sytri_3x

ssytri_3x

Functions

void ssytri_3x(
    const char*          uplo,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
    const f32*  restrict E,
    const INT*  restrict ipiv,
          f32*  restrict work,
    const INT            nb,
          INT*           info
);

void ssytri_3x(const char *uplo, const INT n, f32 *restrict A, const INT lda, const f32 *restrict E, const INT *restrict ipiv, f32 *restrict work, const INT nb, INT *info)

SSYTRI_3X computes the inverse of a real symmetric indefinite matrix A using the factorization computed by SSYTRF_RK or SSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the blocked version of the algorithm, calling Level 3 BLAS.

• Only diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and

• If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

On exit, if info=0, the symmetric inverse of the original matrix. If uplo='U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If uplo='L'

: the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

For a 1-by-1 diagonal block

D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

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, diagonal of the block diagonal matrix D and factors U or L as computed by ssytrf_rk or ssytrf_bk:

in

lda

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

in

E

Array of dimension n. On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced.

in

ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by ssytrf_rk or ssytrf_bk.

out

work

Array of dimension (n+nb+1,nb+3).

in

nb

Block size.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i)=0; the matrix is singular and its inverse could not be computed.

dsytri_3x

Functions

void dsytri_3x(
    const char*          uplo,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
    const f64*  restrict E,
    const INT*  restrict ipiv,
          f64*  restrict work,
    const INT            nb,
          INT*           info
);

void dsytri_3x(const char *uplo, const INT n, f64 *restrict A, const INT lda, const f64 *restrict E, const INT *restrict ipiv, f64 *restrict work, const INT nb, INT *info)

DSYTRI_3X computes the inverse of a real symmetric indefinite matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the blocked version of the algorithm, calling Level 3 BLAS.

• Only diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and

• If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

On exit, if info=0, the symmetric inverse of the original matrix. If uplo='U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If uplo='L'

: the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

For a 1-by-1 diagonal block

D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

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, diagonal of the block diagonal matrix D and factors U or L as computed by dsytrf_rk or dsytrf_bk:

in

lda

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

in

E

Array of dimension n. On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced.

in

ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by dsytrf_rk or dsytrf_bk.

out

work

Array of dimension (n+nb+1,nb+3).

in

nb

Block size.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i)=0; the matrix is singular and its inverse could not be computed.

csytri_3x

Functions

void csytri_3x(
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
    const c64*  restrict E,
    const INT*  restrict ipiv,
          c64*  restrict work,
    const INT            nb,
          INT*           info
);

void csytri_3x(const char *uplo, const INT n, c64 *restrict A, const INT lda, const c64 *restrict E, const INT *restrict ipiv, c64 *restrict work, const INT nb, INT *info)

CSYTRI_3X computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by CSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the blocked version of the algorithm, calling Level 3 BLAS.

• Only diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and

• If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

On exit, if info=0, the symmetric inverse of the original matrix. If uplo='U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If uplo='L'

: the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

For a 1-by-1 diagonal block

D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

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

Complex array of dimension (lda,n). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by csytrf_rk or csytrf_bk:

in

lda

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

in

E

Complex array of dimension n. On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced.

in

ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by csytrf_rk or csytrf_bk.

out

work

Complex array of dimension (n+nb+1,nb+3).

in

nb

Block size.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i)=0; the matrix is singular and its inverse could not be computed.

zsytri_3x

Functions

void zsytri_3x(
    const char*          uplo,
    const INT            n,
          c128* restrict A,
    const INT            lda,
    const c128* restrict E,
    const INT*  restrict ipiv,
          c128* restrict work,
    const INT            nb,
          INT*           info
);

void zsytri_3x(const char *uplo, const INT n, c128 *restrict A, const INT lda, const c128 *restrict E, const INT *restrict ipiv, c128 *restrict work, const INT nb, INT *info)

ZSYTRI_3X computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the blocked version of the algorithm, calling Level 3 BLAS.

• Only diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and

• If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

On exit, if info=0, the symmetric inverse of the original matrix. If uplo='U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If uplo='L'

: the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

For a 1-by-1 diagonal block

D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

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

Complex array of dimension (lda,n). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by zsytrf_rk or zsytrf_bk:

in

lda

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

in

E

Complex array of dimension n. On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced.

in

ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by zsytrf_rk or zsytrf_bk.

out

work

Complex array of dimension (n+nb+1,nb+3).

in

nb

Block size.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i)=0; the matrix is singular and its inverse could not be computed.