Cream of the Crop 26

home *** CD-ROM | disk | FTP | other *** search

/ Cream of the Crop 26 / Cream of the Crop 26.iso / os2 / octa209b.zip / octave-2.09 / doc / octave.i08 (.txt) < prev next >

Wrap

GNU Info File | 1997-08-20 | 46KB | 991 lines

This is Info file octave, produced by Makeinfo-1.64 from the input file octave.tex. START-INFO-DIR-ENTRY * Octave: (octave). Interactive language for numerical computations. END-INFO-DIR-ENTRY Copyright (C) 1996, 1997 John W. Eaton. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions. File: octave, Node: Differential-Algebraic Equations, Prev: Ordinary Differential Equations, Up: Differential Equations Differential-Algebraic Equations ================================ The function `dassl' can be used Solve DAEs of the form 0 = f (x-dot, x, t), x(t=0) = x_0, x-dot(t=0) = x-dot_0 using Petzold's DAE solver DASSL. - Loadable Function: [X, XDOT] = dassl (FCN, X0, XDOT0, T, T_CRIT) Return a matrix of states and their first derivatives with respect to T. Each row in the result matrices correspond to one of the elements in the vector T. The first element of T corresponds to the initial state X0 and derivative XDOT0, so that the first row of the output X is X0 and the first row of the output XDOT is XDOT0. The first argument, FCN, is a string that names the function to call to compute the vector of residuals for the set of equations. It must have the form RES = f (X, XDOT, T) where X, XDOT, and RES are vectors, and T is a scalar. The second and third arguments to `dassl' specify the initial condition of the states and their derivatives, and the fourth argument specifies a vector of output times at which the solution is desired, including the time corresponding to the initial condition. The set of initial states and derivatives are not strictly required to be consistent. In practice, however, DASSL is not very good at determining a consistent set for you, so it is best if you ensure that the initial values result in the function evaluating to zero. The fifth argument is optional, and may be used to specify a set of times that the DAE solver should not integrate past. It is useful for avoiding difficulties with singularities and points where there is a discontinuity in the derivative. - Loadable Function: dassl_options (OPT, VAL) When called with two arguments, this function allows you set options parameters for the function `lsode'. Given one argument, `dassl_options' returns the value of the corresponding option. If no arguments are supplied, the names of all the available options and their current values are displayed. See K. E. Brenan, et al., `Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations', North-Holland (1989) for more information about the implementation of DASSL. File: octave, Node: Optimization, Next: Statistics, Prev: Differential Equations, Up: Top Optimization ************ * Menu: * Quadratic Programming:: * Nonlinear Programming:: * Linear Least Squares:: File: octave, Node: Quadratic Programming, Next: Nonlinear Programming, Prev: Optimization, Up: Optimization Quadratic Programming ===================== File: octave, Node: Nonlinear Programming, Next: Linear Least Squares, Prev: Quadratic Programming, Up: Optimization Nonlinear Programming ===================== File: octave, Node: Linear Least Squares, Prev: Nonlinear Programming, Up: Optimization Linear Least Squares ==================== - Function File: [BETA, V, R] = gls (Y, X, O) Generalized least squares estimation for the multivariate model `Y = X * B + E' with `mean (E) = 0' and `cov (vec (E)) = (S^2)*O', where Y is a T by P matrix, X is a T by K matrix, B is a K by P matrix, E is a T by P matrix, and O is a TP by TP matrix. Each row of Y and X is an observation and each column a variable. The return values BETA, V, and R are defined as follows. BETA The GLS estimator for B. V The GLS estimator for `S^2'. R The matrix of GLS residuals, `R = Y - X * BETA'. - Function File: [BETA, SIGMA, R] = ols (Y, X) Ordinary least squares estimation for the multivariate model `Y = X*B + E' with `mean (E) = 0' and `cov (vec (E)) = kron (S, I)'. where Y is a T by P matrix, X is a T by K matrix, B is a K by P matrix, and E is a T by P matrix. Each row of Y and X is an observation and each column a variable. The return values BETA, SIGMA, and R are defined as follows. BETA The OLS estimator for B, `BETA = pinv (X) * Y', where `pinv (X)' denotes the pseudoinverse of X. SIGMA The OLS estimator for the matrix S, SIGMA = (Y-X*BETA)' * (Y-X*BETA) / (T-rank(X)) R The matrix of OLS residuals, `R = Y - X * BETA'. File: octave, Node: Statistics, Next: Sets, Prev: Optimization, Up: Top Statistics ********** I hope that someday Octave will include more statistics functions. If you would like to help improve Octave in this area, please contact (bug-octave@bevo.che.wisc.edu). - Function File: mean (X) If X is a vector, compute the mean of the elements of X mean (x) = SUM_i x(i) / N If X is a matrix, compute the mean for each column and return them in a row vector. - Function File: median (X) If X is a vector, compute the median value of the elements of X. x(ceil(N/2)), N odd median(x) = (x(N/2) + x((N/2)+1))/2, N even If X is a matrix, compute the median value for each column and return them in a row vector. - Function File: std (X) If X is a vector, compute the standard deviation of the elements of X. std (x) = sqrt (sumsq (x - mean (x)) / (n - 1)) If X is a matrix, compute the standard deviation for each column and return them in a row vector. - Function File: cov (X, Y) If each row of X and Y is an observation and each column is a variable, the (I,J)-th entry of `cov (X, Y)' is the covariance between the I-th variable in X and the J-th variable in Y. If called with one argument, compute `cov (X, X)'. - Function File: corrcoef (X, Y) If each row of X and Y is an observation and each column is a variable, the (I,J)-th entry of `corrcoef (X, Y)' is the correlation between the I-th variable in X and the J-th variable in Y. If called with one argument, compute `corrcoef (X, X)'. - Function File: kurtosis (X) If X is a vector of length N, return the kurtosis kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3 of X. If X is a matrix, return the row vector containing the kurtosis of each column. - Function File: mahalanobis (X, Y) Return the Mahalanobis' D-square distance between the multivariate samples X and Y, which must have the same number of components (columns), but may have a different number of observations (rows). - Function File: skewness (X) If X is a vector of length N, return the skewness skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3) of X. If X is a matrix, return the row vector containing the skewness of each column. File: octave, Node: Sets, Next: Polynomial Manipulations, Prev: Statistics, Up: Top Octave has a limited set of functions for managing sets of data, where a set is defined as a collection unique elements. - Function File: create_set (X) Return a row vector containing the unique values in X, sorted in ascending order. For example, create_set ([ 1, 2; 3, 4; 4, 2 ]) => [ 1, 2, 3, 4 ] - Function File: union (X, Y) Return the set of elements that are in either of the sets X and Y. For example, union ([ 1, 2, 4 ], [ 2, 3, 5 ]) => [ 1, 2, 3, 4, 5 ] - Function File: intersection (X, Y) Return the set of elements that are in both sets X and Y. For example, intersection ([ 1, 2, 3 ], [ 2, 3, 5 ]) => [ 2, 3 ] - Function File: complement (X, Y) Return the elements of set Y that are not in set X. For example, complement ([ 1, 2, 3 ], [ 2, 3, 5 ]) => 5 File: octave, Node: Polynomial Manipulations, Next: Control Theory, Prev: Sets, Up: Top Polynomial Manipulations ************************ In Octave, a polynomial is represented by its coefficients (arranged in descending order). For example, a vector C of length N+1 corresponds to the following polynomial of order N p(x) = C(1) x^N + ... + C(N) x + C(N+1). - Function File: compan (C) Compute the companion matrix corresponding to polynomial coefficient vector C. The companion matrix is _ _ | -c(2)/c(1) -c(3)/c(1) ... -c(N)/c(1) -c(N+1)/c(1) | | 1 0 ... 0 0 | | 0 1 ... 0 0 | A = | . . . . . | | . . . . . | | . . . . . | |_ 0 0 ... 1 0 _| The eigenvalues of the companion matrix are equal to the roots of the polynomial. - Function File: conv (A, B) Convolve two vectors. `y = conv (a, b)' returns a vector of length equal to `length (a) + length (b) - 1'. If A and B are polynomial coefficient vectors, `conv' returns the coefficients of the product polynomial. - Function File: deconv (Y, A) Deconvolve two vectors. `[b, r] = deconv (y, a)' solves for B and R such that `y = conv (a, b) + r'. If Y and A are polynomial coefficient vectors, B will contain the coefficients of the polynomial quotient and R will be a remander polynomial of lowest order. - Function File: poly (A) If A is a square N-by-N matrix, `poly (A)' is the row vector of the coefficients of `det (z * eye (N) - a)', the characteristic polynomial of A. If X is a vector, `poly (X)' is a vector of coefficients of the polynomial whose roots are the elements of X. - Function File: polyderiv (C) Return the coefficients of the derivative of the polynomial whose coefficients are given by vector C. - Function File: polyfit (N, Y, N) Return the coefficients of a polynomial P(X) of degree N that minimizes `sumsq (p(x(i)) - y(i))', to best fit the data in the least squares sense. - Function File: polyinteg (C) Return the coefficients of the integral the polynomial whose coefficients are represented by the vector C. The constant of integration is set to zero. - Function File: polyreduce (C) Reduces a polynomial coefficient vector to a minimum number of terms by stripping off any leading zeros. - Function File: polyval (C, X) Evaluate a polynomial. `polyval (C, X)' will evaluate the polynomial