Incompatible dimensions in building constraints

[jywang2016]

Hi! Thanks for your (and your team) amazing work in CVXR package. I use this package for some control purposes, and an Error appeared when I try to build constraints about state-space equations.

` library(CVXR)

A <- matrix(c(2,-1,1,0.2),byrow = T,nrow = 2)
B <- matrix(c(1,0),byrow = T,nrow = 2)

N <- 7
Q <- diag(2)
R <- 2
N <- 7

x0 <- matrix(c(3,1),byrow = T)
u <- Variable(rows = 1, cols = N)
x <- Variable(rows = 2, cols = N)
objective <- Minimize(sum(Q %% x) + sum(R %% u))

constraints <- list(u >= -1,
u <= 1 ,
x >= -5,
x <= 5,
x[,1] == x0,
#x[,2:N] == A %% x[,1:(N-1)] + B %% u[,1:(N-1)]
x[,2] == A %% x[,1] + B %% u[,1]) `

Error in mul_shapes(size(object@args[[1]]), size(object@args[[2]])) : Incompatible dimensions.
If I use the second last lines ( #x[,2:N] == A %*% x[,1:(N-1)] + B %*% u[,1:(N-1)] ), the console proceed with an Error like above. I have to use the for loop to complete modeling (add constraints one by one). And the dimensions in the second last lines seem compatible.

By the way, I have another try on the building constraints for the one-dimension state-space equation in the way like x[2:N] == A %*% x[1:(N-1)] + B %*% u[1:(N-1)], it works. Therefore, I am not sure the problem lies in syntax or the matrix multiplication bug.

Thanks for your help!

[bnaras]

Please provide a full reproducible example. The above is syntactically wrong, and incomplete.

[bnaras]

Here. for example, is what I get after fixing the syntax.

> library(CVXR)
> A <- matrix(c(2,-1,1,0.2),byrow = T,nrow = 2)
> B <- matrix(c(1,0),byrow = T,nrow = 2)
> N <- 7
> Q <- diag(2)
> R <- 2
> N <- 7
> x0 <- matrix(c(3,1),byrow = T)
> u <- Variable(rows = 1, cols = N)
> x <- Variable(rows = 2, cols = N)
> objective <- Minimize(sum(Q %*% x) + sum(R %*% u))
> constraints <- list(u >= -1,
+ u <= 1 ,
+ x >= -5,
+ x <= 5,
+ x[,1] == x0,
+ x[,2] == A %*% x[,1] + B %*% u[,1])
> p <- Problem(objective, constraints)
> res <- solve(p)
res$getValue(u)
res$getValue(x)
>  
    [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]   -1   -1   -1   -1   -1   -1   -1
>  
    [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    3  4.0   -5   -5   -5   -5   -5
[2,]    1  3.2   -5   -5   -5   -5   -5
> res$getValue(x)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    3  4.0   -5   -5   -5   -5   -5
[2,]    1  3.2   -5   -5   -5   -5   -5
> res$getValue(x)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    3  4.0   -5   -5   -5   -5   -5
[2,]    1  3.2   -5   -5   -5   -5   -5

[jywang2016]

Thanks for your reply. I'm sorry for these mistakes.
In my case, here is the code:

library(CVXR)
A <- matrix(c(2,-1,1,0.2),byrow = T,nrow = 2)
B <- matrix(c(1,0),byrow = T,nrow = 2)
N <- 7
Q <- diag(2)
R <- 2

x0 <- matrix(c(3,1),byrow = T)
u <- Variable(rows = 1, cols = N)
x <- Variable(rows = 2, cols = N)
objective <- Minimize(sum(Q %*% x) + sum(R %*% u))
constraints <- list(u >= -1,
                    u <= 1 ,
                    x >= -5,
                    x <= 5,
                    x[,1] == x0,
                    x[,2] == A %*% x[,1] + B %*% u[,1])

for(i in 3:N)
{
  constraints <- c(constraints, x[,i] == A %*% x[,i-1] + B %*% u[,i-1])
}

p <- Problem(objective, constraints)
res <- solve(p)
res$getValue(u)
res$getValue(x)

The chunk above is reproducible and complete. The point concerned is why can't I just use x[,2:N] == A %*% x[,1:(N-1)] + B %*% u[,1:(N-1)] to build the constraints. If I modify the code as follows:

library(CVXR)
A <- matrix(c(2,-1,1,0.2),byrow = T,nrow = 2)
B <- matrix(c(1,0),byrow = T,nrow = 2)
N <- 7
Q <- diag(2)
R <- 2

x0 <- matrix(c(3,1),byrow = T)
u <- Variable(rows = 1, cols = N)
x <- Variable(rows = 2, cols = N)
objective <- Minimize(sum(Q %*% x) + sum(R %*% u))
constraints <- list(u >= -1,
                    u <= 1 ,
                    x >= -5,
                    x <= 5,
                    x[,1] == x0,
                    x[,2:N] == A %*% x[,1:(N-1)] + B %*% u[,1:(N-1)])

# why can't I just use x[,2:N] == A %*% x[,1:(N-1)] + B %*% u[,1:(N-1)]

p <- Problem(objective, constraints)
res <- solve(p)
res$getValue(u)
res$getValue(x)

The error Error in mul_shapes(size(object@args[[1]]), size(object@args[[2]])) : Incompatible dimensions would appear in the console. I think that dimensions are correct after checking twice. And I want to know where is the mistake.

Thanks for your help!

[bnaras]

This appears to be a bug, most likely a dimension being dropped in the indexing (drop=FALSE in R parlance). Here is a simplified example that will make its way into our future tests.

> B <- matrix(c(1,0),byrow = T,nrow = 2)
> N <- 7
> u <- Variable(rows = 1, cols = N)
> B %*% u[, 1:(N-1)]  ## Fails when result should be 2 x 6
Error in mul_shapes(size(object@args[[1]]), size(object@args[[2]])) : 
  Incompatible dimensions
> B <- matrix(c(1,0,0,1),byrow = T,nrow = 2)
> u <- Variable(rows = 2, cols = N)
> B %*% u[, 1:(N-1)]
MulExpression(Constant(CONSTANT, POSITIVE, (2,2)), c("Expression(AFFINE, UNKNOWN, 2)", "Expression(AFFINE, UNKNOWN, 6)"))> 

[jywang2016]

Thanks for your help! Looking forward to the future version of CVXR.

[bnaras]

Fixed in version 0.97.