n2fb n2fb_r n2gb n2gb_r n2pb n2pb_r

n2pb_r() void n2pb_r ( int  m, int  md, int  n, double  x[], double  b[][2], double  v[], int  lv, int  iv[], int  liv, int *  info, int *  m1, int *  m2, double  yy[], int  ldyyp, double  yyp[], int *  irev  ) Nonlinear least squares approximation (adaptive algorithm) (simply bounded) (limited storage) (reverse communication version) Purpose n2pb_r minimizes the sum of the squares of m nonlinear functions in n variables, subject to simple bound constraints bl[i] <= x[i] <= bu[i], 1 <= i <= n, by the adaptive algorithm which combines and augments a Gauss-Newton, Levenberg-Marquardt and other techniques for better convergence. minimize the sum of fi(x1, x2, ..., xn)^2 (sum for i = 1 to m) The user must provide the function and Jacobian values in accordance with irev. The function and Jacobian can be calculated in chunks rather than all at once. n2pb_r is the reverse communication version of n2pb. Parameters [in] m Number of data. (m > 0) [in] md Maximum number of residual components provided by a single evaluation of function values. (0 < md <= m) [in] n Number of parameters. (0 < n <= m) [in,out] x[] Array x[lx] (lx >= n) [in] An initial estimate of the solution vector. [out] irev = 0: The obtained solution vector.   irev = 1: The abscissa where the function (residual) values shoule be evaluated.   irev = 30, 31: The abscissa where the Jacobian shoule be evaluated.   irev = 50: Recent approximation of the solution vector. [in] b[][] Array b[lb][2] (lb >= n) Lower and upper bounds on solution vector x.   b[i][0] <= x[i] <= b[i][1] (i = 0 to n-1) [in,out] v[] Array v[lv] The array for the floating point parameters and work space. [in]   v[25] (tuner1): Parameter to check for false convergence (0 <= tuner1 <= 0.5) (default = 0.1)   v[30] (atol): Absolute function convergence tolerance (0 <= atol) (default = max(1e-20, eps^2), where eps is the machine epsilon)   v[31] (rtol): Relative function convergence tolerance (eps <= rtol <= 0.1) (default = max(1e-10, eps^(2/3))   v[32] (xctol): X-convergence tolerance (0 <= xctol <= 1) (default = eps^(1/2))   v[33] (xftol): False convergence tolerance (0 <= xftol <= 1) (default = 100*eps)   v[34] (lmax0): Maximum 2-norm allowed for scaled very first step (0 < lmax0) (default = 1)   v[35] (lmaxs), v[36] (sctol): Parameters to test for singular convergence (0 < lmaxs, 0 <= sctol <= 1) (default: lmaxs = 1, sctol = max(1e-10, eps^(2/3))).     If the function reduction predicted for a step of length bounded by lmaxs is less than sctol*abs(f), returns with info = 7 (f is the function value at the start of the current iteration).   v[37] (dinit): If nonnegative, all components of the scale vector d[] is initialized to this value (-10 <= dinit) (default = 0)   v[38] (dtol): Tolerance for adaptive scaling (0 =< dtol) (default = 1e-6)   v[39] (d0): Initial value for adaptive scaling (0 <= d0) (default = 1)   v[40] (dfac): Factor for adaptive scaling (0 <= dfac <= 1) (default = 0.6)     A scale factor d[i] is chosen by adaptive scaling so that d[i]*x[i] has about the same magnitude for all i.     Let d1[i] = max(||Ji||, dfac*d[i]) where ||Ji|| is the 2-norm of the i-th column of Jacobian matrix, then d[i] is chosen as follows.       if d1[i] >= dtol then d[i] = d1[i]       if d1[i] < dtol then d[i] = d0 [out]   v[0] (dgnorm): 2-norm of diag(d)^(-1)*g (g is most recently computed gradient)   v[1] (dstnorm): 2-norm of diag(d)^(-1)*s (s is the current step)   v[9] (f): Current function value (half the sum of squares)   v[12] (f0): Function value at the start of the current iteration [in] lv The length of array v[] (lv >= 105 + n*(2*n + 22) + m) [in,out] iv[] Array iv[liv] The array for the integer parameters and work space. [in]   iv[0]: If = 0, all parameters in v[] and iv[] will be initialized to the default values before starting calculation.     If = 12, v[] and iv[] are assumed to have already been set by the user and will not be initialized by the routine. Since the subroutine ivset assigns iv[0] = 12, user can first call ivset to set default values to v[] and iv[], and then change some necessary entries to non-default values and start calculation with such non-default parameters.   