# 15.3 Class Env¶

- mosek.Env¶
The

**MOSEK**global environment.

- Env.Env¶
Env()

Env(licensefile=None, debugfile=None)

Constructor of a new environment.

- Parameters:
`licensefile`

(`str`

) – License file to use. (input)`debugfile`

(`str`

) – File where the memory debugging log is written. (input)

- Env.Task¶
Task() -> task

Task(numcon, numvar) -> task

Creates a new task.

- Parameters:
`numcon`

(`int`

) – An optional hint about the maximal number of constraints in the task. (input)`numvar`

(`int`

) – An optional hint about the maximal number of variables in the task. (input)

- Return:
`task`

(`Task`

) – A new task.

- Env.__del__¶
__del__()

Free the underlying native allocation.

- Env.axpy¶
axpy(n,alpha,x,y)

Adds \(\alpha x\) to \(y\), i.e. performs the update

\[y := \alpha x + y.\]Note that the result is stored overwriting \(y\). It must not overlap with the other input arrays.

- Parameters:
`n`

(`int`

) – Length of the vectors. (input)`alpha`

(`float`

) – The scalar that multiplies \(x\). (input)`x`

(`float`

`[]`

) – The \(x\) vector. (input)`y`

(`float`

`[]`

) – The \(y\) vector. (input/output)

- Groups:

- Env.checkinall¶
checkinall()

Check in all unused license features to the license token server.

- Groups:

- Env.checkinlicense¶
checkinlicense(feature)

Check in a license feature to the license server. By default all licenses consumed by functions using a single environment are kept checked out for the lifetime of the

**MOSEK**environment. This function checks in a given license feature back to the license server immediately.If the given license feature is not checked out at all, or it is in use by a call to

`Task.optimize`

, calling this function has no effect.Please note that returning a license to the license server incurs a small overhead, so frequent calls to this function should be avoided.

- Parameters:
`feature`

(`mosek.feature`

) – Feature to check in to the license system. (input)- Groups:

- Env.checkoutlicense¶
checkoutlicense(feature)

Checks out a license feature from the license server. Normally the required license features will be automatically checked out the first time they are needed by the function

`Task.optimize`

. This function can be used to check out one or more features ahead of time.The feature will remain checked out until the environment is deleted or the function

`Env.checkinlicense`

is called.If a given feature is already checked out when this function is called, the call has no effect.

- Parameters:
`feature`

(`mosek.feature`

) – Feature to check out from the license system. (input)- Groups:

- Env.computesparsecholesky¶
computesparsecholesky(numthreads, ordermethod, tolsingular, anzc, aptrc, asubc, avalc) -> (perm, diag, lnzc, lptrc, lensubnval, lsubc, lvalc)

The function computes a Cholesky factorization of a sparse positive semidefinite matrix. Sparsity is exploited during the computations to reduce the amount of space and work required. Both the input and output matrices are represented using the sparse format.

To be precise, given a symmetric matrix \(A \in \real^{n\times n}\) the function computes a nonsingular lower triangular matrix \(L\), a diagonal matrix \(D\) and a permutation matrix \(P\) such that

\[LL^T - D = P A P^T.\]If

`ordermethod`

is zero then reordering heuristics are not employed and \(P\) is the identity.If a pivot during the computation of the Cholesky factorization is less than

\[-\rho\cdot\max((PAP^T)_{jj},1.0)\]then the matrix is declared negative semidefinite. On the hand if a pivot is smaller than

\[\rho\cdot\max((PAP^T)_{jj},1.0),\]then \(D_{jj}\) is increased from zero to

\[\rho\cdot\max((PAP^T)_{jj},1.0).\]Therefore, if \(A\) is sufficiently positive definite then \(D\) will be the zero matrix. Here \(\rho\) is set equal to value of

`tolsingular`

.- Parameters:
`numthreads`

(`int`

) – The number threads that can be used to do the computation. 0 means the code makes the choice. NOTE: API change in version 10: in versions up to 9 the argument in this position indicated whether to use multithreading or not. (input)`ordermethod`

