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

  • '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

Array of dimension n*(n+1)/2. 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. On exit, if info=0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = inv(A)(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = inv(A)(i,j) for j<=i<=n-1.

in
ipiv

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

out
work

Workspace array of dimension n.

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 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

  • '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

Array of dimension n*(n+1)/2. 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. On exit, if info=0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = inv(A)(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = inv(A)(i,j) for j<=i<=n-1.

in
ipiv

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

out
work

Workspace array of dimension n.

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 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

  • '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

Complex array of dimension n*(n+1)/2. 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. On exit, if info=0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = inv(A)(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = inv(A)(i,j) for j<=i<=n-1.

in
ipiv

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

out
work

Complex workspace array of dimension n.

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 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

  • '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

Complex array of dimension n*(n+1)/2. 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. On exit, if info=0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = inv(A)(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = inv(A)(i,j) for j<=i<=n-1.

in
ipiv

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

out
work

Complex workspace array of dimension n.

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.