sycon_rook#

Functions

void ssycon_rook(
    const char*          uplo,
    const INT            n,
    const f32*  restrict A,
    const INT            lda,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void ssycon_rook(const char *uplo, const INT n, const f32 *restrict A, const INT lda, const INT *restrict ipiv, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)#

SSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

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.

in
A

Array of dimension (lda,n). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ssytrf_rook.

in
lda

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

in
ipiv

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

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as rcond=1/(anorm*ainvnm), where ainvnm is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Array of dimension 2*n.

out
iwork

Integer array of dimension n.

out
info

  • info=0: successful exit

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

Functions

void dsycon_rook(
    const char*          uplo,
    const INT            n,
    const f64*  restrict A,
    const INT            lda,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dsycon_rook(const char *uplo, const INT n, const f64 *restrict A, const INT lda, const INT *restrict ipiv, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)#

DSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

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.

in
A

Array of dimension (lda,n). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by dsytrf_rook.

in
lda

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

in
ipiv

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

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as rcond=1/(anorm*ainvnm), where ainvnm is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Array of dimension 2*n.

out
iwork

Integer array of dimension n.

out
info

  • info=0: successful exit

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

Functions

void csycon_rook(
    const char*          uplo,
    const INT            n,
    const c64*  restrict A,
    const INT            lda,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          INT*           info
);
void csycon_rook(const char *uplo, const INT n, const c64 *restrict A, const INT lda, const INT *restrict ipiv, const f32 anorm, f32 *rcond, c64 *restrict work, INT *info)#

CSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

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.

in
A

Complex array of dimension (lda,n). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by csytrf_rook.

in
lda

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

in
ipiv

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

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as rcond=1/(anorm*ainvnm), where ainvnm is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Complex array of dimension 2*n.

out
info

  • info=0: successful exit

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

Functions

void zsycon_rook(
    const char*          uplo,
    const INT            n,
    const c128* restrict A,
    const INT            lda,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          INT*           info
);
void zsycon_rook(const char *uplo, const INT n, const c128 *restrict A, const INT lda, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, INT *info)#

ZSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

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.

in
A

Complex array of dimension (lda,n). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by zsytrf_rook.

in
lda

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

in
ipiv

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

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as rcond=1/(anorm*ainvnm), where ainvnm is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Complex array of dimension 2*n.

out
info

  • info=0: successful exit

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