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General Size Matrix/Vector CLAPACK Operations
[General Size Matrices and Vectors]


Functions

Gan_Bool gan_clapack_pptrf (Gan_SquMatrix *A, int *error_code)
 Function to apply the Cholesky LAPACK operation pptrf.
Gan_Bool gan_clapack_pptri (Gan_SquMatrix *A)
 Computes a symmetric matrix from its Cholesky factorisation.
Gan_Bool gan_clapack_getf2 (Gan_Matrix *A, long *ipiv, int *error_code)
 Function to apply the LU decomposition operation getf2.
Gan_Bool gan_clapack_getrf (Gan_Matrix *A, long *ipiv, int *error_code)
 Function to apply the LU decomposition operation getrf.
Gan_Bool gan_clapack_getri (Gan_Matrix *A, long *ipiv, double *work, unsigned long work_size)
 Computes a symmetric matrix from its Cholesky factorisation.
Gan_Bool gan_clapack_geqrf (Gan_Matrix *A, Gan_Vector *tau, double *work, unsigned long work_size)
 Apply the QR decomposition LAPACK operation geqrf.
Gan_Bool gan_clapack_gelqf (Gan_Matrix *A, Gan_Vector *tau, double *work, unsigned long work_size)
 Apply the LQ decomposition LAPACK operation gelqf.
Gan_Bool gan_clapack_orgqr (Gan_Matrix *A, Gan_Vector *tau, double *work, unsigned long work_size)
 Construct the orthogonal factor $ Q $ given a QR decomposition.
Gan_Bool gan_clapack_orglq (Gan_Matrix *A, Gan_Vector *tau, double *work, unsigned long work_size)
 Construct the orthogonal factor $ Q $ given an LQ decomposition.
Gan_Bool gan_clapack_gesv (Gan_Matrix *A, Gan_Matrix *B, long *ipiv)
 Solve matrix equation Solve matrix equation A*X=B for square matrix A.
Gan_Bool gan_clapackf_pptrf (Gan_SquMatrix_f *A, int *error_code)
 Function to apply the Cholesky LAPACK operation pptrf.
Gan_Bool gan_clapackf_pptri (Gan_SquMatrix_f *A)
 Computes a symmetric matrix from its Cholesky factorisation.
Gan_Bool gan_clapackf_getf2 (Gan_Matrix_f *A, long *ipiv, int *error_code)
 Function to apply the LU decomposition operation getf2.
Gan_Bool gan_clapackf_getrf (Gan_Matrix_f *A, long *ipiv, int *error_code)
 Function to apply the LU decomposition operation getrf.
Gan_Bool gan_clapackf_getri (Gan_Matrix_f *A, long *ipiv, float *work, unsigned long work_size)
 Computes a symmetric matrix from its Cholesky factorisation.
Gan_Bool gan_clapackf_geqrf (Gan_Matrix_f *A, Gan_Vector_f *tau, float *work, unsigned long work_size)
 Apply the QR decomposition LAPACK operation geqrf.
Gan_Bool gan_clapackf_gelqf (Gan_Matrix_f *A, Gan_Vector_f *tau, float *work, unsigned long work_size)
 Apply the LQ decomposition LAPACK operation gelqf.
Gan_Bool gan_clapackf_orgqr (Gan_Matrix_f *A, Gan_Vector_f *tau, float *work, unsigned long work_size)
 Construct the orthogonal factor $ Q $ given a QR decomposition.
Gan_Bool gan_clapackf_orglq (Gan_Matrix_f *A, Gan_Vector_f *tau, float *work, unsigned long work_size)
 Construct the orthogonal factor $ Q $ given an LQ decomposition.
Gan_Bool gan_clapackf_gesv (Gan_Matrix_f *A, Gan_Matrix_f *B, long *ipiv)
 Solve matrix equation Solve matrix equation A*X=B for square matrix A.

Function Documentation

Gan_Bool gan_clapack_gelqf (  Gan_Matrix *  A,
Gan_Vector *  tau,
double *  work,
unsigned long  work_size
) 
 

Apply the LQ decomposition LAPACK operation gelqf.

Parameters:
A Pointer to a rectangular matrix
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Applies the LQ decomposition LAPACK operation gelqf:

\[ A = L Q \]

for matrix A, lower triangular matrix $ R $ and orthogonal matrix $ Q $. The result is overwritten on the input matrix A. tau on output contains the scalar factors of elementary reflectors (see the CLAPACK documentation). work is a workspace array, or NULL if the workspace is to be allocated and freed internally.

See also:
gan_clapack_orglq().

Gan_Bool gan_clapack_geqrf (  Gan_Matrix *  A,
Gan_Vector *  tau,
double *  work,
unsigned long  work_size
) 
 

Apply the QR decomposition LAPACK operation geqrf.

