Annotation of rpl/lapack/lapack/zlaqhe.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER EQUED, UPLO
! 10: INTEGER LDA, N
! 11: DOUBLE PRECISION AMAX, SCOND
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION S( * )
! 15: COMPLEX*16 A( LDA, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
! 22: * in the vector S.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * UPLO (input) CHARACTER*1
! 28: * Specifies whether the upper or lower triangular part of the
! 29: * Hermitian matrix A is stored.
! 30: * = 'U': Upper triangular
! 31: * = 'L': Lower triangular
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A. N >= 0.
! 35: *
! 36: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 37: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 38: * n by n upper triangular part of A contains the upper
! 39: * triangular part of the matrix A, and the strictly lower
! 40: * triangular part of A is not referenced. If UPLO = 'L', the
! 41: * leading n by n lower triangular part of A contains the lower
! 42: * triangular part of the matrix A, and the strictly upper
! 43: * triangular part of A is not referenced.
! 44: *
! 45: * On exit, if EQUED = 'Y', the equilibrated matrix:
! 46: * diag(S) * A * diag(S).
! 47: *
! 48: * LDA (input) INTEGER
! 49: * The leading dimension of the array A. LDA >= max(N,1).
! 50: *
! 51: * S (input) DOUBLE PRECISION array, dimension (N)
! 52: * The scale factors for A.
! 53: *
! 54: * SCOND (input) DOUBLE PRECISION
! 55: * Ratio of the smallest S(i) to the largest S(i).
! 56: *
! 57: * AMAX (input) DOUBLE PRECISION
! 58: * Absolute value of largest matrix entry.
! 59: *
! 60: * EQUED (output) CHARACTER*1
! 61: * Specifies whether or not equilibration was done.
! 62: * = 'N': No equilibration.
! 63: * = 'Y': Equilibration was done, i.e., A has been replaced by
! 64: * diag(S) * A * diag(S).
! 65: *
! 66: * Internal Parameters
! 67: * ===================
! 68: *
! 69: * THRESH is a threshold value used to decide if scaling should be done
! 70: * based on the ratio of the scaling factors. If SCOND < THRESH,
! 71: * scaling is done.
! 72: *
! 73: * LARGE and SMALL are threshold values used to decide if scaling should
! 74: * be done based on the absolute size of the largest matrix element.
! 75: * If AMAX > LARGE or AMAX < SMALL, scaling is done.
! 76: *
! 77: * =====================================================================
! 78: *
! 79: * .. Parameters ..
! 80: DOUBLE PRECISION ONE, THRESH
! 81: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
! 82: * ..
! 83: * .. Local Scalars ..
! 84: INTEGER I, J
! 85: DOUBLE PRECISION CJ, LARGE, SMALL
! 86: * ..
! 87: * .. External Functions ..
! 88: LOGICAL LSAME
! 89: DOUBLE PRECISION DLAMCH
! 90: EXTERNAL LSAME, DLAMCH
! 91: * ..
! 92: * .. Intrinsic Functions ..
! 93: INTRINSIC DBLE
! 94: * ..
! 95: * .. Executable Statements ..
! 96: *
! 97: * Quick return if possible
! 98: *
! 99: IF( N.LE.0 ) THEN
! 100: EQUED = 'N'
! 101: RETURN
! 102: END IF
! 103: *
! 104: * Initialize LARGE and SMALL.
! 105: *
! 106: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
! 107: LARGE = ONE / SMALL
! 108: *
! 109: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
! 110: *
! 111: * No equilibration
! 112: *
! 113: EQUED = 'N'
! 114: ELSE
! 115: *
! 116: * Replace A by diag(S) * A * diag(S).
! 117: *
! 118: IF( LSAME( UPLO, 'U' ) ) THEN
! 119: *
! 120: * Upper triangle of A is stored.
! 121: *
! 122: DO 20 J = 1, N
! 123: CJ = S( J )
! 124: DO 10 I = 1, J - 1
! 125: A( I, J ) = CJ*S( I )*A( I, J )
! 126: 10 CONTINUE
! 127: A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
! 128: 20 CONTINUE
! 129: ELSE
! 130: *
! 131: * Lower triangle of A is stored.
! 132: *
! 133: DO 40 J = 1, N
! 134: CJ = S( J )
! 135: A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
! 136: DO 30 I = J + 1, N
! 137: A( I, J ) = CJ*S( I )*A( I, J )
! 138: 30 CONTINUE
! 139: 40 CONTINUE
! 140: END IF
! 141: EQUED = 'Y'
! 142: END IF
! 143: *
! 144: RETURN
! 145: *
! 146: * End of ZLAQHE
! 147: *
! 148: END
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