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pascal

Pascal matrix

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Syntax

P = pascal(n)
P = pascal(n,1)
P = pascal(n,2)
P = pascal(___,classname)

Description

example

P = pascal(n)返回一个Pascal’s Matrixof ordern.Pis a symmetric positive definite matrix with integer entries taken from Pascal's triangle. The inverse ofPhas integer entries.

P = pascal(n,1)returns the lower triangular Cholesky factor (up to the signs of the columns) of the Pascal matrix.Pisinvolutary, that is, it is its own inverse.

P = pascal(n,2)返回一个transposed and permuted version ofpascal(n,1). In this case,Pis a cube root of the identity matrix.

P = pascal(___,classname)返回一个matrix of classclassnameusing any of the input argument combinations in previous syntaxes.classnamecan be'single'or'double'.

Examples

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Open Live Script

Compute the fourth-order Pascal matrix.

A = pascal(4)
A =1 1 1 1 1 2 3 4 1 3 6 10 1 4 10 20

Compute the lower triangular Cholesky factor of the third-order Pascal matrix, and verify it is involutary.

A = pascal(3,1)
A =1 0 0 1 -1 0 1 -2 1
inv(A)
ans =1 0 0 1 -1 0 1 -2 1

Input Arguments

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Matrix order, specified as a scalar, nonnegative integer.

Example:pascal(10)

Data Types:single|double|int8|int16|int32|int64|uint8|uint16|uint32|uint64|logical|char

Matrix class, specified as either'double'or'single'.

Example:pascal(10,'single')

Data Types:char

More About

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Pascal’s Matrix

Pascal’s triangle is a triangle formed by rows of numbers. The first row has entry1. Each succeeding row is formed by adding adjacent entries of the previous row, substituting a0where no adjacent entry exists. Thepascal函数形式Pascal’s matrix by selecting the portion of Pascal’s triangle that corresponds to the specified matrix dimensions, as outlined in the graphic. The matrix outlined corresponds to the MATLAB®commandpascal(4).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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Introduced before R2006a

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