Annotation of rpl/lapack/lapack/dlaqgb.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 2: $ AMAX, 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 KL, KU, LDAB, M, N
! 12: DOUBLE PRECISION AMAX, COLCND, ROWCND
! 13: * ..
! 14: * .. Array Arguments ..
! 15: DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DLAQGB equilibrates a general M by N band matrix A with KL
! 22: * subdiagonals and KU superdiagonals using the row and scaling factors
! 23: * in the vectors R and C.
! 24: *
! 25: * Arguments
! 26: * =========
! 27: *
! 28: * M (input) INTEGER
! 29: * The number of rows of the matrix A. M >= 0.
! 30: *
! 31: * N (input) INTEGER
! 32: * The number of columns of the matrix A. N >= 0.
! 33: *
! 34: * KL (input) INTEGER
! 35: * The number of subdiagonals within the band of A. KL >= 0.
! 36: *
! 37: * KU (input) INTEGER
! 38: * The number of superdiagonals within the band of A. KU >= 0.
! 39: *
! 40: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
! 41: * On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
! 42: * The j-th column of A is stored in the j-th column of the
! 43: * array AB as follows:
! 44: * AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
! 45: *
! 46: * On exit, the equilibrated matrix, in the same storage format
! 47: * as A. See EQUED for the form of the equilibrated matrix.
! 48: *
! 49: * LDAB (input) INTEGER
! 50: * The leading dimension of the array AB. LDA >= KL+KU+1.
! 51: *
! 52: * R (input) DOUBLE PRECISION array, dimension (M)
! 53: * The row scale factors for A.
! 54: *
! 55: * C (input) DOUBLE PRECISION array, dimension (N)
! 56: * The column scale factors for A.
! 57: *
! 58: * ROWCND (input) DOUBLE PRECISION
! 59: * Ratio of the smallest R(i) to the largest R(i).
! 60: *
! 61: * COLCND (input) DOUBLE PRECISION
! 62: * Ratio of the smallest C(i) to the largest C(i).
! 63: *
! 64: * AMAX (input) DOUBLE PRECISION
! 65: * Absolute value of largest matrix entry.
! 66: *
! 67: * EQUED (output) CHARACTER*1
! 68: * Specifies the form of equilibration that was done.
! 69: * = 'N': No equilibration
! 70: * = 'R': Row equilibration, i.e., A has been premultiplied by
! 71: * diag(R).
! 72: * = 'C': Column equilibration, i.e., A has been postmultiplied
! 73: * by diag(C).
! 74: * = 'B': Both row and column equilibration, i.e., A has been
! 75: * replaced by diag(R) * A * diag(C).
! 76: *
! 77: * Internal Parameters
! 78: * ===================
! 79: *
! 80: * THRESH is a threshold value used to decide if row or column scaling
! 81: * should be done based on the ratio of the row or column scaling
! 82: * factors. If ROWCND < THRESH, row scaling is done, and if
! 83: * COLCND < THRESH, column scaling is done.
! 84: *
! 85: * LARGE and SMALL are threshold values used to decide if row scaling
! 86: * should be done based on the absolute size of the largest matrix
! 87: * element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
! 88: *
! 89: * =====================================================================
! 90: *
! 91: * .. Parameters ..
! 92: DOUBLE PRECISION ONE, THRESH
! 93: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
! 94: * ..
! 95: * .. Local Scalars ..
! 96: INTEGER I, J
! 97: DOUBLE PRECISION CJ, LARGE, SMALL
! 98: * ..
! 99: * .. External Functions ..
! 100: DOUBLE PRECISION DLAMCH
! 101: EXTERNAL DLAMCH
! 102: * ..
! 103: * .. Intrinsic Functions ..
! 104: INTRINSIC MAX, MIN
! 105: * ..
! 106: * .. Executable Statements ..
! 107: *
! 108: * Quick return if possible
! 109: *
! 110: IF( M.LE.0 .OR. N.LE.0 ) THEN
! 111: EQUED = 'N'
! 112: RETURN
! 113: END IF
! 114: *
! 115: * Initialize LARGE and SMALL.
! 116: *
! 117: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
! 118: LARGE = ONE / SMALL
! 119: *
! 120: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
! 121: $ THEN
! 122: *
! 123: * No row scaling
! 124: *
! 125: IF( COLCND.GE.THRESH ) THEN
! 126: *
! 127: * No column scaling
! 128: *
! 129: EQUED = 'N'
! 130: ELSE
! 131: *
! 132: * Column scaling
! 133: *
! 134: DO 20 J = 1, N
! 135: CJ = C( J )
! 136: DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
! 137: AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
! 138: 10 CONTINUE
! 139: 20 CONTINUE
! 140: EQUED = 'C'
! 141: END IF
! 142: ELSE IF( COLCND.GE.THRESH ) THEN
! 143: *
! 144: * Row scaling, no column scaling
! 145: *
! 146: DO 40 J = 1, N
! 147: DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
! 148: AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
! 149: 30 CONTINUE
! 150: 40 CONTINUE
! 151: EQUED = 'R'
! 152: ELSE
! 153: *
! 154: * Row and column scaling
! 155: *
! 156: DO 60 J = 1, N
! 157: CJ = C( J )
! 158: DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
! 159: AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
! 160: 50 CONTINUE
! 161: 60 CONTINUE
! 162: EQUED = 'B'
! 163: END IF
! 164: *
! 165: RETURN
! 166: *
! 167: * End of DLAQGB
! 168: *
! 169: END
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