sptrf#

ssptrf

Functions

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

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

SSPTRF computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method:

A = U*D*U**T or A = L*D*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

Parameters

in

uplo

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

= ‘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

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array of dimension n*(n+1)/2. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix.

out

ipiv

Details of the interchanges and the block structure of D. Array of dimension n, 0-based indexing.

If ipiv[k] >= 0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.
If uplo = ‘U’ and ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k]-1 were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If uplo = ‘L’ and ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k]-1 were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

dsptrf

Functions

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

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

DSPTRF computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method:

A = U*D*U**T or A = L*D*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

Parameters

in

uplo

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

= ‘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

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array of dimension n*(n+1)/2. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix.

out

ipiv

Details of the interchanges and the block structure of D. Array of dimension n, 0-based indexing.

If ipiv[k] >= 0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.
If uplo = ‘U’ and ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k]-1 were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If uplo = ‘L’ and ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k]-1 were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

csptrf

Functions

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

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

CSPTRF computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method:

A = U*D*U**T or A = L*D*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

Parameters

in

uplo

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

= ‘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

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array of dimension n*(n+1)/2. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix.

out

ipiv

Details of the interchanges and the block structure of D. Array of dimension n, 0-based indexing.

If ipiv[k] >= 0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.
If uplo = ‘U’ and ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k]-1 were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If uplo = ‘L’ and ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k]-1 were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

zsptrf

Functions

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

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

ZSPTRF computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method:

A = U*D*U**T or A = L*D*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

Parameters

in

uplo

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

= ‘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

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array of dimension n*(n+1)/2. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix.

out

ipiv

Details of the interchanges and the block structure of D. Array of dimension n, 0-based indexing.

If ipiv[k] >= 0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.
If uplo = ‘U’ and ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k]-1 were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If uplo = ‘L’ and ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k]-1 were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

out

info

Exit status:

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

sptrf#

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