Annotation of rpl/lapack/lapack/zlaqhb.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, 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 KD, LDAB, N
! 11: DOUBLE PRECISION AMAX, SCOND
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION S( * )
! 15: COMPLEX*16 AB( LDAB, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLAQHB equilibrates a symmetric band matrix A using the scaling
! 22: * factors 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: * symmetric 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: * KD (input) INTEGER
! 37: * The number of super-diagonals of the matrix A if UPLO = 'U',
! 38: * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
! 39: *
! 40: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
! 41: * On entry, the upper or lower triangle of the symmetric band
! 42: * matrix A, stored in the first KD+1 rows of the array. The
! 43: * j-th column of A is stored in the j-th column of the array AB
! 44: * as follows:
! 45: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 46: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 47: *
! 48: * On exit, if INFO = 0, the triangular factor U or L from the
! 49: * Cholesky factorization A = U'*U or A = L*L' of the band
! 50: * matrix A, in the same storage format as A.
! 51: *
! 52: * LDAB (input) INTEGER
! 53: * The leading dimension of the array AB. LDAB >= KD+1.
! 54: *
! 55: * S (output) DOUBLE PRECISION array, dimension (N)
! 56: * The scale factors for A.
! 57: *
! 58: * SCOND (input) DOUBLE PRECISION
! 59: * Ratio of the smallest S(i) to the largest S(i).
! 60: *
! 61: * AMAX (input) DOUBLE PRECISION
! 62: * Absolute value of largest matrix entry.
! 63: *
! 64: * EQUED (output) CHARACTER*1
! 65: * Specifies whether or not equilibration was done.
! 66: * = 'N': No equilibration.
! 67: * = 'Y': Equilibration was done, i.e., A has been replaced by
! 68: * diag(S) * A * diag(S).
! 69: *
! 70: * Internal Parameters
! 71: * ===================
! 72: *
! 73: * THRESH is a threshold value used to decide if scaling should be done
! 74: * based on the ratio of the scaling factors. If SCOND < THRESH,
! 75: * scaling is done.
! 76: *
! 77: * LARGE and SMALL are threshold values used to decide if scaling should
! 78: * be done based on the absolute size of the largest matrix element.
! 79: * If AMAX > LARGE or AMAX < SMALL, scaling is done.
! 80: *
! 81: * =====================================================================
! 82: *
! 83: * .. Parameters ..
! 84: DOUBLE PRECISION ONE, THRESH
! 85: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
! 86: * ..
! 87: * .. Local Scalars ..
! 88: INTEGER I, J
! 89: DOUBLE PRECISION CJ, LARGE, SMALL
! 90: * ..
! 91: * .. External Functions ..
! 92: LOGICAL LSAME
! 93: DOUBLE PRECISION DLAMCH
! 94: EXTERNAL LSAME, DLAMCH
! 95: * ..
! 96: * .. Intrinsic Functions ..
! 97: INTRINSIC DBLE, MAX, MIN
! 98: * ..
! 99: * .. Executable Statements ..
! 100: *
! 101: * Quick return if possible
! 102: *
! 103: IF( N.LE.0 ) THEN
! 104: EQUED = 'N'
! 105: RETURN
! 106: END IF
! 107: *
! 108: * Initialize LARGE and SMALL.
! 109: *
! 110: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
! 111: LARGE = ONE / SMALL
! 112: *
! 113: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
! 114: *
! 115: * No equilibration
! 116: *
! 117: EQUED = 'N'
! 118: ELSE
! 119: *
! 120: * Replace A by diag(S) * A * diag(S).
! 121: *
! 122: IF( LSAME( UPLO, 'U' ) ) THEN
! 123: *
! 124: * Upper triangle of A is stored in band format.
! 125: *
! 126: DO 20 J = 1, N
! 127: CJ = S( J )
! 128: DO 10 I = MAX( 1, J-KD ), J - 1
! 129: AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
! 130: 10 CONTINUE
! 131: AB( KD+1, J ) = CJ*CJ*DBLE( AB( KD+1, J ) )
! 132: 20 CONTINUE
! 133: ELSE
! 134: *
! 135: * Lower triangle of A is stored.
! 136: *
! 137: DO 40 J = 1, N
! 138: CJ = S( J )
! 139: AB( 1, J ) = CJ*CJ*DBLE( AB( 1, J ) )
! 140: DO 30 I = J + 1, MIN( N, J+KD )
! 141: AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
! 142: 30 CONTINUE
! 143: 40 CONTINUE
! 144: END IF
! 145: EQUED = 'Y'
! 146: END IF
! 147: *
! 148: RETURN
! 149: *
! 150: * End of ZLAQHB
! 151: *
! 152: END
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