laed0#

Functions

void slaed0(
    const INT  icompq,
    const INT  qsiz,
    const INT  n,
          f32* D,
          f32* E,
          f32* Q,
    const INT  ldq,
          f32* qstore,
    const INT  ldqs,
          f32* work,
          INT* iwork,
          INT* info
);
void slaed0(const INT icompq, const INT qsiz, const INT n, f32 *D, f32 *E, f32 *Q, const INT ldq, f32 *qstore, const INT ldqs, f32 *work, INT *iwork, INT *info)#

SLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

Parameters

in
icompq

= 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix.

in
qsiz

The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. qsiz >= n if icompq = 1.

in
n

The dimension of the symmetric tridiagonal matrix. n >= 0.

inout
D

Double precision array, dimension (n). On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues.

in
E

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

inout
Q

Double precision array, dimension (ldq, n). On entry, Q must contain an n-by-n orthogonal matrix. If icompq = 0, Q is not referenced. If icompq = 1, on entry Q is a subset of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form. If icompq = 2, on entry Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix.

in
ldq

The leading dimension of the array Q. If eigenvectors are desired, then ldq >= max(1,n). In any case, ldq >= 1.

out
qstore

Double precision array, dimension (ldqs, n). Referenced only when icompq = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

in
ldqs

The leading dimension of the array qstore. If icompq = 1, then ldqs >= max(1,n). In any case, ldqs >= 1.

out
work

Double precision workspace array. If icompq = 0 or 1, dimension at least 1 + 3*n + 2*n*lg(n) + 3*n^2. If icompq = 2, dimension at least 4*n + n^2.

out
iwork

Integer workspace array. If icompq = 0 or 1, dimension at least 6 + 6*n + 5*n*lg(n). If icompq = 2, dimension at least 3 + 5*n.

out
info

  • = 0: successful exit.

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

  • > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns info/(n+1) through mod(info,n+1).

Functions

void dlaed0(
    const INT  icompq,
    const INT  qsiz,
    const INT  n,
          f64* D,
          f64* E,
          f64* Q,
    const INT  ldq,
          f64* qstore,
    const INT  ldqs,
          f64* work,
          INT* iwork,
          INT* info
);
void dlaed0(const INT icompq, const INT qsiz, const INT n, f64 *D, f64 *E, f64 *Q, const INT ldq, f64 *qstore, const INT ldqs, f64 *work, INT *iwork, INT *info)#

DLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

Parameters

in
icompq

= 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix.

in
qsiz

The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. qsiz >= n if icompq = 1.

in
n

The dimension of the symmetric tridiagonal matrix. n >= 0.

inout
D

Double precision array, dimension (n). On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues.

in
E

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

inout
Q

Double precision array, dimension (ldq, n). On entry, Q must contain an n-by-n orthogonal matrix. If icompq = 0, Q is not referenced. If icompq = 1, on entry Q is a subset of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form. If icompq = 2, on entry Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix.

in
ldq

The leading dimension of the array Q. If eigenvectors are desired, then ldq >= max(1,n). In any case, ldq >= 1.

out
qstore

Double precision array, dimension (ldqs, n). Referenced only when icompq = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

in
ldqs

The leading dimension of the array qstore. If icompq = 1, then ldqs >= max(1,n). In any case, ldqs >= 1.

out
work

Double precision workspace array. If icompq = 0 or 1, dimension at least 1 + 3*n + 2*n*lg(n) + 3*n^2. If icompq = 2, dimension at least 4*n + n^2.

out
iwork

Integer workspace array. If icompq = 0 or 1, dimension at least 6 + 6*n + 5*n*lg(n). If icompq = 2, dimension at least 3 + 5*n.

out
info

  • = 0: successful exit.

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

  • > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns info/(n+1) through mod(info,n+1).

Functions

void claed0(
    const INT  qsiz,
    const INT  n,
          f32* D,
          f32* E,
          c64* Q,
    const INT  ldq,
          c64* qstore,
    const INT  ldqs,
          f32* rwork,
          INT* iwork,
          INT* info
);
void claed0(const INT qsiz, const INT n, f32 *D, f32 *E, c64 *Q, const INT ldq, c64 *qstore, const INT ldqs, f32 *rwork, INT *iwork, INT *info)#

Using the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.

Parameters

in
qsiz

The dimension of the unitary matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N.

in
n

The dimension of the symmetric tridiagonal matrix. N >= 0.

inout
D

Single precision array, dimension (N). On entry, the diagonal elements of the tridiagonal matrix. On exit, the eigenvalues in ascending order.

inout
E

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

inout
Q

Complex*16 array, dimension (LDQ, N). On entry, Q must contain a QSIZ x N matrix whose columns are unitarily orthonormal.

in
ldq

The leading dimension of the array Q. LDQ >= max(1,N).

out
qstore

Complex*16 array, dimension (LDQS, N). Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

in
ldqs

The leading dimension of the array QSTORE. LDQS >= max(1,N).

out
rwork

Single precision array, dimension (1 + 3*N + 2*N*lg(N) + 3*N**2).

out
iwork

Integer array, dimension (6 + 6*N + 5*N*lg(N)).

out
info

= 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

Functions

void zlaed0(
    const INT   qsiz,
    const INT   n,
          f64*  D,
          f64*  E,
          c128* Q,
    const INT   ldq,
          c128* qstore,
    const INT   ldqs,
          f64*  rwork,
          INT*  iwork,
          INT*  info
);
void zlaed0(const INT qsiz, const INT n, f64 *D, f64 *E, c128 *Q, const INT ldq, c128 *qstore, const INT ldqs, f64 *rwork, INT *iwork, INT *info)#

Using the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.

Parameters

in
qsiz

The dimension of the unitary matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N.

in
n

The dimension of the symmetric tridiagonal matrix. N >= 0.

inout
D

Double precision array, dimension (N). On entry, the diagonal elements of the tridiagonal matrix. On exit, the eigenvalues in ascending order.

inout
E

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

inout
Q

Complex*16 array, dimension (LDQ, N). On entry, Q must contain a QSIZ x N matrix whose columns are unitarily orthonormal.

in
ldq

The leading dimension of the array Q. LDQ >= max(1,N).

out
qstore

Complex*16 array, dimension (LDQS, N). Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.

in
ldqs

The leading dimension of the array QSTORE. LDQS >= max(1,N).

out
rwork

Double precision array, dimension (1 + 3*N + 2*N*lg(N) + 3*N**2).

out
iwork

Integer array, dimension (6 + 6*N + 5*N*lg(N)).

out
info

= 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

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