Parameters:
A Pointer to a rectangular matrix
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Applies the QR decomposition LAPACK operation geqrf:

\[ A = Q R \]

for matrix A, orthogonal matrix $ Q $ and upper triangular matrix $ R $. The result is overwritten on the input matrix A. tau on output contains the scalar factors of elementary reflectors (see the CLAPACK documentation). work is a workspace array, or NULL if the workspace is to be allocated and freed internally.

See also:
gan_clapack_orgqr().

Gan_Bool gan_clapack_gesv (  Gan_Matrix *  A,
Gan_Matrix *  B,
long *  ipiv
) 
 

Solve matrix equation Solve matrix equation A*X=B for square matrix A.

Parameters:
A Input matrix A
B Input matrix B, overwritten with output matrix X
ipiv Array of integer pivot indices
Returns:
GAN_TRUE on success, GAN_FALSE on failure.

Gan_Bool gan_clapack_getf2 (  Gan_Matrix *  A,
long *  ipiv,
int *  error_code
) 
 

Function to apply the LU decomposition operation getf2.

Parameters:
A Pointer to a general square matrix.
ipiv Array of integer pivot indices
error_code A pointer to an error code value or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to apply the LAPACK LU decomposition operation getf2. The factors are overwritten in the matrix A.

If an error occurs, such as A being singular, GAN_FALSE is returned and either the error is returned in error_code (if error_code is not NULL) or the error handling module is invoked (if error_code is NULL).

Gan_Bool gan_clapack_getrf (  Gan_Matrix *  A,
long *  ipiv,
int *  error_code
) 
 

Function to apply the LU decomposition operation getrf.

Parameters:
A Pointer to a general square matrix.
ipiv Array of integer pivot indices
error_code A pointer to an error code value or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to apply the LAPACK LU decomposition operation getrf. The factors are overwritten in the matrix A.

If an error occurs, such as A being singular, GAN_FALSE is returned and either the error is returned in error_code (if error_code is not NULL) or the error handling module is invoked (if error_code is NULL).

Gan_Bool gan_clapack_getri (  Gan_Matrix *  A,
long *  ipiv,
double *  work,
unsigned long  work_size
) 
 

Computes a symmetric matrix from its Cholesky factorisation.

Parameters:
A Pointer to a lower triangular matrix
ipiv Array of integer pivot indices
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to compute a symmetric matrix from its Cholesky factorisation using the LAPACK operation getri. The result is overwritten on the input matrix A.

Gan_Bool gan_clapack_orglq (  Gan_Matrix *  A,
Gan_Vector *  tau,
double *  work,
unsigned long  work_size
) 
 

Construct the orthogonal factor $ Q $ given an LQ decomposition.

Parameters:
A Pointer to a LQ matrix computed by gan_clapack_gelqf()
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Construct the orthogonal factor Q given an LQ decomposition.
See also:
gan_clapack_gelqf().

Gan_Bool gan_clapack_orgqr (  Gan_Matrix *  A,
Gan_Vector *  tau,
double *  work,
unsigned long  work_size
) 
 

Construct the orthogonal factor $ Q $ given a QR decomposition.

Parameters:
A Pointer to a QR matrix computed by gan_clapack_geqrf()
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Construct the orthogonal factor $ Q $ given a QR decomposition.
See also:
gan_clapack_geqrf().

Gan_Bool gan_clapack_pptrf (  Gan_SquMatrix *  A,
int *  error_code
) 
 

Function to apply the Cholesky LAPACK operation pptrf.

Parameters:
A Pointer to a symmetric matrix.
error_code A pointer to an error code value or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to apply the Cholesky factorisation LAPACK operation pptrf, computing $ L $ from symmetric matrix A defined by

\[ A = L L^{\top} \]

for lower triangular matrix $ L $. The result $ L $ is overwritten on the input matrix A.

If an error occurs, such as A not being positive definite, GAN_FALSE is returned and either the error is returned in error_code (if error_code is not NULL) or the error handling module is invoked (if error_code is NULL).

Gan_Bool gan_clapack_pptri (  Gan_SquMatrix *  A  ) 
 

Computes a symmetric matrix from its Cholesky factorisation.

Parameters:
A Pointer to a lower triangular matrix.
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to compute a symmetric matrix from its Cholesky factorisation using the LAPACK operation pptri. The result is overwritten on the input matrix A.

Gan_Bool gan_clapackf_gelqf (  Gan_Matrix_f *  A,
Gan_Vector_f *  tau,
float *  work,
unsigned long  work_size
) 
 

Apply the LQ decomposition LAPACK operation gelqf.

Parameters:
A Pointer to a rectangular matrix
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Applies the LQ decomposition LAPACK operation gelqf:

\[ A = L Q \]

for matrix A, lower triangular matrix $ R $ and orthogonal matrix $ Q $. The result is overwritten on the input matrix A. tau on output contains the scalar factors of elementary reflectors (see the CLAPACK documentation). work is a workspace array, or NULL if the workspace is to be allocated and freed internally.