(`int`

) – If nonzero, then a sparsity preserving ordering will be employed. (input)`tolsingular`

(`float`

) – A positive parameter controlling when a pivot is declared zero. (input)`anzc`

(`int`

`[]`

) –`anzc[j]`

is the number of nonzeros in the \(j\)-th column of \(A\). (input)`aptrc`

(`int`

`[]`

) –`aptrc[j]`

is a pointer to the first element in column \(j\) of \(A\). (input)`asubc`

(`int`

`[]`

) – Row indexes for each column stored in increasing order. (input)`avalc`

(`float`

`[]`

) – The value corresponding to row indexed stored in`asubc`

. (input)

- Return:
`perm`

(`int`

`[]`

) – Permutation array used to specify the permutation matrix \(P\) computed by the function.`diag`

(`float`

`[]`

) – The diagonal elements of matrix \(D\).`lnzc`

(`int`

`[]`

) –`lnzc[j]`

is the number of non zero elements in column \(j\) of \(L\).`lptrc`

(`int`

`[]`

) –`lptrc[j]`

is a pointer to the first row index and value in column \(j\) of \(L\).`lensubnval`

(`int`

) – Number of elements in`lsubc`

and`lvalc`

.`lsubc`

(`int`

`[]`

) – Row indexes for each column stored in increasing order.`lvalc`

(`float`

`[]`

) – The values corresponding to row indexed stored in`lsubc`

.

- Groups:

- Env.dot¶
dot(n,x,y) -> (xty)

Computes the inner product of two vectors \(x,y\) of length \(n\geq 0\), i.e

\[x\cdot y= \sum_{i=1}^n x_i y_i.\]Note that if \(n=0\), then the result of the operation is 0.

- Parameters:
`n`

(`int`

) – Length of the vectors. (input)`x`

(`float`

`[]`

) – The \(x\) vector. (input)`y`

(`float`

`[]`

) – The \(y\) vector. (input)

- Return:
`xty`

(`float`

) – The result of the inner product between \(x\) and \(y\).- Groups:

- Env.echointro¶
echointro(longver)

Prints an intro to message stream.

- Parameters:
`longver`

(`int`

) – If non-zero, then the intro is slightly longer. (input)- Groups:

- Env.expirylicenses¶
expirylicenses() -> (expiry)

Reports when the first license feature expires. It reports the number of days to the expiry of the first feature of all the features that were ever checked out from the start of the process, or from the last call to

`Env.resetexpirylicenses`

, until now.- Return:
`expiry`

(`int`

) – If nonnegative, then it is the minimum number days to expiry of any feature that has been checked out.- Groups:

- Env.gemm¶
gemm(transa,transb,m,n,k,alpha,a,b,beta,c)

Performs a matrix multiplication plus addition of dense matrices. Given \(A\), \(B\) and \(C\) of compatible dimensions, this function computes

\[C:= \alpha op(A)op(B) + \beta C\]where \(\alpha,\beta\) are two scalar values. The function \(op(X)\) denotes \(X\) if transX is

`transpose.no`

, or \(X^T\) if set to`transpose.yes`

. The matrix \(C\) has \(m\) rows and \(n\) columns, and the other matrices must have compatible dimensions.The result of this operation is stored in \(C\). It must not overlap with the other input arrays.

