SUBROUTINE ZLAUUM( UPLO, N, A, LDA, INFO ) * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * Purpose * ======= * * ZLAUUM 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) COMPLEX*16 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 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, IB, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMM, ZHERK, ZLAUU2, ZTRMM * .. * .. 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( 'ZLAUUM', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'ZLAUUM', UPLO, N, -1, -1, -1 ) * IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL ZLAUU2( 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 ZTRMM( 'Right', 'Upper', 'Conjugate transpose', \$ 'Non-unit', I-1, IB, CONE, A( I, I ), LDA, \$ A( 1, I ), LDA ) CALL ZLAUU2( 'Upper', IB, A( I, I ), LDA, INFO ) IF( I+IB.LE.N ) THEN CALL ZGEMM( 'No transpose', 'Conjugate transpose', \$ I-1, IB, N-I-IB+1, CONE, A( 1, I+IB ), \$ LDA, A( I, I+IB ), LDA, CONE, A( 1, I ), \$ LDA ) CALL ZHERK( '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 ZTRMM( 'Left', 'Lower', 'Conjugate transpose', \$ 'Non-unit', IB, I-1, CONE, A( I, I ), LDA, \$ A( I, 1 ), LDA ) CALL ZLAUU2( 'Lower', IB, A( I, I ), LDA, INFO ) IF( I+IB.LE.N ) THEN CALL ZGEMM( 'Conjugate transpose', 'No transpose', IB, \$ I-1, N-I-IB+1, CONE, A( I+IB, I ), LDA, \$ A( I+IB, 1 ), LDA, CONE, A( I, 1 ), LDA ) CALL ZHERK( 'Lower', 'Conjugate 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 ZLAUUM * END