Annotation of rpl/lapack/lapack/dlaqge.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
! 2: $ EQUED )
! 3: *
! 4: * -- LAPACK auxiliary routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER EQUED
! 11: INTEGER LDA, M, N
! 12: DOUBLE PRECISION AMAX, COLCND, ROWCND
! 13: * ..
! 14: * .. Array Arguments ..
! 15: DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DLAQGE equilibrates a general M by N matrix A using the row and
! 22: * column scaling factors in the vectors R and C.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * M (input) INTEGER
! 28: * The number of rows of the matrix A. M >= 0.
! 29: *
! 30: * N (input) INTEGER
! 31: * The number of columns of the matrix A. N >= 0.
! 32: *
! 33: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 34: * On entry, the M by N matrix A.
! 35: * On exit, the equilibrated matrix. See EQUED for the form of
! 36: * the equilibrated matrix.
! 37: *
! 38: * LDA (input) INTEGER
! 39: * The leading dimension of the array A. LDA >= max(M,1).
! 40: *
! 41: * R (input) DOUBLE PRECISION array, dimension (M)
! 42: * The row scale factors for A.
! 43: *
! 44: * C (input) DOUBLE PRECISION array, dimension (N)
! 45: * The column scale factors for A.
! 46: *
! 47: * ROWCND (input) DOUBLE PRECISION
! 48: * Ratio of the smallest R(i) to the largest R(i).
! 49: *
! 50: * COLCND (input) DOUBLE PRECISION
! 51: * Ratio of the smallest C(i) to the largest C(i).
! 52: *
! 53: * AMAX (input) DOUBLE PRECISION
! 54: * Absolute value of largest matrix entry.
! 55: *
! 56: * EQUED (output) CHARACTER*1
! 57: * Specifies the form of equilibration that was done.
! 58: * = 'N': No equilibration
! 59: * = 'R': Row equilibration, i.e., A has been premultiplied by
! 60: * diag(R).
! 61: * = 'C': Column equilibration, i.e., A has been postmultiplied
! 62: * by diag(C).
! 63: * = 'B': Both row and column equilibration, i.e., A has been
! 64: * replaced by diag(R) * A * diag(C).
! 65: *
! 66: * Internal Parameters
! 67: * ===================
! 68: *
! 69: * THRESH is a threshold value used to decide if row or column scaling
! 70: * should be done based on the ratio of the row or column scaling
! 71: * factors. If ROWCND < THRESH, row scaling is done, and if
! 72: * COLCND < THRESH, column scaling is done.
! 73: *
! 74: * LARGE and SMALL are threshold values used to decide if row scaling
! 75: * should be done based on the absolute size of the largest matrix
! 76: * element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
! 77: *
! 78: * =====================================================================
! 79: *
! 80: * .. Parameters ..
! 81: DOUBLE PRECISION ONE, THRESH
! 82: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
! 83: * ..
! 84: * .. Local Scalars ..
! 85: INTEGER I, J
! 86: DOUBLE PRECISION CJ, LARGE, SMALL
! 87: * ..
! 88: * .. External Functions ..
! 89: DOUBLE PRECISION DLAMCH
! 90: EXTERNAL DLAMCH
! 91: * ..
! 92: * .. Executable Statements ..
! 93: *
! 94: * Quick return if possible
! 95: *
! 96: IF( M.LE.0 .OR. N.LE.0 ) THEN
! 97: EQUED = 'N'
! 98: RETURN
! 99: END IF
! 100: *
! 101: * Initialize LARGE and SMALL.
! 102: *
! 103: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
! 104: LARGE = ONE / SMALL
! 105: *
! 106: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
! 107: $ THEN
! 108: *
! 109: * No row scaling
! 110: *
! 111: IF( COLCND.GE.THRESH ) THEN
! 112: *
! 113: * No column scaling
! 114: *
! 115: EQUED = 'N'
! 116: ELSE
! 117: *
! 118: * Column scaling
! 119: *
! 120: DO 20 J = 1, N
! 121: CJ = C( J )
! 122: DO 10 I = 1, M
! 123: A( I, J ) = CJ*A( I, J )
! 124: 10 CONTINUE
! 125: 20 CONTINUE
! 126: EQUED = 'C'
! 127: END IF
! 128: ELSE IF( COLCND.GE.THRESH ) THEN
! 129: *
! 130: * Row scaling, no column scaling
! 131: *
! 132: DO 40 J = 1, N
! 133: DO 30 I = 1, M
! 134: A( I, J ) = R( I )*A( I, J )
! 135: 30 CONTINUE
! 136: 40 CONTINUE
! 137: EQUED = 'R'
! 138: ELSE
! 139: *
! 140: * Row and column scaling
! 141: *
! 142: DO 60 J = 1, N
! 143: CJ = C( J )
! 144: DO 50 I = 1, M
! 145: A( I, J ) = CJ*R( I )*A( I, J )
! 146: 50 CONTINUE
! 147: 60 CONTINUE
! 148: EQUED = 'B'
! 149: END IF
! 150: *
! 151: RETURN
! 152: *
! 153: * End of DLAQGE
! 154: *
! 155: END
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