Annotation of rpl/lapack/lapack/zlaqsp.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLAQSP( UPLO, N, AP, 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 N
! 11: DOUBLE PRECISION AMAX, SCOND
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION S( * )
! 15: COMPLEX*16 AP( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLAQSP equilibrates a symmetric 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: * 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: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 37: * On entry, the upper or lower triangle of the symmetric matrix
! 38: * A, packed columnwise in a linear array. The j-th column of A
! 39: * is stored in the array AP as follows:
! 40: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 41: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 42: *
! 43: * On exit, the equilibrated matrix: diag(S) * A * diag(S), in
! 44: * the same storage format as A.
! 45: *
! 46: * S (input) DOUBLE PRECISION array, dimension (N)
! 47: * The scale factors for A.
! 48: *
! 49: * SCOND (input) DOUBLE PRECISION
! 50: * Ratio of the smallest S(i) to the largest S(i).
! 51: *
! 52: * AMAX (input) DOUBLE PRECISION
! 53: * Absolute value of largest matrix entry.
! 54: *
! 55: * EQUED (output) CHARACTER*1
! 56: * Specifies whether or not equilibration was done.
! 57: * = 'N': No equilibration.
! 58: * = 'Y': Equilibration was done, i.e., A has been replaced by
! 59: * diag(S) * A * diag(S).
! 60: *
! 61: * Internal Parameters
! 62: * ===================
! 63: *
! 64: * THRESH is a threshold value used to decide if scaling should be done
! 65: * based on the ratio of the scaling factors. If SCOND < THRESH,
! 66: * scaling is done.
! 67: *
! 68: * LARGE and SMALL are threshold values used to decide if scaling should
! 69: * be done based on the absolute size of the largest matrix element.
! 70: * If AMAX > LARGE or AMAX < SMALL, scaling is done.
! 71: *
! 72: * =====================================================================
! 73: *
! 74: * .. Parameters ..
! 75: DOUBLE PRECISION ONE, THRESH
! 76: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
! 77: * ..
! 78: * .. Local Scalars ..
! 79: INTEGER I, J, JC
! 80: DOUBLE PRECISION CJ, LARGE, SMALL
! 81: * ..
! 82: * .. External Functions ..
! 83: LOGICAL LSAME
! 84: DOUBLE PRECISION DLAMCH
! 85: EXTERNAL LSAME, DLAMCH
! 86: * ..
! 87: * .. Executable Statements ..
! 88: *
! 89: * Quick return if possible
! 90: *
! 91: IF( N.LE.0 ) THEN
! 92: EQUED = 'N'
! 93: RETURN
! 94: END IF
! 95: *
! 96: * Initialize LARGE and SMALL.
! 97: *
! 98: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
! 99: LARGE = ONE / SMALL
! 100: *
! 101: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
! 102: *
! 103: * No equilibration
! 104: *
! 105: EQUED = 'N'
! 106: ELSE
! 107: *
! 108: * Replace A by diag(S) * A * diag(S).
! 109: *
! 110: IF( LSAME( UPLO, 'U' ) ) THEN
! 111: *
! 112: * Upper triangle of A is stored.
! 113: *
! 114: JC = 1
! 115: DO 20 J = 1, N
! 116: CJ = S( J )
! 117: DO 10 I = 1, J
! 118: AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
! 119: 10 CONTINUE
! 120: JC = JC + J
! 121: 20 CONTINUE
! 122: ELSE
! 123: *
! 124: * Lower triangle of A is stored.
! 125: *
! 126: JC = 1
! 127: DO 40 J = 1, N
! 128: CJ = S( J )
! 129: DO 30 I = J, N
! 130: AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
! 131: 30 CONTINUE
! 132: JC = JC + N - J + 1
! 133: 40 CONTINUE
! 134: END IF
! 135: EQUED = 'Y'
! 136: END IF
! 137: *
! 138: RETURN
! 139: *
! 140: * End of ZLAQSP
! 141: *
! 142: END
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