- Parameters:
`transa`

(`mosek.transpose`

) – Indicates whether the matrix \(A\) must be transposed. (input)`transb`

(`mosek.transpose`

) – Indicates whether the matrix \(B\) must be transposed. (input)`m`

(`int`

) – Indicates the number of rows of matrix \(C\). (input)`n`

(`int`

) – Indicates the number of columns of matrix \(C\). (input)`k`

(`int`

) – Specifies the common dimension along which \(op(A)\) and \(op(B)\) are multiplied. For example, if neither \(A\) nor \(B\) are transposed, then this is the number of columns in \(A\) and also the number of rows in \(B\). (input)`alpha`

(`float`

) – A scalar value multiplying the result of the matrix multiplication. (input)`a`

(`float`

`[]`

) – The pointer to the array storing matrix \(A\) in a column-major format. (input)`b`

(`float`

`[]`

) – The pointer to the array storing matrix \(B\) in a column-major format. (input)`beta`

(`float`

) – A scalar value that multiplies \(C\). (input)`c`

(`float`

`[]`

) – The pointer to the array storing matrix \(C\) in a column-major format. (input/output)

- Groups:

- Env.gemv¶
gemv(transa,m,n,alpha,a,x,beta,y)

Computes the multiplication of a scaled dense matrix times a dense vector, plus a scaled dense vector. Precisely, if

`trans`

is`transpose.no`

then the update is\[y := \alpha A x + \beta y,\]and if

`trans`

is`transpose.yes`

then\[y := \alpha A^T x + \beta y,\]where \(\alpha,\beta\) are scalar values and \(A\) is a matrix with \(m\) rows and \(n\) columns.

Note that the result is stored overwriting \(y\). It must not overlap with the other input arrays.

- Parameters:
`transa`

(`mosek.transpose`

) – Indicates whether the matrix \(A\) must be transposed. (input)`m`

(`int`

) – Specifies the number of rows of the matrix \(A\). (input)`n`

(`int`

) – Specifies the number of columns of the matrix \(A\). (input)`alpha`

(`float`

) – A scalar value multiplying the matrix \(A\). (input)`a`

(`float`

`[]`

) – A pointer to the array storing matrix \(A\) in a column-major format. (input)`x`

(`float`

`[]`

) – A pointer to the array storing the vector \(x\). (input)`beta`

(`float`

) – A scalar value multiplying the vector \(y\). (input)`y`

(`float`

`[]`

) – A pointer to the array storing the vector \(y\). (input/output)

- Groups:

- Env.getcodedesc¶
@staticmethod getcodedesc(code) -> (symname,str)

Obtains a short description of the meaning of the response code given by

`code`

.- Parameters:
`code`

(`mosek.rescode`

) – A valid**MOSEK**response code. (input)- Return:
`symname`

(`str`

) – Symbolic name corresponding to`code`

.`str`

(`str`

) – Obtains a short description of a response code.

- Groups:

- Env.getversion¶
@staticmethod getversion() -> (major,minor,revision)

Obtains

**MOSEK**version information.- Return:
`major`

(`int`

) – Major version number.`minor`

(`int`

) – Minor version number.`revision`

(`int`

) – Revision number.

- Groups:

- Env.licensecleanup¶
@staticmethod licensecleanup()

Stops all threads and deletes all handles used by the license system. If this function is called, it must be called as the last

**MOSEK**API call. No other**MOSEK**API calls are valid after this.- Groups:

- Env.linkfiletostream¶
linkfiletostream(whichstream,filename,append)

Sends all output from the stream defined by

`whichstream`

to the file given by`filename`

.- Parameters:
`whichstream`

(`mosek.streamtype`

) – Index of the stream. (input)`filename`

(`str`

) – A valid file name. (input)`append`

(`int`

) – If this argument is 0 the file will be overwritten, otherwise it will be appended to. (input)

- Groups:

- Env.optimizebatch¶
optimizebatch(israce, maxtime, numthreads, task, trmcode, rcode)

optimizebatch(israce,maxtime,numthreads,task) -> (trmcode,rcode)

Optimize a number of tasks in parallel using a specified number of threads. All callbacks and log output streams are disabled.

Assuming that each task takes about same time and there many more tasks than number of threads then a linear speedup can be achieved, also known as strong scaling. A typical application of this method is to solve many small tasks of similar type; in this case it is recommended that each of them is allocated a single thread by setting

`iparam.num_threads`

to \(1\).If the parameters

`israce`

or`maxtime`

are used, then the result may not be deterministic, in the sense that the tasks which complete first may vary between runs.The remaining behavior, including termination and response codes returned for each task, are the same as if each task was optimized separately.

