stein#

Functions

void sstein(
    const INT           n,
    const f32* restrict D,
    const f32* restrict E,
    const INT           m,
    const f32* restrict W,
    const INT* restrict iblock,
    const INT* restrict isplit,
          f32* restrict Z,
    const INT           ldz,
          f32* restrict work,
          INT* restrict iwork,
          INT* restrict ifail,
          INT*          info
);
void sstein(const INT n, const f32 *restrict D, const f32 *restrict E, const INT m, const f32 *restrict W, const INT *restrict iblock, const INT *restrict isplit, f32 *restrict Z, const INT ldz, f32 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

SSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration.

The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5).

Parameters

in
n

The order of the matrix. n >= 0.

in
D

Double precision array, dimension (n). The n diagonal elements of the tridiagonal matrix T.

in
E

Double precision array, dimension (n-1). The (n-1) subdiagonal elements of the tridiagonal matrix T.

in
m

The number of eigenvectors to be found. 0 <= m <= n.

in
W

Double precision array, dimension (m). The eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array W from SSTEBZ with ORDER = ‘B’ is expected here.)

in
iblock

Integer array, dimension (m). The submatrix indices associated with the corresponding eigenvalues in W; iblock[i]=0 if eigenvalue W[i] belongs to the first submatrix from the top, =1 if W[i] belongs to the second submatrix, etc. (0-based block numbers.)

in
isplit

Integer array, dimension (nsplit). The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 0 to isplit[0], the second of rows/columns isplit[0]+1 through isplit[1], etc. (0-based endpoint indices.)

out
Z

Double precision array, dimension (ldz, m). The computed eigenvectors. The eigenvector associated with the eigenvalue W[i] is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations.

in
ldz

The leading dimension of the array Z. ldz >= max(1,n).

out
work

Double precision array, dimension (5*n).

out
iwork

Integer array, dimension (n).

out
ifail

Integer array, dimension (m). On normal exit, all elements of ifail are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array ifail (0-based indices).

out
info

  • = 0: successful exit.

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

  • > 0: if info = i, then i eigenvectors failed to converge in MAXITS iterations. Their indices are stored in array ifail.

Functions

void dstein(
    const INT           n,
    const f64* restrict D,
    const f64* restrict E,
    const INT           m,
    const f64* restrict W,
    const INT* restrict iblock,
    const INT* restrict isplit,
          f64* restrict Z,
    const INT           ldz,
          f64* restrict work,
          INT* restrict iwork,
          INT* restrict ifail,
          INT*          info
);
void dstein(const INT n, const f64 *restrict D, const f64 *restrict E, const INT m, const f64 *restrict W, const INT *restrict iblock, const INT *restrict isplit, f64 *restrict Z, const INT ldz, f64 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

DSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration.

The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5).

Parameters

in
n

The order of the matrix. n >= 0.

in
D

Double precision array, dimension (n). The n diagonal elements of the tridiagonal matrix T.

in
E

Double precision array, dimension (n-1). The (n-1) subdiagonal elements of the tridiagonal matrix T.

in
m

The number of eigenvectors to be found. 0 <= m <= n.

in
W

Double precision array, dimension (m). The eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array W from DSTEBZ with ORDER = ‘B’ is expected here.)

in
iblock

Integer array, dimension (m). The submatrix indices associated with the corresponding eigenvalues in W; iblock[i]=0 if eigenvalue W[i] belongs to the first submatrix from the top, =1 if W[i] belongs to the second submatrix, etc. (0-based block numbers.)

in
isplit

Integer array, dimension (nsplit). The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 0 to isplit[0], the second of rows/columns isplit[0]+1 through isplit[1], etc. (0-based endpoint indices.)

out
Z

Double precision array, dimension (ldz, m). The computed eigenvectors. The eigenvector associated with the eigenvalue W[i] is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations.

in
ldz

The leading dimension of the array Z. ldz >= max(1,n).

out
work

Double precision array, dimension (5*n).

out
iwork

Integer array, dimension (n).

out
ifail

Integer array, dimension (m). On normal exit, all elements of ifail are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array ifail (0-based indices).

out
info

  • = 0: successful exit.

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

  • > 0: if info = i, then i eigenvectors failed to converge in MAXITS iterations. Their indices are stored in array ifail.

