stevd#

Functions

void sstevd(
    const char* jobz,
    const INT   n,
          f32*  D,
          f32*  E,
          f32*  Z,
    const INT   ldz,
          f32*  work,
    const INT   lwork,
          INT*  iwork,
    const INT   liwork,
          INT*  info
);
void sstevd(const char *jobz, const INT n, f32 *D, f32 *E, f32 *Z, const INT ldz, f32 *work, const INT lwork, INT *iwork, const INT liwork, INT *info)#

SSTEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix.

If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

in
jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors.

in
n

The order of the matrix. N >= 0.

inout
D

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

inout
E

Double precision array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A, stored in elements 0 to N-2. On exit, the contents of E are destroyed.

out
Z

Double precision array, dimension (LDZ, N). If JOBZ = ‘V’, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with D(i). If JOBZ = ‘N’, then Z is not referenced.

in
ldz

The leading dimension of the array Z. LDZ >= 1, and if JOBZ = ‘V’, LDZ >= max(1,N).

out
work

Double precision array, dimension (LWORK). On exit, if INFO = 0, WORK(0) returns the optimal LWORK.

in
lwork

The dimension of the array WORK. If JOBZ = ‘N’ or N <= 1 then LWORK must be at least 1. If JOBZ = ‘V’ and N > 1 then LWORK must be at least (1 + 4*N + N**2). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

out
iwork

Integer array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(0) returns the optimal LIWORK.

in
liwork

The dimension of the array IWORK. If JOBZ = ‘N’ or N <= 1 then LIWORK must be at least 1. If JOBZ = ‘V’ and N > 1 then LIWORK must be at least 3+5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

out
info

  • = 0: successful exit

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

  • > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of E did not converge to zero.

Functions

void dstevd(
    const char* jobz,
    const INT   n,
          f64*  D,
          f64*  E,
          f64*  Z,
    const INT   ldz,
          f64*  work,
    const INT   lwork,
          INT*  iwork,
    const INT   liwork,
          INT*  info
);
void dstevd(const char *jobz, const INT n, f64 *D, f64 *E, f64 *Z, const INT ldz, f64 *work, const INT lwork, INT *iwork, const INT liwork, INT *info)#

DSTEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix.

If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

in
jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors.

in
n

The order of the matrix. N >= 0.

inout
D

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

inout
E

Double precision array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A, stored in elements 0 to N-2. On exit, the contents of E are destroyed.

out
Z

Double precision array, dimension (LDZ, N). If JOBZ = ‘V’, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with D(i). If JOBZ = ‘N’, then Z is not referenced.

in
ldz

The leading dimension of the array Z. LDZ >= 1, and if JOBZ = ‘V’, LDZ >= max(1,N).

out
work

Double precision array, dimension (LWORK). On exit, if INFO = 0, WORK(0) returns the optimal LWORK.

in
lwork

The dimension of the array WORK. If JOBZ = ‘N’ or N <= 1 then LWORK must be at least 1. If JOBZ = ‘V’ and N > 1 then LWORK must be at least (1 + 4*N + N**2). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

out
iwork

Integer array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(0) returns the optimal LIWORK.

in
liwork

The dimension of the array IWORK. If JOBZ = ‘N’ or N <= 1 then LIWORK must be at least 1. If JOBZ = ‘V’ and N > 1 then LIWORK must be at least 3+5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

out
info

  • = 0: successful exit

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

  • > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of E did not converge to zero.

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