sycon#

Functions

void ssycon(
    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(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 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.

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

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.

in
A

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

in
lda

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

in
ipiv

Details of the interchanges and the block structure of D as determined by SSYTRF. Integer array, dimension (n).

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

Double precision array, dimension (2*n).

out
iwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

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

Functions

void dsycon(
    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(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 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.

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

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.

in
A

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

in
lda

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

in
ipiv

Details of the interchanges and the block structure of D as determined by DSYTRF. Integer array, dimension (n).

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

Double precision array, dimension (2*n).

out
iwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

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

Functions

void csycon(
    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(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 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.

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

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.

in
A

The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF. Complex*16 array, dimension (lda, n).

in
lda

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

in
ipiv

Details of the interchanges and the block structure of D as determined by CSYTRF. Integer array, dimension (n).

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*16 array, dimension (2*n).

out
info

  • = 0: successful exit

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

Functions

void zsycon(
    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(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 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.

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

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.

in
A

The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. Complex*16 array, dimension (lda, n).

in
lda

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

in
ipiv

Details of the interchanges and the block structure of D as determined by ZSYTRF. Integer array, dimension (n).

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*16 array, dimension (2*n).

out
info

  • = 0: successful exit

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

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