See also:
gan_clapack_orglq().

Gan_Bool gan_clapackf_geqrf (  Gan_Matrix_f *  A,
Gan_Vector_f *  tau,
float *  work,
unsigned long  work_size
) 
 

Apply the QR decomposition LAPACK operation geqrf.

Parameters:
A Pointer to a rectangular matrix
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Applies the QR decomposition LAPACK operation geqrf:

\[ A = Q R \]

for matrix A, orthogonal matrix $ Q $ and upper triangular matrix $ R $. The result is overwritten on the input matrix A. tau on output contains the scalar factors of elementary reflectors (see the CLAPACK documentation). work is a workspace array, or NULL if the workspace is to be allocated and freed internally.

See also:
gan_clapack_orgqr().

Gan_Bool gan_clapackf_gesv (  Gan_Matrix_f *  A,
Gan_Matrix_f *  B,
long *  ipiv
) 
 

Solve matrix equation Solve matrix equation A*X=B for square matrix A.

Parameters:
A Input matrix A
B Input matrix B, overwritten with output matrix X
ipiv Array of integer pivot indices
Returns:
GAN_TRUE on success, GAN_FALSE on failure.

Gan_Bool gan_clapackf_getf2 (  Gan_Matrix_f *  A,
long *  ipiv,
int *  error_code
) 
 

Function to apply the LU decomposition operation getf2.

Parameters:
A Pointer to a general square matrix.
ipiv Array of integer pivot indices
error_code A pointer to an error code value or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to apply the LAPACK LU decomposition operation getf2. The factors are overwritten in the matrix A.

If an error occurs, such as A being singular, GAN_FALSE is returned and either the error is returned in error_code (if error_code is not NULL) or the error handling module is invoked (if error_code is NULL).

Gan_Bool gan_clapackf_getrf (  Gan_Matrix_f *  A,
long *  ipiv,
int *  error_code
) 
 

Function to apply the LU decomposition operation getrf.

Parameters:
A Pointer to a general square matrix.
ipiv Array of integer pivot indices
error_code A pointer to an error code value or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to apply the LAPACK LU decomposition operation getrf. The factors are overwritten in the matrix A.

If an error occurs, such as A being singular, GAN_FALSE is returned and either the error is returned in error_code (if error_code is not NULL) or the error handling module is invoked (if error_code is NULL).

Gan_Bool gan_clapackf_getri (  Gan_Matrix_f *  A,
long *  ipiv,
float *  work,
unsigned long  work_size
) 
 

Computes a symmetric matrix from its Cholesky factorisation.

Parameters:
A Pointer to a lower triangular matrix
ipiv Array of integer pivot indices
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to compute a symmetric matrix from its Cholesky factorisation using the LAPACK operation getri. The result is overwritten on the input matrix A.

Gan_Bool gan_clapackf_orglq (  Gan_Matrix_f *  A,
Gan_Vector_f *  tau,
float *  work,
unsigned long  work_size
) 
 

Construct the orthogonal factor $ Q $ given an LQ decomposition.

Parameters:
A Pointer to a LQ matrix computed by gan_clapack_gelqf()
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Construct the orthogonal factor Q given an LQ decomposition.
See also:
gan_clapack_gelqf().

Gan_Bool gan_clapackf_orgqr (  Gan_Matrix_f *  A,
Gan_Vector_f *  tau,
float *  work,
unsigned long  work_size
) 
 

Construct the orthogonal factor $ Q $ given a QR decomposition.

Parameters:
A Pointer to a QR matrix computed by gan_clapack_geqrf()
tau A vector of scalar factors of elementary reflectors
work Workspace array
work_size size of the work array
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Construct the orthogonal factor $ Q $ given a QR decomposition.
See also:
gan_clapack_geqrf().

Gan_Bool gan_clapackf_pptrf (  Gan_SquMatrix_f *  A,
int *  error_code
) 
 

Function to apply the Cholesky LAPACK operation pptrf.

Parameters:
A Pointer to a symmetric matrix.
error_code A pointer to an error code value or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to apply the Cholesky factorisation LAPACK operation pptrf, computing $ L $ from symmetric matrix A defined by

\[ A = L L^{\top} \]

for lower triangular matrix $ L $. The result $ L $ is overwritten on the input matrix A.

If an error occurs, such as A not being positive definite, GAN_FALSE is returned and either the error is returned in error_code (if error_code is not NULL) or the error handling module is invoked (if error_code is NULL).

Gan_Bool gan_clapackf_pptri (  Gan_SquMatrix_f *  A  ) 
 

Computes a symmetric matrix from its Cholesky factorisation.

Parameters:
A Pointer to a lower triangular matrix.
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Function to compute a symmetric matrix from its Cholesky factorisation using the LAPACK operation pptri. The result is overwritten on the input matrix A.

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