at the specified value of X. If X is a vector or matrix, the polynomial is evaluated at each of the elements of X. - Function File: polyvalm (C, X) Evaluate a polynomial in the matrix sense. `polyvalm (C, X)' will evaluate the polynomial in the matrix sense, i.e. matrix multiplication is used instead of element by element multiplication as is used in polyval. The argument X must be a square matrix. - Function File: residue (B, A, TOL) If B and A are vectors of polynomial coefficients, then residue calculates the partial fraction expansion corresponding to the ratio of the two polynomials. The function `residue' returns R, P, K, and E, where the vector R contains the residue terms, P contains the pole values, K contains the coefficients of a direct polynomial term (if it exists) and E is a vector containing the powers of the denominators in the partial fraction terms. Assuming B and A represent polynomials P (s) and Q(s) we have: P(s) M r(m) N ---- = SUM ------------- + SUM k(i)*s^(N-i) Q(s) m=1 (s-p(m))^e(m) i=1 where M is the number of poles (the length of the R, P, and E vectors) and N is the length of the K vector. The argument TOL is optional, and if not specified, a default value of 0.001 is assumed. The tolerance value is used to determine whether poles with small imaginary components are declared real. It is also used to determine if two poles are distinct. If the ratio of the imaginary part of a pole to the real part is less than TOL, the imaginary part is discarded. If two poles are farther apart than TOL they are distinct. For example, b = [1, 1, 1]; a = [1, -5, 8, -4]; [r, p, k, e] = residue (b, a); => r = [-2, 7, 3] => p = [2, 2, 1] => k = [](0x0) => e = [1, 2, 1] which implies the following partial fraction expansion s^2 + s + 1 -2 7 3 ------------------- = ----- + ------- + ----- s^3 - 5s^2 + 8s - 4 (s-2) (s-2)^2 (s-1) - Function File: roots (V) For a vector V with N components, return the roots of the polynomial v(1) * z^(N-1) + ... + v(N-1) * z + v(N). File: octave, Node: Control Theory, Next: Signal Processing, Prev: Polynomial Manipulations, Up: Top Control Theory ************** Most of the functions described in this chapter were contributed by A. Scottedward Hodel (A.S.Hodel@eng.auburn.edu) and R. Bruce Tenison (Bruce.Tenison@eng.auburn.edu). They have also written a larger collection of functions for solving linear control problems. It is currently being updated for Octave version 2, with snapshots of the sources available from (ftp://ftp.eng.auburn.edu/pub/hodel). - Function File: [N, M, P] = abcddim (A, B, C, D) Check for compatibility of the dimensions of the matrices defining the linear system [A, B, C, D] corresponding to dx/dt = a x + b u y = c x + d u or a similar discrete-time system. If the matrices are compatibly dimensioned, then `abcddim' returns N The number of system states. M The number of system inputs. P The number of system outputs. Otherwise `abcddim' returns N = M = P = -1. - Function File: are (A, B, C, OPT) Return the solution, X, of the algebraic Riccati equation a' * x + x * a - x * b * x + c = 0 for identically dimensioned square matrices A, B, and C. If B is not square, `are' attempts to use `B*B'' instead. If C is not square, `are' attempts to use `C'*C') instead. To form the solution, Laub's Schur method (IEEE Transactions on Automatic Control, 1979) is applied to the appropriate Hamiltonian matrix. The optional argument OPT is passed to the eigenvalue balancing routine. If it is omitted, a value of `"B"' is assumed. - Function File: c2d (A, B, T) Convert the continuous time system described by: dx/dt = a x + b u into a discrete time equivalent model x[k+1] = Ad x[k] + Bd u[k] via the matrix exponential assuming a zero-order hold on the input and sample time T. - Function File: dare (A, B, C, R, OPT) Return the solution, X of the discrete-time algebraic Riccati equation a' x a - x + a' x b (r + b' x b)^(-1) b' x a + c = 0 for matrices with dimensions: A N by N. B N by M. C N by N, symmetric positive semidefinite. R M by M, symmetric positive definite (invertible). If C is not square, then the function attempts to use `C'*C' instead. To form the solution, Laub's Schur method (IEEE Transactions on Automatic Control, 1979) is applied to the appropriate symplectic matrix. See also Ran and Rodman, `Stable Hermitian Solutions of Discrete Algebraic Riccati Equations', Mathematics of Control, Signals and Systems, Volume 5, Number 2 (1992). The optional argument OPT is passed to the eigenvalue balancing routine. If it is omitted, a value of `"B"' is assumed. - Function File: dgram (A, B) Return the discrete controllability or observability gramian for the discrete time system described by x[k+1] = A x[k] + B u[k] y[k] = C x[k] + D u[k] For example, `dgram (A, B)' returns the discrete controllability gramian and `dgram (A', C')' returns the observability gramian. - Function File: [L, M, P, E] = dlqe (A, G, C, SIGW, SIGV, Z) Construct the linear quadratic estimator (Kalman filter) for the discrete time system x[k+1] = A x[k] + B u[k] + G w[k] y[k] = C x[k] + D u[k] + w[k] where W, V are zero-mean gaussian noise processes with respective intensities `SIGW = cov (W, W)' and `SIGV = cov (V, V)'. If specified, Z is `cov (W, V)'. Otherwise `cov (W, V) = 0'. The observer structure is z[k+1] = A z[k] + B u[k] + k(y[k] - C z[k] - D u[k]) The following values are returned: L The observer gain, (A - ALC). is stable. M The Riccati equation solution. P The estimate error covariance after the measurement update. E The closed loop poles of (A - ALC). - Function File: [K, P, E] = dlqr (A, B, Q, R, Z) Construct the linear quadratic regulator for the discrete time system x[k+1] = A x[k] + B u[k] to minimize the cost functional J = Sum (x' Q x + u' R u) Z omitted or J = Sum (x' Q x + u' R u + 2 x' Z u) Z included. The following values are returned: K The state feedback gain, (A - BK) is stable. P The solution of algebraic Riccati equation. E The closed loop poles of (A - BK). - Function File: dlyap (A, B) Solve the discrete-time Lyapunov equation `a x a' - x + b = 0' for square matrices A, B. If B is not square, then the function attempts to solve either `a x a' - x + b b' = 0' or `a' x a - x + b' b = 0', whichever is appropriate. Uses Schur decomposition method as in Kitagawa `An Algorithm for Solving the Matrix Equation X = FXF' + S', International Journal of Control, Volume 25, Number 5, pages 745-753 (1977); column-by-column solution method as suggested in Hammerling, `Numerical Solution of the Stable, Non-Negative Definite Lyapunov Equation', IMA Journal of Numerical Analysis, Volume 2, pages 303-323 (1982). - Function File: is_controllable (A, B, TOL) Return 1 if the pair (A, B) is controllable. Otherwise, return 0. The optional argument TOL is a roundoff parameter. If it is omitted, a value of `2*eps' is used. Currently, `is_controllable' just constructs the controllability matrix and checks rank. - Function File: is_observable (A, C, TOL) Return 1 if the pair (A, C) is observable. Otherwise, return 0. The optional argument TOL is a roundoff parameter. If it is omitted, a value of `2*eps' is used. - Function File: [K, P, E] = lqe (A, G, C, SIGW, SIGV, Z) Construct the linear quadratic estimator (Kalman filter) for the continuous time system dx -- = a x + b u dt y = c x + d u where W and V are zero-mean gaussian noise processes with respective intensities sigw = cov (w, w) sigv = cov (v, v) The optional argument Z is the cross-covariance `cov (W, V)'. If it is omitted, `cov (W, V) = 0' is assumed. Observer structure is `dz/dt = A z + B u + k (y - C z - D u)' The following values are returned: K The observer gain, (A - KC) is stable. P The solution of algebraic Riccati equation. E The vector of closed loop poles of (A - KC). - Function File: [K, P, E] = lqr (A, B, Q, R, Z) construct the linear quadratic regulator for the continuous time system dx -- = A x + B u dt to minimize the cost functional infinity / J = | x' Q x + u' R u / t=0 Z omitted or infinity / J = | x' Q x + u' R u + 2 x' Z u / t=0 Z included. The following values are returned: K The state feedback gain, (A - BK) is stable. P The stabilizing solution of appropriate algebraic Riccati equation. E The vector of the closed loop poles of (A - BK). - Function File: lyap (A, B, C) Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart algorithm (Communications of the ACM, 1972). If A, B, and C are specified, then `lyap' returns the solution of the Sylvester equation a x + x b + c = 0 If only `(a, b)' are specified, then `lyap' returns the solution of the Lyapunov equation a' x + x a + b = 0 If B is not square, then `lyap' returns the solution of either a' x + x a + b' b = 0 or a x + x a' + b b' = 0 whichever is appropriate. - Function File: tzero (A, B, C, D, OPT) Compute the transmission zeros of [A, B, C, D]. The optional argument OPT is passed to the eigenvalue balancing routine. If it is omitted, a value of `"B"' is assumed. File: octave, Node: Signal Processing, Next: Image Processing, Prev: Control Theory, Up: Top Signal Processing ***************** I hope that someday Octave will include more signal processing functions. If you would like to help improve Octave in this area, please contact (bug-octave@bevo.che.wisc.edu). - Function File: detrend (X, P) If X is a vector, `detrend (X, P)' removes the best fit of a polynomial of order P from the data X. If X is a matrix, `detrend (X, P)' does the same for each column in X. The second argument is optional. If it is not specified, a value of 1 is assumed. This corresponds to removing a linear trend. - Function: fft (A, N) Compute the FFT of A using subroutines from FFTPACK. If A is a matrix, `fft' computes the FFT for each column of A. If called with two arguments, N is expected to be an integer specifying the number of elements of A to use. If A is a matrix, N specifies