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SUBROUTINE <a name="DLAUUM.1"></a><a href="dlauum.f.html#DLAUUM.1">DLAUUM</a>( UPLO, N, A, LDA, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INFO, LDA, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION A( LDA, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DLAUUM.18"></a><a href="dlauum.f.html#DLAUUM.1">DLAUUM</a> computes the product U * U' or L' * L, where the triangular
</span><span class="comment">*</span><span class="comment"> factor U or L is stored in the upper or lower triangular part of
</span><span class="comment">*</span><span class="comment"> the array A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
</span><span class="comment">*</span><span class="comment"> overwriting the factor U in A.
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
</span><span class="comment">*</span><span class="comment"> overwriting the factor L in A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This is the blocked form of the algorithm, calling Level 3 BLAS.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether the triangular factor stored in the array A
</span><span class="comment">*</span><span class="comment"> is upper or lower triangular:
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the triangular factor U or L. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the triangular factor U or L.
</span><span class="comment">*</span><span class="comment"> On exit, if UPLO = 'U', the upper triangle of A is
</span><span class="comment">*</span><span class="comment"> overwritten with the upper triangle of the product U * U';
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', the lower triangle of A is overwritten with
</span><span class="comment">*</span><span class="comment"> the lower triangle of the product L' * L.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -k, the k-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
INTEGER I, IB, NB
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.66"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER <a name="ILAENV.67"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL <a name="LSAME.68"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.68"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL DGEMM, <a name="DLAUU2.71"></a><a href="dlauu2.f.html#DLAUU2.1">DLAUU2</a>, DSYRK, DTRMM, <a name="XERBLA.71"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
UPPER = <a name="LSAME.81"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.82"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) 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 <a name="XERBLA.90"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DLAUUM.90"></a><a href="dlauum.f.html#DLAUUM.1">DLAUUM</a>'</span>, -INFO )
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 )
$ RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine the block size for this environment.
</span><span class="comment">*</span><span class="comment">
</span> NB = <a name="ILAENV.101"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DLAUUM.101"></a><a href="dlauum.f.html#DLAUUM.1">DLAUUM</a>'</span>, UPLO, N, -1, -1, -1 )
<span class="comment">*</span><span class="comment">
</span> IF( NB.LE.1 .OR. NB.GE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Use unblocked code
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="DLAUU2.107"></a><a href="dlauu2.f.html#DLAUU2.1">DLAUU2</a>( UPLO, N, A, LDA, INFO )
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Use blocked code
</span><span class="comment">*</span><span class="comment">
</span> IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the product U * U'.
</span><span class="comment">*</span><span class="comment">
</span> DO 10 I = 1, N, NB
IB = MIN( NB, N-I+1 )
CALL DTRMM( <span class="string">'Right'</span>, <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>,
$ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
$ LDA )
CALL <a name="DLAUU2.121"></a><a href="dlauu2.f.html#DLAUU2.1">DLAUU2</a>( <span class="string">'Upper'</span>, IB, A( I, I ), LDA, INFO )
IF( I+IB.LE.N ) THEN
CALL DGEMM( <span class="string">'No transpose'</span>, <span class="string">'Transpose'</span>, 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( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, IB, N-I-IB+1,
$ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
$ LDA )
END IF
10 CONTINUE
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the product L' * L.
</span><span class="comment">*</span><span class="comment">
</span> DO 20 I = 1, N, NB
IB = MIN( NB, N-I+1 )
CALL DTRMM( <span class="string">'Left'</span>, <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, IB,
$ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
CALL <a name="DLAUU2.139"></a><a href="dlauu2.f.html#DLAUU2.1">DLAUU2</a>( <span class="string">'Lower'</span>, IB, A( I, I ), LDA, INFO )
IF( I+IB.LE.N ) THEN
CALL DGEMM( <span class="string">'Transpose'</span>, <span class="string">'No transpose'</span>, 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( <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, IB, N-I-IB+1, ONE,
$ A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
END IF
20 CONTINUE
END IF
END IF
<span class="comment">*</span><span class="comment">
</span> RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="DLAUUM.153"></a><a href="dlauum.f.html#DLAUUM.1">DLAUUM</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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