sycon_3

ssycon_3

Functions

void ssycon_3(
    const char*          uplo,
    const INT            n,
    const f32*  restrict A,
    const INT            lda,
    const f32*  restrict E,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void ssycon_3(const char *uplo, const INT n, const f32 *restrict A, const INT lda, const f32 *restrict E, const INT *restrict ipiv, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)

SSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric 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.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver SSYTRS_3.

• 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.

  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

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.

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

in

uplo

• 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T)

• 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)

in

n

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

in

A

Array of dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by ssytrf_rk and ssytrf_bk:

dsycon_3

Functions

void dsycon_3(
    const char*          uplo,
    const INT            n,
    const f64*  restrict A,
    const INT            lda,
    const f64*  restrict E,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void dsycon_3(const char *uplo, const INT n, const f64 *restrict A, const INT lda, const f64 *restrict E, const INT *restrict ipiv, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)

DSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric 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.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver DSYTRS_3.

• 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.

  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

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.

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

in

uplo

• 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T)

• 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)

in

n

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

in

A

Array of dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by dsytrf_rk and dsytrf_bk:

csycon_3

Functions

void csycon_3(
    const char*          uplo,
    const INT            n,
    const c64*  restrict A,
    const INT            lda,
    const c64*  restrict E,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          INT*           info
);

void csycon_3(const char *uplo, const INT n, const c64 *restrict A, const INT lda, const c64 *restrict E, const INT *restrict ipiv, const f32 anorm, f32 *rcond, c64 *restrict work, INT *info)

CSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric 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.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver CSYTRS_3.

• 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.

  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

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 zsytrf_bk.

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

in

uplo

• 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T)

• 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)

in

n

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

in

A

Complex array of dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by csytrf_rk and zsytrf_bk:

zsycon_3

Functions

void zsycon_3(
    const char*          uplo,
    const INT            n,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict E,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          INT*           info
);

void zsycon_3(const char *uplo, const INT n, const c128 *restrict A, const INT lda, const c128 *restrict E, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, INT *info)

ZSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric 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.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver ZSYTRS_3.

• 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.

  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

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.

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

in

uplo

• 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T)

• 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)

in

n

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

in

A

Complex array of dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by zsytrf_rk and zsytrf_bk: