zandbox/derivative-matrix-list.md
In r-cas/caracas: Computer Algebra
Issues with derivatives, matrices and lists/vectors
load_all()
## Loading caracas
##
## Attaching package: 'testthat'
## The following object is masked from 'package:devtools':
##
## test_file
Helper functions
do_unbracket <- function(x){
gsub("\\[(.+?)\\]", "\\1", x)
}
do_bracket <- function(x){
paste0("[", x, "]")
}
do_split_rows <- function(x){
xx3 <- strsplit(x, "\\],")[[1]]
for (i in 1:(length(xx3)-1))
xx3[i] <- paste(xx3[i], "]")
xx3
xx3 <- lapply(xx3, function(o) gsub("[[:space:]]*", "", o))
xx3
xx4 <- gsub("\\[+(.+?)\\]+", "\\1", xx3)
## split by ,
out <- strsplit(xx4, ",")
}
do_comma <- function(x){
if (is.list(x))
lapply(x, paste, collapse=", ")
else
paste0(x, collapse=", ")
}
Michaelis menten
N <- 3
y <- as_sym(matrix(paste0("y", 1:N)))
x <- as_sym(matrix(paste0("x", 1:N)))
b <- as_sym(paste0("b", 1:2))
num <- b[1] * x
den <- b[2] + x
Different representations
## mu a matrix; a convention?
mu1 <- num / den
mu1
## [caracas]: ⎡ b₁⋅x₁ b₁⋅x₂ b₁⋅x₃ ⎤
## ⎢─────── ─────── ───────⎥
## ⎣b₂ + x₁ b₂ + x₂ b₂ + x₃⎦ᵀ
symbol_is_matrix(mu1)
## [1] TRUE
mu2 <-mu1 %>% remove_mat_prefix %>% do_unbracket %>% as_sym
mu2
## [caracas]: ⎡ b₁⋅x₁ b₁⋅x₂ b₁⋅x₃ ⎤
## ⎢───────, ───────, ───────⎥
## ⎣b₂ + x₁ b₂ + x₂ b₂ + x₃⎦
symbol_is_matrix(mu2)
## [1] FALSE
mu3 <- as_sym(do_unbracket(mu2))
mu3
## [caracas]: ⎛ b₁⋅x₁ b₁⋅x₂ b₁⋅x₃ ⎞
## ⎜───────, ───────, ───────⎟
## ⎝b₂ + x₁ b₂ + x₂ b₂ + x₃⎠
symbol_is_matrix(mu3)
## [1] FALSE
mu1$pyobj
## Matrix([[b1*x1/(b2 + x1)], [b1*x2/(b2 + x2)], [b1*x3/(b2 + x3)]])
mu2$pyobj
## [b1*x1/(b2 + x1), b1*x2/(b2 + x2), b1*x3/(b2 + x3)]
mu3$pyobj
## (b1*x1/(b2 + x1), b1*x2/(b2 + x2), b1*x3/(b2 + x3))
gradients
g1 <- der(mu1, b)
g2 <- der(mu2, b)
g3 <- der(mu3, b)
g1
## [caracas]: ⎡ ⎡ -b₁⋅x₁ ⎤⎤
## ⎢ ⎢──────────⎥⎥
## ⎢⎡ x₁ ⎤ ⎢ 2⎥⎥
## ⎢⎢───────⎥ ⎢(b₂ + x₁) ⎥⎥
## ⎢⎢b₂ + x₁⎥ ⎢ ⎥⎥
## ⎢⎢ ⎥ ⎢ -b₁⋅x₂ ⎥⎥
## ⎢⎢ x₂ ⎥ ⎢──────────⎥⎥
## ⎢⎢───────⎥ ⎢ 2⎥⎥
## ⎢⎢b₂ + x₂⎥ ⎢(b₂ + x₂) ⎥⎥
## ⎢⎢ ⎥ ⎢ ⎥⎥
## ⎢⎢ x₃ ⎥ ⎢ -b₁⋅x₃ ⎥⎥
## ⎢⎢───────⎥ ⎢──────────⎥⎥
## ⎢⎣b₂ + x₃⎦ ⎢ 2⎥⎥
## ⎣ ⎣(b₂ + x₃) ⎦⎦
g2
## [caracas]: ⎡ x₁ x₂ x₃ ⎤
## ⎢ ─────── ─────── ─────── ⎥
## ⎢ b₂ + x₁ b₂ + x₂ b₂ + x₃ ⎥
## ⎢ ⎥
## ⎢ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎥
## ⎢────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
g3
