sptri#

Functions

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

SSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

  • = ‘U’: Upper triangular, form is A = U*D*U**T

  • = ‘L’: Lower triangular, form is A = L*D*L**T

in
n

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

inout
AP

On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSPTRF, stored as a packed triangular matrix of dimension n*(n+1)/2. On exit, if info = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix.

in
ipiv

Details of the interchanges and the block structure of D as determined by SSPTRF. Array of dimension n.

out
work

Workspace array of dimension n.

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) = 0; the matrix is singular and its inverse could not be computed.

Functions

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

DSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

  • = ‘U’: Upper triangular, form is A = U*D*U**T

  • = ‘L’: Lower triangular, form is A = L*D*L**T

in
n

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

inout
AP

On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangular matrix of dimension n*(n+1)/2. On exit, if info = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix.

in
ipiv

Details of the interchanges and the block structure of D as determined by DSPTRF. Array of dimension n.

out
work

Workspace array of dimension n.

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) = 0; the matrix is singular and its inverse could not be computed.

Functions

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

CSPTRI computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

  • = ‘U’: Upper triangular, form is A = U*D*U**T

  • = ‘L’: Lower triangular, form is A = L*D*L**T

in
n

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

inout
AP

On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSPTRF, stored as a packed triangular matrix of dimension n*(n+1)/2. On exit, if info = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix.

in
ipiv

Details of the interchanges and the block structure of D as determined by CSPTRF. Array of dimension n.

out
work

Workspace array of dimension n.

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) = 0; the matrix is singular and its inverse could not be computed.

Functions

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

ZSPTRI computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

  • = ‘U’: Upper triangular, form is A = U*D*U**T

  • = ‘L’: Lower triangular, form is A = L*D*L**T

in
n

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

inout
AP

On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSPTRF, stored as a packed triangular matrix of dimension n*(n+1)/2. On exit, if info = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix.

in
ipiv

Details of the interchanges and the block structure of D as determined by ZSPTRF. Array of dimension n.

out
work

Workspace array of dimension n.

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) = 0; the matrix is singular and its inverse could not be computed.

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