- Parameters:
`israce`

(`bool`

) – If nonzero, then the function is terminated after the first task has been completed. (input)`maxtime`

(`float`

) – Time limit for the function: if nonnegative, then the function is terminated after maxtime (seconds) has expired. (input)`numthreads`

(`int`

) – Number of threads to be employed. (input)`task`

(`Task`

`[]`

) – An array of tasks to optimize in parallel. (input)`trmcode`

(`mosek.rescode`

`[]`

) – The termination code for each task. (output)`rcode`

(`mosek.rescode`

`[]`

) – The response code for each task. (output)

- Return:
`trmcode`

(`mosek.rescode`

`[]`

) – The termination code for each task.`rcode`

(`mosek.rescode`

`[]`

) – The response code for each task.

- Groups:

- Env.potrf¶
potrf(uplo,n,a)

Computes a Cholesky factorization of a real symmetric positive definite dense matrix.

- Parameters:
`uplo`

(`mosek.uplo`

) – Indicates whether the upper or lower triangular part of the matrix is stored. (input)`n`

(`int`

) – Dimension of the symmetric matrix. (input)`a`

(`float`

`[]`

) – A symmetric matrix stored in column-major order. Only the lower or the upper triangular part is used, accordingly with the`uplo`

parameter. It will contain the result on exit. (input/output)

- Groups:

- Env.putlicensecode¶
putlicensecode(code)

Input a runtime license code. This function has an effect only before the first optimization.

- Parameters:
`code`

(`int`

`[]`

) – A runtime license code. (input)- Groups:

- Env.putlicensedebug¶
putlicensedebug(licdebug)

Enables debug information for the license system. If

`licdebug`

is non-zero, then**MOSEK**will print debug info regarding the license checkout.- Parameters:
`licdebug`

(`int`

) – Whether license checkout debug info should be printed. (input)- Groups:

- Env.putlicensepath¶
putlicensepath(licensepath)

Set the path to the license file. This function has an effect only before the first optimization.

- Parameters:
`licensepath`

(`str`

) – A path specifying where to search for the license. (input)- Groups:

- Env.putlicensewait¶
putlicensewait(licwait)

Control whether

**MOSEK**should wait for an available license if no license is available. If`licwait`

is non-zero, then**MOSEK**will wait for`licwait-1`

milliseconds between each check for an available license.- Parameters:
`licwait`

(`int`

) – Whether**MOSEK**should wait for a license if no license is available. (input)- Groups:

- Env.resetexpirylicenses¶
resetexpirylicenses()

Reset the license expiry reporting startpoint.

- Groups:

- Env.set_Stream¶
set_Stream(whichstream, callback)

Directs all output from a environment stream to a callback function.

- Parameters:
`whichstream`

(`streamtype`

) – Index of the stream. (input)`callback`

(`streamfunc`

) – The callback function. (input)

- Env.sparsetriangularsolvedense¶
sparsetriangularsolvedense(transposed,lnzc,lptrc,lsubc,lvalc,b)

The function solves a triangular system of the form

\[L x = b\]or

\[L^T x = b\]where \(L\) is a sparse lower triangular nonsingular matrix. This implies in particular that diagonals in \(L\) are nonzero.

- Parameters:
`transposed`

(`mosek.transpose`

) – Controls whether to use with \(L\) or \(L^T\). (input)`lnzc`

(`int`

`[]`

) –`lnzc[j]`

is the number of nonzeros in column`j`

. (input)`lptrc`

(`int`

`[]`

) –`lptrc[j]`

is a pointer to the first row index and value in column`j`

. (input)`lsubc`

(`int`

`[]`

) – Row indexes for each column stored sequentially. Must be stored in increasing order for each column. (input)`lvalc`

(`float`

`[]`

) – The value corresponding to the row index stored in`lsubc`

. (input)`b`

(`float`

`[]`

) – The right-hand side of linear equation system to be solved as a dense vector. (input/output)

- Groups:

- Env.syeig¶
syeig(uplo,n,a,w)

syeig(uplo,n,a) -> (w)

Computes all eigenvalues of a real symmetric matrix \(A\). Given a matrix \(A\in\real^{n\times n}\) it returns a vector \(w\in\real^n\) containing the eigenvalues of \(A\).

