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! 57: * = 'Y': Equilibration was done, i.e., A has been replaced by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