---
name: "sc_OverlapOrthog"
section: "3"
platform: "linux"
package: "libsc-doc"
version: "2.3.1-22"
release: "Debian 12 (Bookworm)"
platforms: ["linux"]
url: "https://new.carta.tech/sc_OverlapOrthog"
---

# sc\_OverlapOrthog(3)

This class computes the orthogonalizing transform for a basis set.

## NAME

sc::OverlapOrthog - This class computes the orthogonalizing transform for a basis set.

## SYNOPSIS

`#include <orthog.h>`

Inherits **sc::SavableState**.

### Public Types

enum **OrthogMethod** { **Symmetric** =1, **Canonical** =2, **GramSchmidt** =3 }\
 An enum for the types of orthogonalization.

### Public Member Functions

**OverlapOrthog** (**OrthogMethod** method, const **RefSymmSCMatrix** &overlap, const **Ref**\< **SCMatrixKit** \> &result\_kit, double lindep\_tolerance, int debug=0)\
 **OverlapOrthog** (**StateIn** &)\
 void **save\_data\_state** (**StateOut** &)\
 Save the base classes (with save\_data\_state) and the members in the same order that the **StateIn** CTOR initializes them.  void **reinit** (**OrthogMethod** method, const **RefSymmSCMatrix** &overlap, const **Ref**\< **SCMatrixKit** \> &result\_kit, double lindep\_tolerance, int debug=0)\
 double **min\_orthog\_res** () const\
 double **max\_orthog\_res** () const\
 **Ref**\< **OverlapOrthog** \> **copy** () const\
 **OrthogMethod** **orthog\_method** () const\
 Returns the orthogonalization method.  double **lindep\_tol** () const\
 Returns the tolerance for linear dependencies.  **RefSCMatrix** **basis\_to\_orthog\_basis** ()\
 Returns a matrix which does the requested transform from a basis to an orthogonal basis.  **RefSCMatrix** **basis\_to\_orthog\_basis\_inverse** ()\
 Returns the inverse of the transformation returned by basis\_to\_orthog\_basis.  **RefSCDimension** **dim** ()\
 **RefSCDimension** **orthog\_dim** ()\
 int **nlindep** ()\
 Returns the number of linearly dependent functions eliminated from the orthogonal basis.

### Additional Inherited Members

## Detailed Description

This class computes the orthogonalizing transform for a basis set.

## Member Function Documentation

### RefSCMatrix sc::OverlapOrthog::basis\_to\_orthog\_basis ()

Returns a matrix which does the requested transform from a basis to an orthogonal basis. This could be either the symmetric or canonical orthogonalization matrix. The row dimension is the basis dimension and the column dimension is orthogonal basis dimension. An operator $O$ in the orthogonal basis is given by $X O X^T$ where $X$ is the return value of this function.

### void sc::OverlapOrthog::save\_data\_state (StateOut &)` [virtual]`

Save the base classes (with save\_data\_state) and the members in the same order that the **StateIn** CTOR initializes them. This must be implemented by the derived class if the class has data.

Reimplemented from **sc::SavableState**.

## Author

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