- Parameters:
`uplo`

(`mosek.uplo`

) – Indicates whether the upper or lower triangular part is used. (input)`n`

(`int`

) – Dimension of the symmetric input matrix. (input)`a`

(`float`

`[]`

) – A symmetric matrix \(A\) stored in column-major order. Only the part indicated by`uplo`

is used. (input)`w`

(`float`

`[]`

) – Array of length at least`n`

containing the eigenvalues of \(A\). (output)

- Return:
`w`

(`float`

`[]`

) – Array of length at least`n`

containing the eigenvalues of \(A\).- Groups:

- Env.syevd¶
syevd(uplo,n,a,w)

syevd(uplo,n,a) -> (w)

Computes all the eigenvalues and eigenvectors a real symmetric matrix. Given the input matrix \(A\in \real^{n\times n}\), this function returns a vector \(w\in \real^n\) containing the eigenvalues of \(A\) and it also computes the eigenvectors of \(A\). Therefore, this function computes the eigenvalue decomposition of \(A\) as

\[A= U V U^T,\]where \(V=\diag(w)\) and \(U\) contains the eigenvectors of \(A\).

Note that the matrix \(U\) overwrites the input data \(A\).

- Parameters:
`uplo`

(`mosek.uplo`

) – Indicates whether the upper or lower triangular part is used. (input)`n`

(`int`

) – Dimension of the symmetric input matrix. (input)`a`

(`float`

`[]`

) – A symmetric matrix \(A\) stored in column-major order. Only the part indicated by`uplo`

is used. On exit it will be overwritten by the matrix \(U\). (input/output)`w`

(`float`

`[]`

) – Array of length at least`n`

containing the eigenvalues of \(A\). (output)

- Return:
`w`

(`float`

`[]`

) – Array of length at least`n`

containing the eigenvalues of \(A\).- Groups:

- Env.syrk¶
syrk(uplo,trans,n,k,alpha,a,beta,c)

Performs a symmetric rank-\(k\) update for a symmetric matrix.

Given a symmetric matrix \(C\in \real^{n\times n}\), two scalars \(\alpha,\beta\) and a matrix \(A\) of rank \(k\leq n\), it computes either

\[C := \alpha A A^T + \beta C,\]when

`trans`

is set to`transpose.no`

and \(A\in \real^{n\times k}\), or\[C := \alpha A^T A + \beta C,\]when

`trans`

is set to`transpose.yes`

and \(A\in \real^{k\times n}\).Only the part of \(C\) indicated by

`uplo`

is used and only that part is updated with the result. It must not overlap with the other input arrays.- Parameters:
`uplo`

(`mosek.uplo`

) – Indicates whether the upper or lower triangular part of \(C\) is used. (input)`trans`

(`mosek.transpose`

) – Indicates whether the matrix \(A\) must be transposed. (input)`n`

(`int`

) – Specifies the order of \(C\). (input)`k`

(`int`

) – Indicates the number of rows or columns of \(A\), depending on whether or not it is transposed, and its rank. (input)`alpha`

(`float`

) – A scalar value multiplying the result of the matrix multiplication. (input)`a`

(`float`

`[]`

) – The pointer to the array storing matrix \(A\) in a column-major format. (input)`beta`

(`float`

) – A scalar value that multiplies \(C\). (input)`c`

(`float`

`[]`

) – The pointer to the array storing matrix \(C\) in a column-major format. (input/output)

- Groups: