potrf2#

Functions

void spotrf2(
    const char*          uplo,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
          INT*           info
);
void spotrf2(const char *uplo, const INT n, f32 *restrict A, const INT lda, INT *info)#

SPOTRF2 computes the Cholesky factorization of a real symmetric positive definite matrix A using the recursive algorithm.

The factorization has the form 

A = U**T * U,  if uplo = 'U', or
A = L  * L**T, if uplo = 'L',

where U is an upper triangular matrix and L is lower triangular.

This is the recursive version of the algorithm. It divides the matrix into four submatrices: 

    [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = n/2
    [  A21 | A22  ]       n2 = n-n1

The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then calls itself to factor A22.

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

inout
A

Array of dimension (lda, n). On entry, the symmetric matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.

in
lda

The leading dimension of the array A. lda>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-k, the k-th argument had an illegal value

  • info>0: if info=k, the leading principal minor of order k is not positive, and the factorization could not be completed.

Functions

void dpotrf2(
    const char*          uplo,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
          INT*           info
);
void dpotrf2(const char *uplo, const INT n, f64 *restrict A, const INT lda, INT *info)#

DPOTRF2 computes the Cholesky factorization of a real symmetric positive definite matrix A using the recursive algorithm.

The factorization has the form 

A = U**T * U,  if uplo = 'U', or
A = L  * L**T, if uplo = 'L',

where U is an upper triangular matrix and L is lower triangular.

This is the recursive version of the algorithm. It divides the matrix into four submatrices: 

    [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = n/2
    [  A21 | A22  ]       n2 = n-n1

The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then calls itself to factor A22.

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

inout
A

Array of dimension (lda, n). On entry, the symmetric matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.

in
lda

The leading dimension of the array A. lda>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-k, the k-th argument had an illegal value

  • info>0: if info=k, the leading principal minor of order k is not positive, and the factorization could not be completed.

Functions

void cpotrf2(
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
          INT*           info
);
void cpotrf2(const char *uplo, const INT n, c64 *restrict A, const INT lda, INT *info)#

CPOTRF2 computes the Cholesky factorization of a Hermitian positive definite matrix A using the recursive algorithm.

The factorization has the form 

A = U**H * U,  if uplo = 'U', or
A = L  * L**H, if uplo = 'L',

where U is an upper triangular matrix and L is lower triangular.

This is the recursive version of the algorithm. It divides the matrix into four submatrices: 

    [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = n/2
    [  A21 | A22  ]       n2 = n-n1

The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then calls itself to factor A22.

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

inout
A

Array of dimension (lda, n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.

in
lda

The leading dimension of the array A. lda>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-k, the k-th argument had an illegal value

  • info>0: if info=k, the leading principal minor of order k is not positive, and the factorization could not be completed.

Functions

void zpotrf2(
    const char*          uplo,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          INT*           info
);
void zpotrf2(const char *uplo, const INT n, c128 *restrict A, const INT lda, INT *info)#

ZPOTRF2 computes the Cholesky factorization of a Hermitian positive definite matrix A using the recursive algorithm.

The factorization has the form 

A = U**H * U,  if uplo = 'U', or
A = L  * L**H, if uplo = 'L',

where U is an upper triangular matrix and L is lower triangular.

This is the recursive version of the algorithm. It divides the matrix into four submatrices: 

    [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = n/2
    [  A21 | A22  ]       n2 = n-n1

The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then calls itself to factor A22.

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

inout
A

Array of dimension (lda, n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.

in
lda

The leading dimension of the array A. lda>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-k, the k-th argument had an illegal value

  • info>0: if info=k, the leading principal minor of order k is not positive, and the factorization could not be completed.