iv[15] (dtype): Choice of adaptive scaling (default = 1)     = 0: Disable adaptive scaling (scale factor = 1)     = 1: Enable adaptive scaling during all iterations     = 2: Enable adaptive scaling during the first iteration and scale factor is left unchanged thereafter   iv[16] (mxfcal): Maximum number of function evaluations allowed (default = 200)   iv[17] (mxiter): Maximum number of iterations allowed (default = 150)   iv[18] (outlev): Controls the print of intermediate results (default = 0)     != 1: Do not return with irev=50     = 1: Return after every iteration with irev=50 for printing intermediate result   iv[24] (inits): The regression routines use a "secant update" to obtain an approximation S to part of Hessian matrix. Usually initial S matrix can be set to all zeros, but occasionally it is useful to initialize S to other values (default = 0)     = 0: S matrix to initialize to all zeros     = 3: To use differences of function values to estimate the initial S     = 4: To use differences of gradients to estimate the initial S [out]   iv[0]: Return code     = 3: x-convergence     = 4: Relative function convergence     = 5: Both x- and relative function convergence     = 6: Absolute function convergence     = 7: Singular convergence. The Hessian near the current iterate appears to be singular     = 8: False convergence. The iterates appear to be converging to a noncritical point     = 9: Function evaluation limit reached     = 10: Iteration limit reached     = 11: Stopx returned true (external interrupt)     = 12: iv[] and v[] have been allocated and initialized     = 13: f(x) cannot be computed at the initial x[]     = 14: Bad parameters passed to assess (which should not occur)     = 15: liv was too small     = 16: lv was too small     = 17: Restart attempted with m or n changed     = 18: iv[24] is out of range.     = 19...45: v[iv[0]] is out of range     = 50: iv[0] is out of range     = 87...(86+m) = jtol[iv[0]-86] is not positive   iv[5] (nfcall): Number of function evaluations with irev = 1   iv[29] (ngcall): Number of Jacobian evaluations with irev = 30 or 31   iv[30] (niter): Number of iterations performed   iv[43] (lastiv): The least acceptable value of liv   iv[44] (lastv): The least acceptable value of lv   iv[60] (r): The residual vector r corresponding to x is stored in v[] starting at v[iv[60]-1] [in] liv The length of array iv[] (liv >= 82 + 4*n) [out] info = 0: Successful exit (iv[0] = 3 to 6) = -1: The argument m had an illegal value (m < 1) (iv[0] = 66) = -2: The argument nd had an illegal value (nd < 1) (iv[0] = 66) = -3: The argument n had an illegal value (n < 1) (iv[0] = 66) = -8: The argument v[18], ... or v[49] had an illegal value (out of range) (iv[0] = 19 to 50) = -9: The argument lv had an illegal value (lv too small) (iv[0] = 16) = -10: The argument iv[0] had an illegal value (iv[0] out of range) (iv[0] = 80) = -11: The argument liv had an illegal value (liv too small) (iv[0] = 15) = 7: Singular convergence (the Hessian near the current iterate appears to be singular) = 8: False convergence (the iterates appear to be converging to a noncritical point) = 9: Function evaluation limit reached = 10: Iteration limit reached = 14: iv[] and v[] have been allocated (normal exit after a call with iv[0]=13) = 17: Restart attempted with m or n changed = 63: f(x) cannot be computed at the initial x = 65: The gradient could not be computed at x [out] m1 Index of the first function value or the first row of Jacobian matrix to be provided when returned with irev = 1, 30 or 31. (1 <= m1 <= m) [out] m2 Index of the last function value or the last row of Jacobian matrix to be provided when returned with irev = 1, 30 or 31. (m2 = min(m, m1+md-1)) [in] yy[] Array yy[lyy] (lyy >= md) When returned with irev = 1, the function values with the indices i+n1-1 (i = 1to m2-m1+1) at x[] should be provided in yy[i-1] in the next call. [in] ldyyp Leading dimension of the two dimensional array yyp[]. (ldyyp >= md) [in] yyp[][] Array yyp[lyyp][ldyyp] (lyyp >= n) When returned with irev = 30 or 31, (i+m1-1)-th rows of Jacobian matrix (i = 1 to m2-m1+1) at x[] should be provided in yyp[*][i-1] in the next call. [in,out] irev Control variable for reverse communication. [in] Before first call, irev should be initialized to zero. On succeeding calls, irev should not be altered. [out] If irev is not zero, complete the following process and call this routine again. = 0: Computation finished. See return code in info. = 1: User should provide the function values with the indices i+n1-1 (i = 1 to m2-m1+1) at x[] in yy[i-1]. Do not alter any variables other than yy[]. = 30, 31: User should provide the (i+m1-1)-th rows of Jacobian matrix (i = 1 to m2-m1+1) at x[] in yyp[*][i-1]. Do not alter any variables other than yyp[][]. = 50: To be returned with irev = 50 on each iteration if iv[18] = 1. Print the intermediate result (x[], iv[30], iv[5], iv[29], v[9], etc.). Do not alter any variables. Reference netlib/port