upper', ib, a( i, i ), lda, info )
184 IF( i+ib.LE.n ) THEN
185 CALL cgemm( 'No transpose', 'Conjugate transpose',
186 $ i-1, ib, n-i-ib+1, cone, a( 1, i+ib ),
187 $ lda, a( i, i+ib ), lda, cone, a( 1, i ),
188 $ lda )
189 CALL cherk( '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*
196* Compute the product L**H * L.
197*
198 DO 20 i = 1, n, nb
199 ib = min( nb, n-i+1 )
200 CALL ctrmm( 'Left', 'Lower', 'Conjugate transpose',
201 $ 'Non-unit', ib, i-1, cone, a( i, i ), lda,
202 $ a( i, 1 ), lda )
203 CALL clauu2( 'Lower', ib, a( i, i ), lda, info )
204 IF( i+ib.LE.n ) THEN
205 CALL cgemm( 'Conjugate transpose', 'No transpose', ib,
206 $ i-1, n-i-ib+1, cone, a( i+ib, i ), lda,
207 $ a( i+ib, 1 ), lda, cone, a( i, 1 ), lda )
208 CALL cherk( 'Lower', 'Conjugate transpose', ib,
209 $ n-i-ib+1, one, a( i+ib, i ), lda, one,
210 $ a( i, i ), lda )
211 END IF
212 20 CONTINUE
213 END IF
214 END IF
215*
216 RETURN
217*
218* End of CLAUUM
219*
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine ctrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRMM
Definition: ctrmm.f:177
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
subroutine clauu2(UPLO, N, A, LDA, INFO)
CLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblock...
Definition: clauu2.f:102
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