the number of rows of A to use. If N is larger than the size of A, A is resized and padded with zeros. - Loadable Function: ifft (A, N) Compute the inverse FFT of A using subroutines from FFTPACK. If A is a matrix, `fft' computes the inverse FFT for each column of A. If called with two arguments, N is expected to be an integer specifying the number of elements of A to use. If A is a matrix, N specifies the number of rows of A to use. If N is larger than the size of A, A is resized and padded with zeros. - Loadable Function: fft2 (A, N, M) Compute the two dimensional FFT of A. The optional arguments N and M may be used specify the number of rows and columns of A to use. If either of these is larger than the size of A, A is resized and padded with zeros. - Loadable Function: ifft2 (A, N, M) Compute the two dimensional inverse FFT of A. The optional arguments N and M may be used specify the number of rows and columns of A to use. If either of these is larger than the size of A, A is resized and padded with zeros. - Built-in Function: fftconv (A, B, N) Return the convolution of the vectors A and B, as a vector with length equal to the `length (a) + length (b) - 1'. If A and B are the coefficient vectors of two polynomials, the returned value is the coefficient vector of the product polynomial. The computation uses the FFT by calling the function `fftfilt'. If the optional argument N is specified, an N-point FFT is used. - Function File: fftfilt (B, X, N) With two arguments, `fftfilt' filters X with the FIR filter B using the FFT. Given the optional third argument, N, `fftfilt' uses the overlap-add method to filter X with B using an N-point FFT. - Loadable Function: y = filter (B, A, X) Return the solution to the following linear, time-invariant difference equation: N M SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x) k=0 k=0 where N=length(a)-1 and M=length(b)-1. An equivalent form of this equation is: N M y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x) k=1 k=0 where c = a/a(1) and d = b/a(1). In terms of the z-transform, y is the result of passing the discrete- time signal x through a system characterized by the following rational system function: M SUM d(k+1) z^(-k) k=0 H(z) = ---------------------- N 1 + SUM c(k+1) z(-k) k=1 - Loadable Function: [Y, SF] = filter (B, A, X, SI) This is the same as the `filter' function described above, except that SI is taken as the initial state of the system and the final state is returned as SF. The state vector is a column vector whose length is equal to the length of the longest coefficient vector minus one. If SI is not set, the initial state vector is set to all zeros. - Function File: [H, W] = freqz (B, A, N, "whole") Return the complex frequency response H of the rational IIR filter whose numerator and denominator coefficients are B and A, respectively. The response is evaluated at N angular frequencies between 0 and 2*pi. The output value W is a vector of the frequencies. If the fourth argument is omitted, the response is evaluated at frequencies between 0 and pi. If N is omitted, a value of 512 is assumed. If A is omitted, the denominator is assumed to be 1 (this corresponds to a simple FIR filter). For fastest computation, N should factor into a small number of small primes. - Function File: sinc (X) Return sin(pi*x)/(pi*x). File: octave, Node: Image Processing, Next: Audio Processing, Prev: Signal Processing, Up: Top Image Processing **************** Octave can display images with the X Window System using the `xloadimage' program. You do not need to be running X in order to manipulate images, however, so some of these functions may be useful even if you are not able to view the results. Loading images only works with Octave's image format (a file with a matrix containing the image data, and a matrix containing the colormap). Contributions of robust, well-written functions to read other image formats are welcome. If you can provide them, or would like to improve Octave's image processing capabilities in other ways, please contact (bug-octave@bevo.che.wisc.edu). - Function File: colormap (MAP) - Function File: colormap ("default") Set the current colormap. `colormap (MAP)' sets the current colormap to MAP. The color map should be an N row by 3 column matrix. The columns contain red, green, and blue intensities respectively. All entries should be between 0 and 1 inclusive. The new colormap is returned. `colormap ("default")' restores the default colormap (a gray scale colormap with 64 entries). The default colormap is returned. With no arguments, `colormap' returns the current color map. - Function File: gray (N) Return a gray colormap with N entries corresponding to values from 0 to N. The argument N should be a scalar. If it is omitted, 64 is assumed. - Function File: [IMG, MAP] = gray2ind () Convert a gray scale intensity image to an Octave indexed image. - Function File: image (X, ZOOM) Display