## [caracas]: ⎡ x₁ x₂ x₃ ⎤
## ⎢ ─────── ─────── ─────── ⎥
## ⎢ b₂ + x₁ b₂ + x₂ b₂ + x₃ ⎥
## ⎢ ⎥
## ⎢ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎥
## ⎢────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
symbol_is_matrix(g1)
## [1] FALSE
symbol_is_matrix(g2)
## [1] FALSE
symbol_is_matrix(g3)
## [1] FALSE
g1a <- g1$pyobj %>% do_unbracket %>% as_sym
g2a <- g2$pyobj %>% do_unbracket %>% as_sym # Dimension lost
g3a <- g3$pyobj %>% do_unbracket %>% as_sym # Dimension lost
g1a
## [caracas]: ⎡ x₁ x₂ x₃ ⎤
## ⎢ ─────── ─────── ─────── ⎥
## ⎢ b₂ + x₁ b₂ + x₂ b₂ + x₃ ⎥
## ⎢ ⎥
## ⎢ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎥
## ⎢────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
g2a
## [caracas]: ⎡ x₁ x₂ x₃ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎤
## ⎢───────, ───────, ───────, ──────────, ──────────, ──────────⎥
## ⎢b₂ + x₁ b₂ + x₂ b₂ + x₃ 2 2 2⎥
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
g3a
## [caracas]: ⎡ x₁ x₂ x₃ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎤
## ⎢───────, ───────, ───────, ──────────, ──────────, ──────────⎥
## ⎢b₂ + x₁ b₂ + x₂ b₂ + x₃ 2 2 2⎥
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
symbol_is_matrix(g1a)
## [1] TRUE
symbol_is_matrix(g2a)
## [1] FALSE
symbol_is_matrix(g3a)
## [1] FALSE
Jacobi matrix
h1 <- der2(mu1, b)
h2 <- der2(mu2, b)
h3 <- der2(mu3, b)
h1
## [caracas]: ⎡ ⎡ -x₁ ⎤⎤
## ⎢ ⎢──────────⎥⎥
## ⎢ ⎢ 2⎥⎥
## ⎢ ⎢(b₂ + x₁) ⎥⎥
## ⎢ ⎢ ⎥⎥
## ⎢ ⎡0⎤ ⎢ -x₂ ⎥⎥
## ⎢ ⎢ ⎥ ⎢──────────⎥⎥
## ⎢ ⎢0⎥ ⎢ 2⎥⎥
## ⎢ ⎢ ⎥ ⎢(b₂ + x₂) ⎥⎥
## ⎢ ⎣0⎦ ⎢ ⎥⎥
## ⎢ ⎢ -x₃ ⎥⎥
## ⎢ ⎢──────────⎥⎥
## ⎢ ⎢ 2⎥⎥
## ⎢ ⎣(b₂ + x₃) ⎦⎥
## ⎢ ⎥
## ⎢⎡ -x₁ ⎤ ⎡ 2⋅b₁⋅x₁ ⎤⎥
## ⎢⎢──────────⎥ ⎢──────────⎥⎥
## ⎢⎢ 2⎥ ⎢ 3⎥⎥
## ⎢⎢(b₂ + x₁) ⎥ ⎢(b₂ + x₁) ⎥⎥
## ⎢⎢ ⎥ ⎢ ⎥⎥
## ⎢⎢ -x₂ ⎥ ⎢ 2⋅b₁⋅x₂ ⎥⎥
## ⎢⎢──────────⎥ ⎢──────────⎥⎥
## ⎢⎢ 2⎥ ⎢ 3⎥⎥
## ⎢⎢(b₂ + x₂) ⎥ ⎢(b₂ + x₂) ⎥⎥
## ⎢⎢ ⎥ ⎢ ⎥⎥
## ⎢⎢ -x₃ ⎥ ⎢ 2⋅b₁⋅x₃ ⎥⎥
## ⎢⎢──────────⎥ ⎢──────────⎥⎥
## ⎢⎢ 2⎥ ⎢ 3⎥⎥
## ⎣⎣(b₂ + x₃) ⎦ ⎣(b₂ + x₃) ⎦⎦
h2
## [caracas]: ⎡ ⎡ -x₁ -x₂ -x₃ ⎤⎤
## ⎢⎡ 0 0 0 ⎤ ⎢────────── ────────── ──────────⎥⎥
## ⎢⎢ ⎥ ⎢ 2 2 2⎥⎥
## ⎢⎢ -x₁ -x₂ -x₃ ⎥ ⎢(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎥⎥
## ⎢⎢────────── ────────── ──────────⎥ ⎢ ⎥⎥
## ⎢⎢ 2 2 2⎥ ⎢ 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎥⎥
## ⎢⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦ ⎢────────── ────────── ──────────⎥⎥
## ⎢ ⎢ 3 3 3⎥⎥
## ⎣ ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦⎦
h3
