sytf2#

ssytf2

Functions

void ssytf2(
    const char*          uplo,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          INT*           info
);

void ssytf2(const char *uplo, const INT n, f32 *restrict A, const INT lda, INT *restrict ipiv, INT *info)#

SSYTF2 computes the factorization of a real symmetric matrix A 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, U**T is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters

in

uplo

‘U’: Upper triangular factorization (A = U*D*U**T) ‘L’: Lower triangular factorization (A = L*D*L**T)

in

n

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

inout

A

Double precision array, dimension (lda, n). On entry, the symmetric matrix A. If uplo = “U”, the leading n-by-n upper triangular part contains the upper triangular part of A. If uplo = “L”, the leading n-by-n lower triangular part contains the lower triangular part. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in

lda

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

out

ipiv

Integer array, dimension (n). Pivot indices (0-based). If ipiv[k] >= 0: rows/columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 block. If ipiv[k] < 0 (upper): rows/columns k-1 and -ipiv[k]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 block, and ipiv[k-1] = ipiv[k]. If ipiv[k] < 0 (lower): rows/columns k+1 and -ipiv[k]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 block, and ipiv[k+1] = ipiv[k].

out

info

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

dsytf2

Functions

void dsytf2(
    const char*          uplo,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          INT*           info
);

void dsytf2(const char *uplo, const INT n, f64 *restrict A, const INT lda, INT *restrict ipiv, INT *info)#

DSYTF2 computes the factorization of a real symmetric matrix A 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, U**T is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters

in

uplo

‘U’: Upper triangular factorization (A = U*D*U**T) ‘L’: Lower triangular factorization (A = L*D*L**T)

in

n

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

inout

A

Double precision array, dimension (lda, n). On entry, the symmetric matrix A. If uplo = “U”, the leading n-by-n upper triangular part contains the upper triangular part of A. If uplo = “L”, the leading n-by-n lower triangular part contains the lower triangular part. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in

lda

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

out

ipiv

Integer array, dimension (n). Pivot indices (0-based). If ipiv[k] >= 0: rows/columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 block. If ipiv[k] < 0 (upper): rows/columns k-1 and -ipiv[k]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 block, and ipiv[k-1] = ipiv[k]. If ipiv[k] < 0 (lower): rows/columns k+1 and -ipiv[k]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 block, and ipiv[k+1] = ipiv[k].

out

info

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

csytf2

Functions

void csytf2(
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          INT*           info
);

void csytf2(const char *uplo, const INT n, c64 *restrict A, const INT lda, INT *restrict ipiv, INT *info)#

CSYTF2 computes the factorization of a complex symmetric matrix A 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, U**T is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters

in

uplo

‘U’: Upper triangular factorization (A = U*D*U**T) ‘L’: Lower triangular factorization (A = L*D*L**T)

in

n

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

inout

A

Single complex array, dimension (lda, n). On entry, the symmetric matrix A. If uplo = “U”, the leading n-by-n upper triangular part contains the upper triangular part of A. If uplo = “L”, the leading n-by-n lower triangular part contains the lower triangular part. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in

lda

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

out

ipiv

Integer array, dimension (n). Pivot indices (0-based). If ipiv[k] >= 0: rows/columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 block. If ipiv[k] < 0 (upper): rows/columns k-1 and -ipiv[k]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 block, and ipiv[k-1] = ipiv[k]. If ipiv[k] < 0 (lower): rows/columns k+1 and -ipiv[k]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 block, and ipiv[k+1] = ipiv[k].

out

info

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

zsytf2

Functions

void zsytf2(
    const char*          uplo,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          INT*           info
);

void zsytf2(const char *uplo, const INT n, c128 *restrict A, const INT lda, INT *restrict ipiv, INT *info)#

ZSYTF2 computes the factorization of a complex symmetric matrix A 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, U**T is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters

in

uplo

‘U’: Upper triangular factorization (A = U*D*U**T) ‘L’: Lower triangular factorization (A = L*D*L**T)

in

n

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

inout

A

Double complex array, dimension (lda, n). On entry, the symmetric matrix A. If uplo = “U”, the leading n-by-n upper triangular part contains the upper triangular part of A. If uplo = “L”, the leading n-by-n lower triangular part contains the lower triangular part. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in

lda

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

out

ipiv

Integer array, dimension (n). Pivot indices (0-based). If ipiv[k] >= 0: rows/columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 block. If ipiv[k] < 0 (upper): rows/columns k-1 and -ipiv[k]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 block, and ipiv[k-1] = ipiv[k]. If ipiv[k] < 0 (lower): rows/columns k+1 and -ipiv[k]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 block, and ipiv[k+1] = ipiv[k].

out

info

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

sytf2#

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