# active2abs

Convert constraints from active to absolute format

## Syntax

``AbsConSet = active2abs(ActiveConSet,Index)``

## Description

````AbsConSet = active2abs(ActiveConSet,Index)` transforms a constraint matrix to an equivalent matrix expressed in absolute weight format. The transformation equation is$A{w}_{active}=A\left({w}_{absolute}-{w}_{index}\right)\le {b}_{active}.$Therefore$A{w}_{absolute}\le {b}_{active}+A{w}_{index}={b}_{absolute}.$The initial constraint matrix consists of `NCONSTRAINTS` portfolio linear inequality constraints expressed in active weight format (relative to the index portfolio). The index portfolio vector contains `NASSETS` assets.`AbsConSet` is the transformed portfolio linear inequality constraint matrix expressed in absolute weight format, also of the form ```[A b]``` such that `A*w <= b`. The value `w` represents a vector of active asset weights (relative to the index portfolio) whose elements sum to the total portfolio value.```

## Input Arguments

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Portfolio linear inequality constraint matrix expressed in active weight format, formatted as `[A b]` such that ```A*w <= b```, where `A` is a number of constraints (`NCONSTRAINTS`) by number of assets (`NASSETS`) weight coefficient matrix, and `b` and `w` are column vectors of length `NASSETS`. The value `w` represents a vector of active asset weights (relative to the index portfolio) whose elements sum to `0`.

See the output `ConSet` from `portcons` for additional details about constraint matrices.

Data Types: `double`

Index of portfolio weights, specified as an `ASSETS`-by-`1` vector. The sum of the index weights must equal the total portfolio value. For example, a standard portfolio optimization imposes a sum to `1` budget constraint.

Data Types: `double`

## Output Arguments

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Transformed portfolio linear inequality constraint, returned as a matrix and expressed in absolute weight format, also of the form ```[A b]``` such that `A*w <= b`. The value `w` represents a vector of active asset weights (relative to the index portfolio) whose elements sum to the total portfolio value.

## Version History

Introduced before R2006a