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SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* Purpose
* =======
*
* DLAUUM computes the product U * U' or L' * 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the triangular factor stored in the array A
* is upper or lower triangular:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The order of the triangular factor U or L. N >= 0.
*
* A (input/output) 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';
* if UPLO = 'L', the lower triangle of A is overwritten with
* the lower triangle of the product L' * L.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -k, the k-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IB, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DLAUU2, DSYRK, DTRMM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLAUUM', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine the block size for this environment.
*
NB = ILAENV( 1, 'DLAUUM', UPLO, N, -1, -1, -1 )
*
IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code
*
CALL DLAUU2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code
*
IF( UPPER ) THEN
*
* Compute the product U * U'.
*
DO 10 I = 1, N, NB
IB = MIN( NB, N-I+1 )
CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Non-unit',
$ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
$ LDA )
CALL DLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
IF( I+IB.LE.N ) THEN
CALL DGEMM( 'No transpose', 'Transpose', I-1, IB,
$ N-I-IB+1, ONE, A( 1, I+IB ), LDA,
$ A( I, I+IB ), LDA, ONE, A( 1, I ), LDA )
CALL DSYRK( 'Upper', 'No transpose', IB, N-I-IB+1,
$ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
$ LDA )
END IF
10 CONTINUE
ELSE
*
* Compute the product L' * L.
*
DO 20 I = 1, N, NB
IB = MIN( NB, N-I+1 )
CALL DTRMM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB,
$ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
CALL DLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
IF( I+IB.LE.N ) THEN
CALL DGEMM( 'Transpose', 'No transpose', IB, I-1,
$ N-I-IB+1, ONE, A( I+IB, I ), LDA,
$ A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA )
CALL DSYRK( 'Lower', 'Transpose', IB, N-I-IB+1, ONE,
$ A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
END IF
20 CONTINUE
END IF
END IF
*
RETURN
*
* End of DLAUUM
*
END
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