Annotation of rpl/lapack/lapack/zpoequb.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 5: * -- Jason Riedy of Univ. of California Berkeley. --
! 6: * -- November 2008 --
! 7: *
! 8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 9: * -- Univ. of California Berkeley and NAG Ltd. --
! 10: *
! 11: IMPLICIT NONE
! 12: * ..
! 13: * .. Scalar Arguments ..
! 14: INTEGER INFO, LDA, N
! 15: DOUBLE PRECISION AMAX, SCOND
! 16: * ..
! 17: * .. Array Arguments ..
! 18: COMPLEX*16 A( LDA, * )
! 19: DOUBLE PRECISION S( * )
! 20: * ..
! 21: *
! 22: * Purpose
! 23: * =======
! 24: *
! 25: * ZPOEQUB computes row and column scalings intended to equilibrate a
! 26: * symmetric positive definite matrix A and reduce its condition number
! 27: * (with respect to the two-norm). S contains the scale factors,
! 28: * S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
! 29: * elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
! 30: * choice of S puts the condition number of B within a factor N of the
! 31: * smallest possible condition number over all possible diagonal
! 32: * scalings.
! 33: *
! 34: * Arguments
! 35: * =========
! 36: *
! 37: * N (input) INTEGER
! 38: * The order of the matrix A. N >= 0.
! 39: *
! 40: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 41: * The N-by-N symmetric positive definite matrix whose scaling
! 42: * factors are to be computed. Only the diagonal elements of A
! 43: * are referenced.
! 44: *
! 45: * LDA (input) INTEGER
! 46: * The leading dimension of the array A. LDA >= max(1,N).
! 47: *
! 48: * S (output) DOUBLE PRECISION array, dimension (N)
! 49: * If INFO = 0, S contains the scale factors for A.
! 50: *
! 51: * SCOND (output) DOUBLE PRECISION
! 52: * If INFO = 0, S contains the ratio of the smallest S(i) to
! 53: * the largest S(i). If SCOND >= 0.1 and AMAX is neither too
! 54: * large nor too small, it is not worth scaling by S.
! 55: *
! 56: * AMAX (output) DOUBLE PRECISION
! 57: * Absolute value of largest matrix element. If AMAX is very
! 58: * close to overflow or very close to underflow, the matrix
! 59: * should be scaled.
! 60: *
! 61: * INFO (output) INTEGER
! 62: * = 0: successful exit
! 63: * < 0: if INFO = -i, the i-th argument had an illegal value
! 64: * > 0: if INFO = i, the i-th diagonal element is nonpositive.
! 65: *
! 66: * =====================================================================
! 67: *
! 68: * .. Parameters ..
! 69: DOUBLE PRECISION ZERO, ONE
! 70: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 71: * ..
! 72: * .. Local Scalars ..
! 73: INTEGER I
! 74: DOUBLE PRECISION SMIN, BASE, TMP
! 75: COMPLEX*16 ZDUM
! 76: * ..
! 77: * .. External Functions ..
! 78: DOUBLE PRECISION DLAMCH
! 79: EXTERNAL DLAMCH
! 80: * ..
! 81: * .. External Subroutines ..
! 82: EXTERNAL XERBLA
! 83: * ..
! 84: * .. Intrinsic Functions ..
! 85: INTRINSIC MAX, MIN, SQRT, LOG, INT, REAL, DIMAG
! 86: * ..
! 87: * .. Statement Functions ..
! 88: DOUBLE PRECISION CABS1
! 89: * ..
! 90: * .. Statement Function Definitions ..
! 91: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 92: * ..
! 93: * .. Executable Statements ..
! 94: *
! 95: * Test the input parameters.
! 96: *
! 97: * Positive definite only performs 1 pass of equilibration.
! 98: *
! 99: INFO = 0
! 100: IF( N.LT.0 ) THEN
! 101: INFO = -1
! 102: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 103: INFO = -3
! 104: END IF
! 105: IF( INFO.NE.0 ) THEN
! 106: CALL XERBLA( 'ZPOEQUB', -INFO )
! 107: RETURN
! 108: END IF
! 109: *
! 110: * Quick return if possible.
! 111: *
! 112: IF( N.EQ.0 ) THEN
! 113: SCOND = ONE
! 114: AMAX = ZERO
! 115: RETURN
! 116: END IF
! 117:
! 118: BASE = DLAMCH( 'B' )
! 119: TMP = -0.5D+0 / LOG ( BASE )
! 120: *
! 121: * Find the minimum and maximum diagonal elements.
! 122: *
! 123: S( 1 ) = A( 1, 1 )
! 124: SMIN = S( 1 )
! 125: AMAX = S( 1 )
! 126: DO 10 I = 2, N
! 127: S( I ) = A( I, I )
! 128: SMIN = MIN( SMIN, S( I ) )
! 129: AMAX = MAX( AMAX, S( I ) )
! 130: 10 CONTINUE
! 131: *
! 132: IF( SMIN.LE.ZERO ) THEN
! 133: *
! 134: * Find the first non-positive diagonal element and return.
! 135: *
! 136: DO 20 I = 1, N
! 137: IF( S( I ).LE.ZERO ) THEN
! 138: INFO = I
! 139: RETURN
! 140: END IF
! 141: 20 CONTINUE
! 142: ELSE
! 143: *
! 144: * Set the scale factors to the reciprocals
! 145: * of the diagonal elements.
! 146: *
! 147: DO 30 I = 1, N
! 148: S( I ) = BASE ** INT( TMP * LOG( S( I ) ) )
! 149: 30 CONTINUE
! 150: *
! 151: * Compute SCOND = min(S(I)) / max(S(I)).
! 152: *
! 153: SCOND = SQRT( SMIN ) / SQRT( AMAX )
! 154: END IF
! 155: *
! 156: RETURN
! 157: *
! 158: * End of ZPOEQUB
! 159: *
! 160: END
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