sytri_3#

Functions

void ssytri_3(
    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            lwork,
          INT*           info
);
void ssytri_3(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 lwork, INT *info)#

SSYTRI_3 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.

SSYTRI_3 sets the leading dimension of the workspace before calling SSYTRI_3X that actually computes the inverse. 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 max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in
lwork

The length of work. If n=0, lwork>=1, else lwork>=(n+nb+1)*(nb+3). If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

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.

Functions

void dsytri_3(
    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            lwork,
          INT*           info
);
void dsytri_3(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 lwork, INT *info)#

DSYTRI_3 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.

DSYTRI_3 sets the leading dimension of the workspace before calling DSYTRI_3X that actually computes the inverse. 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 max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in
lwork

The length of work. If n=0, lwork>=1, else lwork>=(n+nb+1)*(nb+3). If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

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.

Functions

void csytri_3(
    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            lwork,
          INT*           info
);
void csytri_3(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 lwork, INT *info)#

CSYTRI_3 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.

CSYTRI_3 sets the leading dimension of the workspace before calling CSYTRI_3X that actually computes the inverse. 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 max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in
lwork

The length of work. If n=0, lwork>=1, else lwork>=(n+nb+1)*(nb+3). If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

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.

Functions

void zsytri_3(
    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            lwork,
          INT*           info
);
void zsytri_3(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 lwork, INT *info)#

ZSYTRI_3 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.

ZSYTRI_3 sets the leading dimension of the workspace before calling ZSYTRI_3X that actually computes the inverse. 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 max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in
lwork

The length of work. If n=0, lwork>=1, else lwork>=(n+nb+1)*(nb+3). If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

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.