pptrf#

spptrf

Functions

void spptrf(
    const char*          uplo,
    const INT            n,
          f32*  restrict AP,
          INT*           info
);

void spptrf(const char *uplo, const INT n, f32 *restrict AP, INT *info)#

SPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format.

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.

Further Details:

The packed storage scheme is illustrated by the following example when n=4, uplo='U':

Two-dimensional storage of the symmetric matrix A:

a00 a01 a02 a03
    a11 a12 a13
        a22 a23     (aij = aji)
            a33

Packed storage of the upper triangle of A:

AP = [ a00, a01, a11, a02, a12, a22, a03, a13, a23, a33 ]

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

AP

Array of dimension n*(n+1)/2. On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = A(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = A(i,j) for j<=i<=n-1. See below for further details. On exit, if info=0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.

out

info

info=0: successful exit
info<0: if info=-i, the i-th argument had an illegal value
info>0: if info=i, the leading principal minor of order i is not positive, and the factorization could not be completed.

dpptrf

Functions

void dpptrf(
    const char*          uplo,
    const INT            n,
          f64*  restrict AP,
          INT*           info
);

void dpptrf(const char *uplo, const INT n, f64 *restrict AP, INT *info)#

DPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format.

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.

Further Details:

The packed storage scheme is illustrated by the following example when n=4, uplo='U':

Two-dimensional storage of the symmetric matrix A:

a00 a01 a02 a03
    a11 a12 a13
        a22 a23     (aij = aji)
            a33

Packed storage of the upper triangle of A:

AP = [ a00, a01, a11, a02, a12, a22, a03, a13, a23, a33 ]

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

AP

Array of dimension n*(n+1)/2. On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = A(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = A(i,j) for j<=i<=n-1. See below for further details. On exit, if info=0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.

out

info

info=0: successful exit
info<0: if info=-i, the i-th argument had an illegal value
info>0: if info=i, the leading principal minor of order i is not positive, and the factorization could not be completed.

cpptrf

Functions

void cpptrf(
    const char*          uplo,
    const INT            n,
          c64*  restrict AP,
          INT*           info
);

void cpptrf(const char *uplo, const INT n, c64 *restrict AP, INT *info)#

CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format.

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.

Further Details:

The packed storage scheme is illustrated by the following example when n=4, uplo='U':

Two-dimensional storage of the Hermitian matrix A:

a00 a01 a02 a03
    a11 a12 a13
        a22 a23     (aij = conjg(aji))
            a33

Packed storage of the upper triangle of A:

AP = [ a00, a01, a11, a02, a12, a22, a03, a13, a23, a33 ]

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

AP

Array of dimension n*(n+1)/2. On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = A(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = A(i,j) for j<=i<=n-1. See below for further details. On exit, if info=0, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A.

out

info

info=0: successful exit
info<0: if info=-i, the i-th argument had an illegal value
info>0: if info=i, the leading principal minor of order i is not positive, and the factorization could not be completed.

zpptrf

Functions

void zpptrf(
    const char*          uplo,
    const INT            n,
          c128* restrict AP,
          INT*           info
);

void zpptrf(const char *uplo, const INT n, c128 *restrict AP, INT *info)#

ZPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format.

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.

Further Details:

The packed storage scheme is illustrated by the following example when n=4, uplo='U':

Two-dimensional storage of the Hermitian matrix A:

a00 a01 a02 a03
    a11 a12 a13
        a22 a23     (aij = conjg(aji))
            a33

Packed storage of the upper triangle of A:

AP = [ a00, a01, a11, a02, a12, a22, a03, a13, a23, a33 ]

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

AP

Array of dimension n*(n+1)/2. On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = A(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = A(i,j) for j<=i<=n-1. See below for further details. On exit, if info=0, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A.

out

info

info=0: successful exit
info<0: if info=-i, the i-th argument had an illegal value
info>0: if info=i, the leading principal minor of order i is not positive, and the factorization could not be completed.