## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK

### Package Content

Name | Description
--- | ---
zungqr |
zgeqrf |
zgesvd | Determine singular values of a complex matrix
zgesv | Solve complex system of linear equations A*X=B
zgerq2 |
zgetrf |
zgetri |
zungrq |
zunmrq |
wrapper_zungqr |
wrapper_zgeqrf |
wrapper_zgesvd |
wrapper_zgesv |
wrapper_zgetrf |
wrapper_zgetri |
wrapper_zgerq2 | Wrapper for lapack function zgerq2
wrapper_zungrq |
wrapper_zunmrq | Wrapper for lapack function zunmrq

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zungqr

### Inputs

Name | Description
--- | ---
QR[:, :] | Square or rectangular matrix
tau[:] | elementary reflectors

### Outputs

Name | Description
--- | ---
Q[size(QR, 1), size(QR, 2)] | matrix Q

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zgeqrf

### Inputs

Name | Description
--- | ---
A[:, :] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
Q[size(A, 1), size(A, 2)] | Square upper triangular matrix
R[size(A, 2), size(A, 2)] | Square upper triangular matrix

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zgesvd

Determine singular values of a complex matrix

### Inputs

Name | Description
--- | ---
A[:, :] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
sigma[min(size(A, 1), size(A, 2))] | singular values
U[size(A, 1), size(A, 1)] | Left orthogonal matrix
VT[size(A, 2), size(A, 2)] | Transposed right orthogonal matrix
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zgesv

Solve complex system of linear equations A*X=B

### Inputs

Name | Description
--- | ---
A[:, size(A, 1)] |
B[size(A, 1), :] |

### Outputs

Name | Description
--- | ---
X[size(A, 1), size(B, 2)] |
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zgerq2

### Inputs

Name | Description
--- | ---
A[:, :] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
RQ[size(A, 1), size(A, 2)] | RQ factorization in packed format
tau[:] | elementory reflectors

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zgetrf

### Inputs

Name | Description
--- | ---
A[:, :] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
LU[size(A, 1), size(A, 2)] |
pivots[min(size(A, 1), size(A, 2))] | Pivot vector
info | Information

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zgetri

### Inputs

Name | Description
--- | ---
LU[:, size(LU, 1)] | LU factorization of zgetrf of a complex square matrix
pivots[size(LU, 1)] | Pivot vector of zgetrf

### Outputs

Name | Description
--- | ---
inv[size(LU, 1), size(LU, 2)] |
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zungrq

### Inputs

Name | Description
--- | ---
RQ[:, :] | Square or rectangular matrix
tau[:] | elementary reflectors

### Outputs

Name | Description
--- | ---
Q[size(RQ, 1), size(RQ, 2)] | matrix Q

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.zunmrq

### Inputs

Name | Description
--- | ---
C[:, :] | Matrix to multiply with Q
RQ[:, :] | Matrix as a result of zgerq2
tau[:] | elementary reflectors
left |
trans |

### Outputs

Name | Description
--- | ---
CQ[size(C, 1), size(C, 2)] | Matrix product C*Q, Q*C, C*Q**H, Q**H*C

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zungqr

### Inputs

Name | Description
--- | ---
QR_real[:, :] | Square or rectangular matrix
QR_imag[size(QR_real, 1), size(QR_real, 2)] | Square or rectangular matrix
tau_real[min(size(QR_real, 1), size(QR_real, 2))] | The scalar factors of the elementary reflectors of Q, real part
tau_imag[min(size(QR_real, 1), size(QR_real, 2))] | The scalar factors of the elementary reflectors of Q, imaginary part

### Outputs

Name | Description
--- | ---
Q_real[size(QR_real, 1), size(QR_real, 2)] |
Q_imag[size(QR_real, 1), size(QR_real, 2)] |
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zgeqrf

### Inputs

Name | Description
--- | ---
A_real[:, :] | Square or rectangular matrix
A_imag[size(A_real, 1), size(A_real, 2)] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
QR_real[size(A_real, 1), size(A_real, 2)] | QR factorization in packed format, real part
QR_imag[size(A_real, 1), size(A_real, 2)] | QR factorization in packed format, imaginary part
tau_real[min(size(A_real, 1), size(A_real, 2))] | The scalar factors of the elementary reflectors of Q, real part
tau_imag[min(size(A_real, 1), size(A_real, 2))] | The scalar factors of the elementary reflectors of Q, imaginary part
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zgesvd

