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Diffstat (limited to 'SRC/zlaqhe.f')
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diff --git a/SRC/zlaqhe.f b/SRC/zlaqhe.f new file mode 100644 index 00000000..c508032b --- /dev/null +++ b/SRC/zlaqhe.f @@ -0,0 +1,147 @@ + SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER EQUED, UPLO + INTEGER LDA, N + DOUBLE PRECISION AMAX, SCOND +* .. +* .. Array Arguments .. + DOUBLE PRECISION S( * ) + COMPLEX*16 A( LDA, * ) +* .. +* +* Purpose +* ======= +* +* ZLAQHE equilibrates a Hermitian matrix A using the scaling factors +* in the vector S. +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* Hermitian matrix A is stored. +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* A (input/output) COMPLEX*16 array, dimension (LDA,N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the leading +* n by n upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading n by n lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if EQUED = 'Y', the equilibrated matrix: +* diag(S) * A * diag(S). +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(N,1). +* +* S (input) DOUBLE PRECISION array, dimension (N) +* The scale factors for A. +* +* SCOND (input) DOUBLE PRECISION +* Ratio of the smallest S(i) to the largest S(i). +* +* AMAX (input) DOUBLE PRECISION +* Absolute value of largest matrix entry. +* +* EQUED (output) CHARACTER*1 +* Specifies whether or not equilibration was done. +* = 'N': No equilibration. +* = 'Y': Equilibration was done, i.e., A has been replaced by +* diag(S) * A * diag(S). +* +* Internal Parameters +* =================== +* +* THRESH is a threshold value used to decide if scaling should be done +* based on the ratio of the scaling factors. If SCOND < THRESH, +* scaling is done. +* +* LARGE and SMALL are threshold values used to decide if scaling should +* be done based on the absolute size of the largest matrix element. +* If AMAX > LARGE or AMAX < SMALL, scaling is done. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, THRESH + PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J + DOUBLE PRECISION CJ, LARGE, SMALL +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DLAMCH + EXTERNAL LSAME, DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.LE.0 ) THEN + EQUED = 'N' + RETURN + END IF +* +* Initialize LARGE and SMALL. +* + SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) + LARGE = ONE / SMALL +* + IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN +* +* No equilibration +* + EQUED = 'N' + ELSE +* +* Replace A by diag(S) * A * diag(S). +* + IF( LSAME( UPLO, 'U' ) ) THEN +* +* Upper triangle of A is stored. +* + DO 20 J = 1, N + CJ = S( J ) + DO 10 I = 1, J - 1 + A( I, J ) = CJ*S( I )*A( I, J ) + 10 CONTINUE + A( J, J ) = CJ*CJ*DBLE( A( J, J ) ) + 20 CONTINUE + ELSE +* +* Lower triangle of A is stored. +* + DO 40 J = 1, N + CJ = S( J ) + A( J, J ) = CJ*CJ*DBLE( A( J, J ) ) + DO 30 I = J + 1, N + A( I, J ) = CJ*S( I )*A( I, J ) + 30 CONTINUE + 40 CONTINUE + END IF + EQUED = 'Y' + END IF +* + RETURN +* +* End of ZLAQHE +* + END |