LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dlauum()

 subroutine dlauum ( character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, integer INFO )

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

Purpose:
``` DLAUUM computes the product U * U**T or L**T * 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 DOUBLE PRECISION 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**T; if UPLO = 'L', the lower triangle of A is overwritten with the lower triangle of the product L**T * 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```

Definition at line 101 of file dlauum.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 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*
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 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 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
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