### Inputs

Name | Description
--- | ---
A_real[:, :] | Square or rectangular matrix
A_imag[size(A_real, 1), size(A_real, 2)] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
sigma[min(size(A_real, 1), size(A_real, 2))] | singular values
U_real[size(A_real, 1), size(A_real, 1)] |
U_imag[size(A_real, 1), size(A_real, 1)] |
VT_real[size(A_real, 2), size(A_real, 2)] |
VT_imag[size(A_real, 2), size(A_real, 2)] |
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zgesv

### Inputs

Name | Description
--- | ---
A_real[:, size(A_real, 1)] | Square or rectangular matrix
A_imag[size(A_real, 1), size(A_real, 2)] | Square or rectangular matrix
B_real[size(A_real, 1), :] | Square or rectangular matrix
B_imag[size(B_real, 1), size(B_real, 2)] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
X_real[size(A_real, 1), size(B_real, 2)] |
X_imag[size(A_real, 1), size(B_real, 2)] |
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zgetrf

### Inputs

Name | Description
--- | ---
A_real[:, :] | Square or rectangular matrix
A_imag[size(A_real, 1), size(A_real, 2)] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
LU_real[size(A_real, 1), size(A_real, 2)] | LU factorization in packed format, real part
LU_imag[size(A_real, 1), size(A_real, 2)] | LU factorization in packed format, imaginary part
pivots[min(size(A_real, 1), size(A_real, 2))] | Pivot vector
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zgetri

### Inputs

Name | Description
--- | ---
LU_real[:, :] | LU factorization of zgetrf of a square matrix, real part
LU_imag[size(LU_real, 1), size(LU_real, 2)] | LU factorization of zgetrf of a square matrix, imaginary part
pivots[size(LU_real, 1)] | Pivot vector of zgetrf

### Outputs

Name | Description
--- | ---
inv_real[size(LU_real, 1), size(LU_real, 2)] | Inverse of matrix P*L*U, real part
inv_imag[size(LU_real, 1), size(LU_real, 2)] | Inverse of matrix P*L*U, imaginary part
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zgerq2

Wrapper for lapack function zgerq2

### Inputs

Name | Description
--- | ---
A_real[:, :] | Square or rectangular matrix
A_imag[size(A_real, 1), size(A_real, 2)] | Square or rectangular matrix

### Outputs

Name | Description
--- | ---
RQ_real[size(A_real, 1), size(A_real, 2)] | RQ factorization in packed format, real part
RQ_imag[size(A_real, 1), size(A_real, 2)] | RQ factorization in packed format, imaginary part
tau_real[min(size(A_real, 1), size(A_real, 2))] | The scalar factors of the elementary reflectors of Q, real part
tau_imag[min(size(A_real, 1), size(A_real, 2))] | The scalar factors of the elementary reflectors of Q, imaginary part
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zungrq

### Inputs

Name | Description
--- | ---
RQ_real[:, :] | Square or rectangular matrix
RQ_imag[size(RQ_real, 1), size(RQ_real, 2)] | Square or rectangular matrix
tau_real[min(size(RQ_real, 1), size(RQ_real, 2))] | The scalar factors of the elementary reflectors of Q, real part
tau_imag[min(size(RQ_real, 1), size(RQ_real, 2))] | The scalar factors of the elementary reflectors of Q, imaginary part

### Outputs

Name | Description
--- | ---
Q_real[size(RQ_real, 1), size(RQ_real, 2)] |
Q_imag[size(RQ_real, 1), size(RQ_real, 2)] |
info |

## Modelica_LinearSystems2.WorkInProgress.Math.LAPACK.wrapper_zunmrq

Wrapper for lapack function zunmrq

### Inputs

Name | Description
--- | ---
RQ_real[:, :] | Square or rectangular matrix
RQ_imag[size(RQ_real, 1), size(RQ_real, 2)] | Square or rectangular matrix
tau_real[min(size(RQ_real, 1), size(RQ_real, 2))] | The scalar factors of the elementary reflectors of Q, real part
tau_imag[min(size(RQ_real, 1), size(RQ_real, 2))] | The scalar factors of the elementary reflectors of Q, imaginary part
C_real[:, :] |
C_imag[size(C_real, 1), size(C_real, 2)] |
left |
trans |

### Outputs

Name | Description
--- | ---
QC_real[size(C_real, 1), size(C_real, 2)] |
QC_imag[size(C_real, 1), size(C_real, 2)] |
info |