## [caracas]: ⎡ ⎡ -x₁ -x₂ -x₃ ⎤⎤
## ⎢⎡ 0 0 0 ⎤ ⎢────────── ────────── ──────────⎥⎥
## ⎢⎢ ⎥ ⎢ 2 2 2⎥⎥
## ⎢⎢ -x₁ -x₂ -x₃ ⎥ ⎢(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎥⎥
## ⎢⎢────────── ────────── ──────────⎥ ⎢ ⎥⎥
## ⎢⎢ 2 2 2⎥ ⎢ 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎥⎥
## ⎢⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦ ⎢────────── ────────── ──────────⎥⎥
## ⎢ ⎢ 3 3 3⎥⎥
## ⎣ ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦⎦
symbol_is_matrix(h1)
## [1] FALSE
symbol_is_matrix(h2)
## [1] FALSE
symbol_is_matrix(33)
## [1] FALSE
h1a <- h1$pyobj %>% do_unbracket %>% do_unbracket %>% as_sym
h2a <- h2$pyobj %>% do_unbracket %>% do_unbracket %>% as_sym # Dimension lost
h3a <- h3$pyobj %>% do_unbracket %>% do_unbracket %>% as_sym # Dimension lost
h1a
## [caracas]: ⎡ -x₁ -x₂ -x₃ ⎤
## ⎢ 0 0 0 ────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎢ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎥
## ⎢ ⎥
## ⎢ -x₁ -x₂ -x₃ 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎥
## ⎢────────── ────────── ────────── ────────── ────────── ──────────⎥
## ⎢ 2 2 2 3 3 3⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
h2a
## [caracas]: ⎡ -x₁ -x₂ -x₃ -x₁ -x₂ -x₃
## ⎢0, 0, 0, ──────────, ──────────, ──────────, ──────────, ──────────, ────────
## ⎢ 2 2 2 2 2
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃
##
## 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎤
## ──, ──────────, ──────────, ──────────⎥
## 2 3 3 3⎥
## ) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
h3a
## [caracas]: ⎡ -x₁ -x₂ -x₃ -x₁ -x₂ -x₃
## ⎢0, 0, 0, ──────────, ──────────, ──────────, ──────────, ──────────, ────────
## ⎢ 2 2 2 2 2
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃
##
## 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎤
## ──, ──────────, ──────────, ──────────⎥
## 2 3 3 3⎥
## ) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
symbol_is_matrix(h1a)
## [1] TRUE
symbol_is_matrix(h2a)
## [1] FALSE
symbol_is_matrix(h3a)
## [1] FALSE
r-cas/caracas documentation built on Feb. 28, 2025, 3:39 p.m.
