| Type: | Package |
| Title: | Functions of Complex or Real Variable |
| Version: | 2.1 |
| Date: | 2017-05-18 |
| Author: | Albert Dorador and Uffe Høgsbro Thygesen |
| Maintainer: | Albert Dorador <albert.dorador@estudiant.upc.edu> |
| Description: | Extension of several functions to the complex domain, including the matrix exponential and logarithm, and the determinant. |
| Depends: | R (≥ 3.1.0) |
| Imports: | expm (≥ 0.999-2), Matrix (≥ 1.2-6) |
| License: | GPL-2 |
| ByteCompile: | true |
| Encoding: | UTF-8 |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2017-05-18 07:33:18 UTC; Albert |
| Repository: | CRAN |
| Date/Publication: | 2017-05-18 08:26:26 UTC |
Compute the Determinant of a Matrix
Description
Det computes the determinant of a square matrix.
This function first checks whether the matrix is full rank or not; if not,
the value 0 is returned. This avoids relatively frequent numerical errors
that produce a non-zero determinant when in fact it is zero.
Only if the matrix is full rank does the algorithm proceed to compute the determinant.
If the matrix is complex, the determinant is computed as the product of the eigenvalues; if the matrix
is real, Det calls the base function det for maximum efficiency.
Usage
Det(M)
Arguments
M |
a square matrix, real or complex. |
Value
The determinant of M.
Author(s)
Albert Dorador
Examples
A <- matrix(c(1, 2, 2+3i, 5), ncol = 2) #complex matrix
B <- matrix(1:4, ncol = 2) #real matrix
S <- matrix(c(3, 4+3i, 0, 0), ncol = 2) #Singular matrix
Det(A)
Det(B)
Det(S)
Rounding of Null Imaginary Part of a Complex Number
Description
imaginary parts with values very close to 0 are 'zapped', i.e. treated as 0. Therefore, the number becomes real and changes its class from complex to numeric.
Usage
Imzap(x, tol = 1e-06)
Arguments
x |
a scalar or vector, real or complex. |
tol |
a tolerance, |
Author(s)
Albert Dorador
Examples
x1 <- 1:100
x2 <- c(1:98,2+3i,0-5i)
x3 <- c(1:98,2+0i,7-0i)
x4 <- complex(real = rnorm(100), imaginary = rnorm(100))
Imzap(x1) # inocuous with real vectors
Imzap(x2) # 1 single element is enough to turn the vector into complex
Imzap(x3) # removes extra 0i and changes class from from complex to numeric
Imzap(x4) # inocuous with complex vectors with non-null complex part
Matrix Class
Description
matclass gives the name of the class of the matrix.
If the class of the matrix elements is numeric or integer, the matrix class is real by default.
Usage
matclass(M, real = TRUE)
Arguments
M |
a matrix, of any type and dimensions. |
real |
a logical value. Set to FALSE if you want to opt out of the default treatment of numeric or integer elements. |
Author(s)
Albert Dorador
Examples
A <- matrix(c(1, 2, 2+3i, 5), ncol = 2) # complex matrix
B <- matrix(1:4, ncol = 2) # real matrix
C <- matrix(c(TRUE, TRUE, FALSE, FALSE), ncol = 2) # boolean matrix
D <- matrix(c('a', 'b', 'c', 'd'), ncol = 2) # character matrix
E <- matrix(c(1,2+3i,'a',TRUE),ncol=2) # 1 single character makes it a character matrix
matclass(A)
matclass(B)
matclass(B,FALSE)
matclass(C)
matclass(D)
matclass(E)
Matrix Exponential
Description
matexp computes the exponential of a square matrix A i.e. exp(A).
Usage
matexp(A, ...)
Arguments
A |
a square matrix, real or complex. |
... |
arguments passed to or from other methods. |
Details
This function adapts function expm from package expm
to be able to handle complex matrices, by decomposing the original
matrix into real and purely imaginary matrices and creating a real
block matrix that function expm can successfully process.
If the original matrix is real, matexp calls expm directly for maximum efficiency.
Value
The matrix exponential of A. Method used may be chosen from the options available in expm.
Author(s)
Uffe Høgsbro Thygesen
See Also
Examples
A <- matrix(c(1, 2, 2+3i, 5), ncol = 2) # complex matrix
B <- matrix(1:4, ncol = 2) # real matrix
matexp(A)
matexp(A, "Ward77") # uses Ward77's method in function expm
matexp(B)
matexp(B, "Taylor") # uses Taylor's method in function expm
Matrix Logarithm
Description
matlog computes the (principal) matrix logarithm of a square matrix.
Usage
matlog(A, ...)
Arguments
A |
a square matrix, real or complex. |
... |
arguments passed to or from other methods. |
Details
This function adapts function logm from package expm
to be able to handle complex matrices, by decomposing the original matrix
into real and purely imaginary matrices and creating a real
block matrix that function logm can successfully process.
If the original matrix is real, matlog calls logm directly for maximum efficiency.
Hence, for real matrices, matlog can compute the matrix logarithm in the same instances as logm;
for complex matrices, matlog can compute the matrix logarithm as long as all real
eigenvalues are positive: zero eigenvalues imply singularity (and therefore the log
does not exist) and negative eigenvalues can be problematic as it may be hard and
numerically unstable to calculate Jordan blocks. See references below.
Value
The matrix logarithm of A. Method used may be chosen from the options available in logm.
Author(s)
Albert Dorador
References
For more on the matrix logarithm, visit https://en.wikipedia.org/wiki/Logarithm_of_a_matrix
See Also
Examples
A <- matrix(c(1, 2, 2+3i, 5), ncol = 2) # complex matrix
B <- matrix(c(2, 0, 3, 4), ncol = 2) # real matrix with positive eigenvalues
matlog(A)
matlog(A, "Eigen") # uses Eigen method in function logm
matlog(B)
matlog(B, "Eigen") # uses Eigen method in function logm