steqr#

ssteqr

Functions

void ssteqr(
    const char*          compz,
    const INT            n,
          f32*  restrict D,
          f32*  restrict E,
          f32*  restrict Z,
    const INT            ldz,
          f32*  restrict work,
          INT*           info
);

void ssteqr(const char *compz, const INT n, f32 *restrict D, f32 *restrict E, f32 *restrict Z, const INT ldz, f32 *restrict work, INT *info)#

SSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.

The eigenvectors of a full or band symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to tridiagonal form.

Parameters

in

compz

= ‘N’: Compute eigenvalues only. = ‘V’: Compute eigenvalues and eigenvectors of the original symmetric matrix. On entry, Z must contain the orthogonal matrix used to reduce the original matrix to tridiagonal form. = ‘I’: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix.

in

n

The order of the matrix. n >= 0.

inout

D

Double precision array, dimension (n). On entry, the diagonal elements of the tridiagonal matrix. On exit, if info = 0, the eigenvalues in ascending order.

inout

E

Double precision array, dimension (n-1). On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

inout

Z

Double precision array, dimension (ldz, n). On entry, if compz = ‘V’, then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if info = 0, then if compz = ‘V’, Z contains the orthonormal eigenvectors of the original symmetric matrix, and if compz = ‘I’, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If compz = ‘N’, then Z is not referenced.

in

ldz

The leading dimension of the array Z. ldz >= 1, and if eigenvectors are desired, then ldz >= max(1,n).

out

work

Double precision array, dimension (max(1,2*n-2)). If compz = ‘N’, then work is not referenced.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if info = i, then i elements of E have not converged to zero.

dsteqr

Functions

void dsteqr(
    const char*          compz,
    const INT            n,
          f64*  restrict D,
          f64*  restrict E,
          f64*  restrict Z,
    const INT            ldz,
          f64*  restrict work,
          INT*           info
);

void dsteqr(const char *compz, const INT n, f64 *restrict D, f64 *restrict E, f64 *restrict Z, const INT ldz, f64 *restrict work, INT *info)#

DSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.

The eigenvectors of a full or band symmetric matrix can also be found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to tridiagonal form.

Parameters

in

compz

= ‘N’: Compute eigenvalues only. = ‘V’: Compute eigenvalues and eigenvectors of the original symmetric matrix. On entry, Z must contain the orthogonal matrix used to reduce the original matrix to tridiagonal form. = ‘I’: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix.

in

n

The order of the matrix. n >= 0.

inout

D

Double precision array, dimension (n). On entry, the diagonal elements of the tridiagonal matrix. On exit, if info = 0, the eigenvalues in ascending order.

inout

E

Double precision array, dimension (n-1). On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

inout

Z

Double precision array, dimension (ldz, n). On entry, if compz = ‘V’, then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if info = 0, then if compz = ‘V’, Z contains the orthonormal eigenvectors of the original symmetric matrix, and if compz = ‘I’, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If compz = ‘N’, then Z is not referenced.

in

ldz

The leading dimension of the array Z. ldz >= 1, and if eigenvectors are desired, then ldz >= max(1,n).

out

work

Double precision array, dimension (max(1,2*n-2)). If compz = ‘N’, then work is not referenced.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if info = i, then i elements of E have not converged to zero.

csteqr

Functions

void csteqr(
    const char*          compz,
    const INT            n,
          f32*  restrict D,
          f32*  restrict E,
          c64*  restrict Z,
    const INT            ldz,
          f32*  restrict work,
          INT*           info
);

void csteqr(const char *compz, const INT n, f32 *restrict D, f32 *restrict E, c64 *restrict Z, const INT ldz, f32 *restrict work, INT *info)#

CSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.

The eigenvectors of a full or band complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix to tridiagonal form.

Parameters

in

compz

= ‘N’: Compute eigenvalues only. = ‘V’: Compute eigenvalues and eigenvectors of the original Hermitian matrix. On entry, Z must contain the unitary matrix used to reduce the original matrix to tridiagonal form. = ‘I’: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix.

in

n

The order of the matrix. n >= 0.

inout

D

Single precision array, dimension (n). On entry, the diagonal elements of the tridiagonal matrix. On exit, if info = 0, the eigenvalues in ascending order.

inout

E

Single precision array, dimension (n-1). On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

inout

Z

Single complex array, dimension (ldz, n). On entry, if compz = ‘V’, then Z contains the unitary matrix used in the reduction to tridiagonal form. On exit, if info = 0, then if compz = ‘V’, Z contains the orthonormal eigenvectors of the original Hermitian matrix, and if compz = ‘I’, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If compz = ‘N’, then Z is not referenced.

in

ldz

The leading dimension of the array Z. ldz >= 1, and if eigenvectors are desired, then ldz >= max(1,n).

out

work

Single precision array, dimension (max(1,2*n-2)). If compz = ‘N’, then work is not referenced.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if info = i, then i elements of E have not converged to zero.

zsteqr

Functions

void zsteqr(
    const char*          compz,
    const INT            n,
          f64*  restrict D,
          f64*  restrict E,
          c128* restrict Z,
    const INT            ldz,
          f64*  restrict work,
          INT*           info
);

void zsteqr(const char *compz, const INT n, f64 *restrict D, f64 *restrict E, c128 *restrict Z, const INT ldz, f64 *restrict work, INT *info)#

ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.

The eigenvectors of a full or band complex Hermitian matrix can also be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to tridiagonal form.

Parameters

in

compz

= ‘N’: Compute eigenvalues only. = ‘V’: Compute eigenvalues and eigenvectors of the original Hermitian matrix. On entry, Z must contain the unitary matrix used to reduce the original matrix to tridiagonal form. = ‘I’: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix.

in

n

The order of the matrix. n >= 0.

inout

D

Double precision array, dimension (n). On entry, the diagonal elements of the tridiagonal matrix. On exit, if info = 0, the eigenvalues in ascending order.

inout

E

Double precision array, dimension (n-1). On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

inout

Z

Double complex array, dimension (ldz, n). On entry, if compz = ‘V’, then Z contains the unitary matrix used in the reduction to tridiagonal form. On exit, if info = 0, then if compz = ‘V’, Z contains the orthonormal eigenvectors of the original Hermitian matrix, and if compz = ‘I’, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If compz = ‘N’, then Z is not referenced.

in

ldz

The leading dimension of the array Z. ldz >= 1, and if eigenvectors are desired, then ldz >= max(1,n).

out

work

Double precision array, dimension (max(1,2*n-2)). If compz = ‘N’, then work is not referenced.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if info = i, then i elements of E have not converged to zero.

steqr#

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