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Issues with derivatives, matrices and lists/vectors
load_all()
## Loading caracas
##
## Attaching package: 'testthat'
## The following object is masked from 'package:devtools':
##
## test_file
Helper functions
do_unbracket <- function(x){
gsub("\\[(.+?)\\]", "\\1", x)
}
do_bracket <- function(x){
paste0("[", x, "]")
}
do_split_rows <- function(x){
xx3 <- strsplit(x, "\\],")[[1]]
for (i in 1:(length(xx3)-1))
xx3[i] <- paste(xx3[i], "]")
xx3
xx3 <- lapply(xx3, function(o) gsub("[[:space:]]*", "", o))
xx3
xx4 <- gsub("\\[+(.+?)\\]+", "\\1", xx3)
## split by ,
out <- strsplit(xx4, ",")
}
do_comma <- function(x){
if (is.list(x))
lapply(x, paste, collapse=", ")
else
paste0(x, collapse=", ")
}
Michaelis menten
N <- 3
y <- as_sym(matrix(paste0("y", 1:N)))
x <- as_sym(matrix(paste0("x", 1:N)))
b <- as_sym(paste0("b", 1:2))
num <- b[1] * x
den <- b[2] + x
Different representations
## mu a matrix; a convention?
mu1 <- num / den
mu1
## [caracas]: ⎡ b₁⋅x₁ b₁⋅x₂ b₁⋅x₃ ⎤
## ⎢─────── ─────── ───────⎥
## ⎣b₂ + x₁ b₂ + x₂ b₂ + x₃⎦ᵀ
symbol_is_matrix(mu1)
## [1] TRUE
mu2 <-mu1 %>% remove_mat_prefix %>% do_unbracket %>% as_sym
mu2
## [caracas]: ⎡ b₁⋅x₁ b₁⋅x₂ b₁⋅x₃ ⎤
## ⎢───────, ───────, ───────⎥
## ⎣b₂ + x₁ b₂ + x₂ b₂ + x₃⎦
symbol_is_matrix(mu2)
## [1] FALSE
mu3 <- as_sym(do_unbracket(mu2))
mu3
## [caracas]: ⎛ b₁⋅x₁ b₁⋅x₂ b₁⋅x₃ ⎞
## ⎜───────, ───────, ───────⎟
## ⎝b₂ + x₁ b₂ + x₂ b₂ + x₃⎠
symbol_is_matrix(mu3)
## [1] FALSE
mu1$pyobj
## Matrix([[b1*x1/(b2 + x1)], [b1*x2/(b2 + x2)], [b1*x3/(b2 + x3)]])
mu2$pyobj
## [b1*x1/(b2 + x1), b1*x2/(b2 + x2), b1*x3/(b2 + x3)]
mu3$pyobj
## (b1*x1/(b2 + x1), b1*x2/(b2 + x2), b1*x3/(b2 + x3))
gradients
g1 <- der(mu1, b)
g2 <- der(mu2, b)
g3 <- der(mu3, b)
g1
## [caracas]: ⎡ ⎡ -b₁⋅x₁ ⎤⎤
## ⎢ ⎢──────────⎥⎥
## ⎢⎡ x₁ ⎤ ⎢ 2⎥⎥
## ⎢⎢───────⎥ ⎢(b₂ + x₁) ⎥⎥
## ⎢⎢b₂ + x₁⎥ ⎢ ⎥⎥
## ⎢⎢ ⎥ ⎢ -b₁⋅x₂ ⎥⎥
## ⎢⎢ x₂ ⎥ ⎢──────────⎥⎥
## ⎢⎢───────⎥ ⎢ 2⎥⎥
## ⎢⎢b₂ + x₂⎥ ⎢(b₂ + x₂) ⎥⎥
## ⎢⎢ ⎥ ⎢ ⎥⎥
## ⎢⎢ x₃ ⎥ ⎢ -b₁⋅x₃ ⎥⎥
## ⎢⎢───────⎥ ⎢──────────⎥⎥
## ⎢⎣b₂ + x₃⎦ ⎢ 2⎥⎥
## ⎣ ⎣(b₂ + x₃) ⎦⎦
g2
## [caracas]: ⎡ x₁ x₂ x₃ ⎤
## ⎢ ─────── ─────── ─────── ⎥
## ⎢ b₂ + x₁ b₂ + x₂ b₂ + x₃ ⎥
## ⎢ ⎥
## ⎢ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎥
## ⎢────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
g3
## [caracas]: ⎡ x₁ x₂ x₃ ⎤
## ⎢ ─────── ─────── ─────── ⎥
## ⎢ b₂ + x₁ b₂ + x₂ b₂ + x₃ ⎥
## ⎢ ⎥
## ⎢ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎥
## ⎢────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
symbol_is_matrix(g1)
## [1] FALSE
symbol_is_matrix(g2)
## [1] FALSE
symbol_is_matrix(g3)
## [1] FALSE
g1a <- g1$pyobj %>% do_unbracket %>% as_sym
g2a <- g2$pyobj %>% do_unbracket %>% as_sym # Dimension lost
g3a <- g3$pyobj %>% do_unbracket %>% as_sym # Dimension lost
g1a
## [caracas]: ⎡ x₁ x₂ x₃ ⎤
## ⎢ ─────── ─────── ─────── ⎥
## ⎢ b₂ + x₁ b₂ + x₂ b₂ + x₃ ⎥
## ⎢ ⎥
## ⎢ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎥
## ⎢────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
g2a
## [caracas]: ⎡ x₁ x₂ x₃ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎤
## ⎢───────, ───────, ───────, ──────────, ──────────, ──────────⎥
## ⎢b₂ + x₁ b₂ + x₂ b₂ + x₃ 2 2 2⎥
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
g3a
## [caracas]: ⎡ x₁ x₂ x₃ -b₁⋅x₁ -b₁⋅x₂ -b₁⋅x₃ ⎤
## ⎢───────, ───────, ───────, ──────────, ──────────, ──────────⎥
## ⎢b₂ + x₁ b₂ + x₂ b₂ + x₃ 2 2 2⎥
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
symbol_is_matrix(g1a)
## [1] TRUE
symbol_is_matrix(g2a)
## [1] FALSE
symbol_is_matrix(g3a)
## [1] FALSE
Jacobi matrix
h1 <- der2(mu1, b)
h2 <- der2(mu2, b)
h3 <- der2(mu3, b)
h1
## [caracas]: ⎡ ⎡ -x₁ ⎤⎤
## ⎢ ⎢──────────⎥⎥
## ⎢ ⎢ 2⎥⎥
## ⎢ ⎢(b₂ + x₁) ⎥⎥
## ⎢ ⎢ ⎥⎥
## ⎢ ⎡0⎤ ⎢ -x₂ ⎥⎥
## ⎢ ⎢ ⎥ ⎢──────────⎥⎥
## ⎢ ⎢0⎥ ⎢ 2⎥⎥
## ⎢ ⎢ ⎥ ⎢(b₂ + x₂) ⎥⎥
## ⎢ ⎣0⎦ ⎢ ⎥⎥
## ⎢ ⎢ -x₃ ⎥⎥
## ⎢ ⎢──────────⎥⎥
## ⎢ ⎢ 2⎥⎥
## ⎢ ⎣(b₂ + x₃) ⎦⎥
## ⎢ ⎥
## ⎢⎡ -x₁ ⎤ ⎡ 2⋅b₁⋅x₁ ⎤⎥
## ⎢⎢──────────⎥ ⎢──────────⎥⎥
## ⎢⎢ 2⎥ ⎢ 3⎥⎥
## ⎢⎢(b₂ + x₁) ⎥ ⎢(b₂ + x₁) ⎥⎥
## ⎢⎢ ⎥ ⎢ ⎥⎥
## ⎢⎢ -x₂ ⎥ ⎢ 2⋅b₁⋅x₂ ⎥⎥
## ⎢⎢──────────⎥ ⎢──────────⎥⎥
## ⎢⎢ 2⎥ ⎢ 3⎥⎥
## ⎢⎢(b₂ + x₂) ⎥ ⎢(b₂ + x₂) ⎥⎥
## ⎢⎢ ⎥ ⎢ ⎥⎥
## ⎢⎢ -x₃ ⎥ ⎢ 2⋅b₁⋅x₃ ⎥⎥
## ⎢⎢──────────⎥ ⎢──────────⎥⎥
## ⎢⎢ 2⎥ ⎢ 3⎥⎥
## ⎣⎣(b₂ + x₃) ⎦ ⎣(b₂ + x₃) ⎦⎦
h2
## [caracas]: ⎡ ⎡ -x₁ -x₂ -x₃ ⎤⎤
## ⎢⎡ 0 0 0 ⎤ ⎢────────── ────────── ──────────⎥⎥
## ⎢⎢ ⎥ ⎢ 2 2 2⎥⎥
## ⎢⎢ -x₁ -x₂ -x₃ ⎥ ⎢(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎥⎥
## ⎢⎢────────── ────────── ──────────⎥ ⎢ ⎥⎥
## ⎢⎢ 2 2 2⎥ ⎢ 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎥⎥
## ⎢⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦ ⎢────────── ────────── ──────────⎥⎥
## ⎢ ⎢ 3 3 3⎥⎥
## ⎣ ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦⎦
h3
## [caracas]: ⎡ ⎡ -x₁ -x₂ -x₃ ⎤⎤
## ⎢⎡ 0 0 0 ⎤ ⎢────────── ────────── ──────────⎥⎥
## ⎢⎢ ⎥ ⎢ 2 2 2⎥⎥
## ⎢⎢ -x₁ -x₂ -x₃ ⎥ ⎢(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎥⎥
## ⎢⎢────────── ────────── ──────────⎥ ⎢ ⎥⎥
## ⎢⎢ 2 2 2⎥ ⎢ 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎥⎥
## ⎢⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦ ⎢────────── ────────── ──────────⎥⎥
## ⎢ ⎢ 3 3 3⎥⎥
## ⎣ ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦⎦
symbol_is_matrix(h1)
## [1] FALSE
symbol_is_matrix(h2)
## [1] FALSE
symbol_is_matrix(33)
## [1] FALSE
h1a <- h1$pyobj %>% do_unbracket %>% do_unbracket %>% as_sym
h2a <- h2$pyobj %>% do_unbracket %>% do_unbracket %>% as_sym # Dimension lost
h3a <- h3$pyobj %>% do_unbracket %>% do_unbracket %>% as_sym # Dimension lost
h1a
## [caracas]: ⎡ -x₁ -x₂ -x₃ ⎤
## ⎢ 0 0 0 ────────── ────────── ──────────⎥
## ⎢ 2 2 2⎥
## ⎢ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎥
## ⎢ ⎥
## ⎢ -x₁ -x₂ -x₃ 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎥
## ⎢────────── ────────── ────────── ────────── ────────── ──────────⎥
## ⎢ 2 2 2 3 3 3⎥
## ⎣(b₂ + x₁) (b₂ + x₂) (b₂ + x₃) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
h2a
## [caracas]: ⎡ -x₁ -x₂ -x₃ -x₁ -x₂ -x₃
## ⎢0, 0, 0, ──────────, ──────────, ──────────, ──────────, ──────────, ────────
## ⎢ 2 2 2 2 2
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃
##
## 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎤
## ──, ──────────, ──────────, ──────────⎥
## 2 3 3 3⎥
## ) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
h3a
## [caracas]: ⎡ -x₁ -x₂ -x₃ -x₁ -x₂ -x₃
## ⎢0, 0, 0, ──────────, ──────────, ──────────, ──────────, ──────────, ────────
## ⎢ 2 2 2 2 2
## ⎣ (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃
##
## 2⋅b₁⋅x₁ 2⋅b₁⋅x₂ 2⋅b₁⋅x₃ ⎤
## ──, ──────────, ──────────, ──────────⎥
## 2 3 3 3⎥
## ) (b₂ + x₁) (b₂ + x₂) (b₂ + x₃) ⎦
symbol_is_matrix(h1a)
## [1] TRUE
symbol_is_matrix(h2a)
## [1] FALSE
symbol_is_matrix(h3a)
## [1] FALSE
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