a matrix as a color image. The elements of X are indices into the current colormap and should have values between 1 and the length of the colormap. If ZOOM is omitted, a value of 4 is assumed. - Function File: imagesc (X, ZOOM) Display a scaled version of the matrix X as a color image. The matrix is scaled so that its entries are indices into the current colormap. The scaled matrix is returned. If ZOOM is omitted, a value of 4 is assumed. - Function File: imshow (X, MAP) - Function File: imshow (X, N) - Function File: imshow (I, N) - Function File: imshow (R, G, B) Display images. `imshow (X)' displays an indexed image using the current colormap. `imshow (X, MAP)' displays an indexed image using the specified colormap. `imshow (I, N)' displays a gray scale intensity image. `imshow (R, G, B)' displays an RGB image. - Function File: ind2gray (X, MAP) Convert an Octave indexed image to a gray scale intensity image. If MAP is omitted, the current colormap is used to determine the intensities. - Function File: [R, G, B] = ind2rgb (X, MAP) Convert an indexed image to red, green, and blue color components. If MAP is omitted, the current colormap is used for the conversion. - Function File: [X, MAP] = loadimage (FILE) Load an image file and it's associated color map from the specified FILE. The image must be stored in Octave's image format. - Function File: rgb2ntsc (RGB) Image format conversion. - Function File: ntsc2rgb (YIQ) Image format conversion. - Function File: ocean (N) Create color colormap. The argument N should be a scalar. If it is omitted, 64 is assumed. - Function File: [X, MAP] = rgb2ind (R, G, B) Convert and RGB image to an Octave indexed image. - Function File: saveimage (FILE, X, FMT, MAP) Save the matrix X to FILE in image format FMT. Valid values for FMT are `"img"' Octave's image format. The current colormap is also saved in the file. `"ppm"' Portable pixmap format. `"ps"' PostScript format. Note that images saved in PostScript format can not be read back into Octave with loadimage. If the fourth argument is supplied, the specified colormap will also be saved along with the image. Note: if the colormap contains only two entries and these entries are black and white, the bitmap ppm and PostScript formats are used. If the image is a gray scale image (the entries within each row of the colormap are equal) the gray scale ppm and PostScript image formats are used, otherwise the full color formats are used. - Built-in Variable: IMAGEPATH A colon separated list of directories in which to search for image files. File: octave, Node: Audio Processing, Next: System Utilities, Prev: Image Processing, Up: Top Audio Processing **************** Octave provides a few functions for dealing with audio data. An audio `sample' is a single output value from an A/D converter, i.e., a small integer number (usually 8 or 16 bits), and audio data is just a series of such samples. It can be characterized by three parameters: the sampling rate (measured in samples per second or Hz, e.g. 8000 or 44100), the number of bits per sample (e.g. 8 or 16), and the number of channels (1 for mono, 2 for stereo, etc.). There are many different formats for representing such data. Currently, only the two most popular, *linear encoding* and *mu-law encoding*, are supported by Octave. There is an excellent FAQ on audio formats by Guido van Rossum <guido@cwi.nl> which can be found at any FAQ ftp site, in particular in the directory `/pub/usenet/news.answers/audio-fmts' of the archive site `rtfm.mit.edu'. Octave simply treats audio data as vectors of samples (non-mono data are not supported yet). It is assumed that audio files using linear encoding have one of the extensions `lin' or `raw', and that files holding data in mu-law encoding end in `au', `mu', or `snd'. - Function File: lin2mu (X) If the vector X represents mono audio data in 8- or 16-bit linear encoding, `lin2mu (X)' is the corresponding mu-law encoding. - Function File: mu2lin (X, BPS) If the vector X represents mono audio data in mu-law encoding, `mu2lin' converts it to linear encoding. The optional argument BPS specifies whether the input data uses 8 bit per sample (default) or 16 bit. - Function File: loadaudio (NAME, EXT, BPS) Loads audio data from the file `NAME.EXT' into the vector X. The extension EXT determines how the data in the audio file is interpreted; the extensions `lin' (default) and `raw' correspond to linear, the extensions `au', `mu', or `snd' to mu-law encoding. The argument BPS can be either 8 (default) or 16, and specifies the number of bits per sample used in the audio file. - Function File: saveaudio (NAME, X, EXT, BPS) Saves a vector X of audio data to the file `NAME.EXT'. The optional parameters EXT and BPS determine the encoding and the number of bits per sample used in the audio file (see `loadaudio'); defaults are `lin' and 8, respectively. The following functions for audio I/O require special A/D hardware and operating system support. It is assumed that audio data in linear encoding can be played and recorded by reading from and writing to `/dev/dsp', and that similarly `/dev/audio' is used for mu-law encoding. These file names are system-dependent. Improvements so that these functions will work without modification on a wide variety of hardware are welcome. - Function File: playaudio (NAME, EXT) - Function File: playaudio (X) Plays the audio file `NAME.EXT' or the audio data stored in the vector X. - Function File: record (SEC, SAMPLING_RATE) Records SEC seconds of audio input into the vector X. The default value for SAMPLING_RATE is 8000 samples per second, or 8kHz. The program waits until the user types RET and then immediately starts to record. - Function File: setaudio (TYPE) - Function File: setaudio (TYPE, VALUE) Set or display various properties of your mixer hardware. For example, if `vol' corresponds to the volume property, you can set it to 50 (percent) by `setaudio ("vol", 50)'. This is an simple experimental program to control the audio hardware settings. It assumes that there is a `mixer' program which can be used as `mixer TYPE VALUE', and simply executes `system ("mixer TYPE VALUE")'. Future releases might get rid of this assumption by using the `fcntl' interface. File: octave, Node: System Utilities, Next: Tips, Prev: Audio Processing, Up: Top System Utilities **************** This chapter describes the functions that are available to allow you to get information about what is happening outside of Octave, while it is still running, and use this information in your program. For example, you can get information about environment variables, the current time, and even start other programs from the Octave prompt. * Menu: * Timing Utilities:: * Filesystem Utilities:: * Controlling Subprocesses:: * Process ID Information:: * Environment Variables:: * Current Working Directory:: * Password Database Functions:: * Group Database Functions:: * System Information:: File: octave, Node: Timing Utilities, Next: Filesystem Utilities, Prev: System Utilities, Up: System Utilities Timing Utilities ================ Octave's core set of functions for manipulating time values are patterned after the corresponding functions from the standard C library. Several of these functions use a data structure for time that includes the following elements: `usec' Microseconds after the second (0-999999). `sec' Seconds after the minute (0-61). This number can be 61 to account for leap seconds. `min' Minutes after the hour (0-59). `hour' Hours since midnight (0-23). `mday' Day of the month (1-31). `mon' Months since January (0-11). `year' Years since 1900. `wday' Days since Sunday (0-6). `yday' Days since January 1 (0-365). `isdst' Daylight Savings Time flag. `zone' Time zone. In the descriptions of the following functions, this structure is referred to as a TM_STRUCT. - Loadable Function: time () Return the current time as the number of seconds since the epoch. The epoch is referenced to 00:00:00 CUT (Coordinated Universal Time) 1 Jan 1970. For example, on Monday February 17, 1997 at 07:15:06 CUT, the value returned by `time' was 856163706. - Function File: ctime (T) Convert a value returned from `time' (or any other nonnegative integer), to the local time and return a string of the same form as `asctime'. The function `ctime (time)' is equivalent to `asctime (localtime (time))'. For example, ctime (time ()) => "Mon Feb 17 01:15:06 1997" - Loadable Function: gmtime (T) Given a value returned from time (or any nonnegative integer), return a time structure corresponding to CUT. For example, gmtime (time ()) => { usec = 0 year = 97 mon = 1 mday = 17 sec = 6 zone = CST min = 15 wday = 1 hour = 7 isdst = 0 yday = 47 } - Loadable Function: localtime (T) Given a value returned from time (or any nonnegative integer), return a time structure corresponding to the local time zone. localtime (time ()) => { usec = 0 year = 97 mon = 1 mday = 17 sec = 6 zone = CST min = 15 wday = 1 hour = 1 isdst = 0 yday = 47 } - Loadable Function: mktime (TM_STRUCT) Convert a time structure corresponding to the local time to the number of seconds since the epoch. For example, mktime (localtime (time ()) => 856163706 - Function File: asctime (TM_STRUCT) Convert a time structure to a string using the following five-field format: Thu Mar 28 08:40:14 1996. For example, asctime (localtime (time ()) => "Mon Feb 17 01:15:06 1997\n" This is equivalent to `ctime (time ())'. - Loadable Function: strftime (TM_STRUCT) Format a time structure in a flexible way using `%' substitutions similar to those in `printf'. Except where noted, substituted fields have a fixed size; numeric fields are padded if necessary. Padding is with zeros by default; for fields that display a single number, padding can be changed or inhibited by following the `%' with one of the modifiers described below. Unknown field specifiers are copied as normal characters. All other characters are copied to the output without change. For example, strftime ("%r (%Z) %A %e %B %Y", localtime (time ()) => "01:15:06 AM (CST) Monday 17 February 1997" Octave's `strftime' function supports a superset of the ANSI C field specifiers. Literal character fields: `%' % character. `n' Newline character. `t' Tab character. Numeric modifiers (a nonstandard extension): `- (dash)' Do not pad the field. `_ (underscore)' Pad the field with spaces. Time fields: `%H' Hour (00-23). `%I' Hour (01-12). `%k' Hour (0-23). `%l' Hour (1-12). `%M' Minute (00-59). `%p' Locale's AM or PM. `%r' Time, 12-hour (hh:mm:ss [AP]M). `%R' Time, 24-hour (hh:mm). `%s' Time in seconds since 00:00:00, Jan 1, 1970 (a nonstandard extension). `%S' Second (00-61). `%T' Time, 24-hour (hh:mm:ss). `%X' Locale's time representation (%H:%M:%S). `%Z' Time zone (EDT), or nothing if no time zone is determinable. Date fields: `%a' Locale's abbreviated weekday name (Sun-Sat). `%A' Locale's full weekday name, variable length (Sunday-Saturday). `%b' Locale's abbreviated month name (Jan-Dec). `%B' Locale's full month name, variable length (January-December). `%c' Locale's date and time (Sat Nov 04 12:02:33 EST 1989). `%C' Century (00-99). `%d' Day of month (01-31). `%e' Day of month ( 1-31). `%D' Date (mm/dd/yy). `%h' Same as %b. `%j' Day of year (001-366). `%m' Month (01-12). `%U' Week number of year with Sunday as first day of week (00-53). `%w' Day of week (0-6). `%W' Week number of year with Monday as first day of week (00-53). `%x' Locale's date representation (mm/dd/yy). `%y' Last two digits of year (00-99). `%Y' Year (1970-). Most of the remaining functions described in this section are not patterned after the standard C library. Some are available for compatiblity with MATLAB and others are provided because they are useful. - Function File: clock () Return a vector containing the current year, month (1-12), day (1-31), hour (0-23), minute (0-59) and second (0-61). For example, clock () => [ 1993, 8, 20, 4, 56, 1 ] The function clock is more accurate on systems that have the `gettimeofday' function. - Function File: date () Return the date as a character string in the form DD-MMM-YY. For example, date () => "20-Aug-93" - Function File: etime (T1, T2) Return the difference (in seconds) between two time values returned from `clock'. For example: t0 = clock (); # many computations later... elapsed_time = etime (clock (), t0); will set the variable `elapsed_time' to the number of seconds since the variable `t0' was set. - Built-in Function: [TOTAL, USER, SYSTEM] = cputime (); Return the CPU time used by your Octave session. The first output is the total time spent executing your process and is equal to the sum of second and third outputs, which are the number of CPU seconds spent executing in user mode and the number of CPU seconds spent executing in system mode, respectively. If your system does not have a way to report CPU time usage, `cputime' returns 0 for each of its output values. Note that because Octave used some CPU time to start, it is reasonable to check to see if `cputime' works by checking to see if the total CPU time used is nonzero. - Function File: is_leap_year (YEAR) Return 1 if the given year is a leap year and 0 otherwise. If no arguments are provided, `is_leap_year' will use the current year. For example, is_leap_year (2000) => 1 - Function File: tic () - Function File: toc () These functions set and check a wall-clock timer. For example, tic (); # many computations later... elapsed_time = toc (); will set the variable `elapsed_time' to the number of seconds since the most recent call to the function `tic'. If you are more interested in the CPU time that your process used, you should use the `cputime' function instead. The `tic' and `toc' functions report the actual wall clock time that elapsed between the calls. This may include time spent processing other jobs or doing nothing at all. For example, tic (); sleep (5); toc () => 5 t = cputime (); sleep (5); cputime () - t => 0 (This example also illustrates that the CPU timer may have a fairly coarse resolution.) - Built-in Function: pause (SECONDS) Suspend the execution of the program. If invoked without any arguments, Octave waits until you type a character. With a numeric argument, it pauses for the given number of seconds. For example, the following statement prints a message and then waits 5 seconds before clearing the screen. fprintf (stderr, "wait please...\n"); pause (5); clc; - Built-in Function: sleep (SECONDS) Suspend the execution of the program for the given number of seconds. - Built-in Function: usleep (MICROSECONDS) Suspend the execution of the program for the given number of microseconds. On systems where it is not possible to sleep for periods of time less than one second, `usleep' will pause the execution for `round (MICROSECONDS / 1e6)' seconds.