MATLAB 5.0 Enhancements (Upgrading from MATLAB 4 to MATLAB 5.0)

Upgrading from MATLAB 4 to MATLAB 5.0

New and Enhanced Language Functions

MATLAB 5.0 provided a large number of new language functions as well as enhancements to existing functions.

**Table 1-9: New Elementary and Specialized Math Functions**
Function	Description
`airy`	Airy functions.
`besselh`	Bessel functions of the third kind (Hankel).
`condeig`	Condition number with respect to eigenvalues.
`condest`	1-norm matrix condition estimate.
`dblquad`	Numerical double integration
`mod`	Modulus (signed remainder after division).
`normest`	2-norm estimate.

**Table 1-10: New Time and Date Functions**
Function	Description
`calendar`	Calendar.
`datenum`	Serial date number.
`datestr`	Create date string.
`datetick`	Date formatted tick labels.
`datevec`	Date components.
`eomday`	End of month.
`now`	Current date and time.
`weekday`	Day of the week.

**Table 1-11: New Ordinary Differential Equation Functions**
Function	Description
`ode45, ode23, ode113, ode23s, ode15s`	Solve differential equations, low- and high- order methods.
`odefile`	Define a differential equation problem for ODE solvers.
`odeget`	Extract options from an argument created with `odeset`.
`odeset`	Create and edit input arguments for ODE solvers.

**Table 1-12: New Matrix Functions**
Function	Description
`cholinc`	Incomplete Cholesky factorization.
`gallery`	More than 50 new test matrices.
`luinc`	Incomplete LU factorization.
`repmat`	Replicate and tile an array.
`sprand`	Random uniformly distributed sparse matrices.

**Table 1-13: New Methods for Sparse Matrices**
Method	Description
`bicg`	BiConjugate Gradients method.
`bicgstab`	BiConjugate Gradients Stabilized method.
`cgs`	Conjugate Gradients Squared method.
`eigs`	Find a few eigenvalues and eigenvectors.
`gmres`	Generalized Minimum Residual method.
`pcg`	Preconditioned Conjugate Gradients method.
`qmr`	Quasi-Minimal Residual method.
`svds`	A few singular values.

Subscripting and Assignment Enhancements

In MATLAB 5.0, you can:

Access the last element of an array using the end keyword.
Obtain consistent results for indexing expressions consisting of all ones.
Use scalar expansion in subarray assignments.

A statement like A(ones([m,n])) now always returns an m-by-n array in which each element is A(1). In previous versions, the statement returned different results depending on whether A was or was not an m-by-n matrix.

In previous releases, expressions like A(2:3,4:5) = 5 resulted in an error. MATLAB 5.0 automatically "expands" the 5 to be the right size (that is, 5*ones(2,2)).

Integer Bit Manipulation Functions

The ops directory contains commands that permit bit-level operations on integers. Operations include setting and unsetting, complementing, shifting, and logical AND, OR, and XOR.

**Table 1-14: New Bitwise Functions**
Function	Description
`bitand`	Bitwise `AND`.
`bitcmp`	Complement bits.
`bitget`	Get bit.
`bitmax`	Maximum floating-point integer.
`bitor`	Bitwise `OR`.
`bitset`	Set bit.
`bitshift`	Bitwise shift.
`bitxor`	Bitwise `XOR`.

Dimension Specification for Data Analysis Functions

MATLAB's basic data analysis functions now enable you to supply a second input argument. This argument specifies the dimension along which the function operates. For example, create an array A:

A = [3 2 4; 1 0 5; 8 2 6];

To sum along the first dimension of A, incrementing the row index, specify 1 for the dimension of operation:

sum(A,1)

ans =

    12     4    15

To sum along the second dimension, incrementing the column index, specify 2 for the dimension:

sum(A,2)

ans =

     9
     6
    16

Other functions that accept the dimension specifier include prod, cumprod, and cumsum.

Wildcards in Utility Commands

The asterisk (*) can be used as a wildcard in the clear and whos commands. This allows you, for example, to clear only variables beginning with a given character or characters, as in

clear A*

Empty Arrays

Earlier versions of MATLAB allowed for only one empty matrix, the 0-by-0 matrix denoted by []. MATLAB 5.0 provided for matrices and arrays in which some, but not all, of the dimensions are zero. For example, 1-by-0, 10-by-0-by-20, and [3 4 0 5 2] are all possible array sizes.

The two-character sequence [] continues to denote the 0-by-0 matrix. Empty arrays of other sizes can be created with the functions zeros, ones, rand, or eye. To create a 0-by-5 matrix, for example, use

E = zeros(0,5)

The basic model for empty matrices is that any operation that is defined for m-by-n matrices, and that produces a result with a dimension that is some function of m and n, should still be allowed when m or n is zero. The size of the result should be that same function, evaluated at zero.

For example, horizontal concatenation

C = [A B]

requires that A and B have the same number of rows. So if A is m-by-n and B is m-by-p, then C is m-by-(n+p). This is still true if m or n or p is zero.

Many operations in MATLAB produce row vectors or column vectors. It is now possible for the result to be the empty row vector

r = zeros(1,0)

or the empty column vector

c = zeros(0,1)

Some MATLAB functions, like sum and max, are reductions. For matrix arguments, these functions produce vector results; for vector arguments they produce scalar results. Backwards compatibility issues arise for the argument [], which in MATLAB 4 played the role of both the empty matrix and the empty vector. In MATLAB 5.0, empty inputs with these functions produce these results:

sum([]) is 0
prod([]) is 1
max([]) is []
min([]) is []

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