ppcon

sppcon

Functions

void sppcon(
    const char*          uplo,
    const INT            n,
    const f32*  restrict AP,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void sppcon(const char *uplo, const INT n, const f32 *restrict AP, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)

SPPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF.

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 triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

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

in

AP

Array of dimension n*(n+1)/2. The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

in

anorm

The 1-norm (or infinity-norm) of the symmetric 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 3*n.

out

iwork

Array of dimension n.

out

info

• info=0: successful exit

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

dppcon

Functions

void dppcon(
    const char*          uplo,
    const INT            n,
    const f64*  restrict AP,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void dppcon(const char *uplo, const INT n, const f64 *restrict AP, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)

DPPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF.

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 triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

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

in

AP

Array of dimension n*(n+1)/2. The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

in

anorm

The 1-norm (or infinity-norm) of the symmetric 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 3*n.

out

iwork

Array of dimension n.

out

info

• info=0: successful exit

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

cppcon

Functions

void cppcon(
    const char*          uplo,
    const INT            n,
    const c64*  restrict AP,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);

void cppcon(const char *uplo, const INT n, const c64 *restrict AP, const f32 anorm, f32 *rcond, c64 *restrict work, f32 *restrict rwork, INT *info)

CPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF.

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 triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

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

in

AP

Array of dimension n*(n+1)/2. The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

in

anorm

The 1-norm (or infinity-norm) of the Hermitian 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

rwork

Array of dimension n.

out

info

• info=0: successful exit

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

zppcon

Functions

void zppcon(
    const char*          uplo,
    const INT            n,
    const c128* restrict AP,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);

void zppcon(const char *uplo, const INT n, const c128 *restrict AP, const f64 anorm, f64 *rcond, c128 *restrict work, f64 *restrict rwork, INT *info)

ZPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF.

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 triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

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

in

AP

Array of dimension n*(n+1)/2. The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if uplo='U', AP[i + j*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

in

anorm

The 1-norm (or infinity-norm) of the Hermitian 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

rwork

Array of dimension n.

out

info

• info=0: successful exit

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