Functions

void cstein(
    const INT           n,
    const f32* restrict D,
    const f32* restrict E,
    const INT           m,
    const f32* restrict W,
    const INT* restrict iblock,
    const INT* restrict isplit,
          c64* restrict Z,
    const INT           ldz,
          f32* restrict work,
          INT* restrict iwork,
          INT* restrict ifail,
          INT*          info
);
void cstein(const INT n, const f32 *restrict D, const f32 *restrict E, const INT m, const f32 *restrict W, const INT *restrict iblock, const INT *restrict isplit, c64 *restrict Z, const INT ldz, f32 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

CSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration.

The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5).

Although the eigenvectors are real, they are stored in a complex array, which may be passed to CUNMTR or CUPMTR for back transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form.

Parameters

in
n

The order of the matrix. n >= 0.

in
D

Single precision array, dimension (n). The n diagonal elements of the tridiagonal matrix T.

in
E

Single precision array, dimension (n-1). The (n-1) subdiagonal elements of the tridiagonal matrix T.

in
m

The number of eigenvectors to be found. 0 <= m <= n.

in
W

Single precision array, dimension (m). The eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array W from SSTEBZ with ORDER = ‘B’ is expected here.)

in
iblock

Integer array, dimension (m). The submatrix indices associated with the corresponding eigenvalues in W; iblock[i]=1 if eigenvalue W[i] belongs to the first submatrix from the top, =2 if W[i] belongs to the second submatrix, etc. (1-based block numbers.)

in
isplit

Integer array, dimension (nsplit). The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 0 to isplit[0], the second of rows/columns isplit[0]+1 through isplit[1], etc. (0-based endpoint indices.)

out
Z

Complex*16 array, dimension (ldz, m). The computed eigenvectors. The eigenvector associated with the eigenvalue W[i] is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations. The imaginary parts of the eigenvectors are set to zero.

in
ldz

The leading dimension of the array Z. ldz >= max(1,n).

out
work

Single precision array, dimension (5*n).

out
iwork

Integer array, dimension (n).

out
ifail

Integer array, dimension (m). On normal exit, all elements of ifail are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array ifail (0-based indices).

out
info

  • = 0: successful exit.

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

  • > 0: if info = i, then i eigenvectors failed to converge in MAXITS iterations. Their indices are stored in array ifail.

Functions

void zstein(
    const INT            n,
    const f64*  restrict D,
    const f64*  restrict E,
    const INT            m,
    const f64*  restrict W,
    const INT*  restrict iblock,
    const INT*  restrict isplit,
          c128* restrict Z,
    const INT            ldz,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void zstein(const INT n, const f64 *restrict D, const f64 *restrict E, const INT m, const f64 *restrict W, const INT *restrict iblock, const INT *restrict isplit, c128 *restrict Z, const INT ldz, f64 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

ZSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration.

The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5).

Although the eigenvectors are real, they are stored in a complex array, which may be passed to ZUNMTR or ZUPMTR for back transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form.

Parameters

in
n

The order of the matrix. n >= 0.

in
D

Double precision array, dimension (n). The n diagonal elements of the tridiagonal matrix T.

in
E

Double precision array, dimension (n-1). The (n-1) subdiagonal elements of the tridiagonal matrix T.

in
m

The number of eigenvectors to be found. 0 <= m <= n.

in
W

Double precision array, dimension (m). The eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array W from DSTEBZ with ORDER = ‘B’ is expected here.)

in
iblock

Integer array, dimension (m). The submatrix indices associated with the corresponding eigenvalues in W; iblock[i]=1 if eigenvalue W[i] belongs to the first submatrix from the top, =2 if W[i] belongs to the second submatrix, etc. (1-based block numbers.)

in
isplit

Integer array, dimension (nsplit). The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 0 to isplit[0], the second of rows/columns isplit[0]+1 through isplit[1], etc. (0-based endpoint indices.)

out
Z

Complex*16 array, dimension (ldz, m). The computed eigenvectors. The eigenvector associated with the eigenvalue W[i] is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations. The imaginary parts of the eigenvectors are set to zero.

in
ldz

The leading dimension of the array Z. ldz >= max(1,n).

out
work

Double precision array, dimension (5*n).

out
iwork

Integer array, dimension (n).

out
ifail

Integer array, dimension (m). On normal exit, all elements of ifail are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array ifail (0-based indices).

out
info

  • = 0: successful exit.

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

  • > 0: if info = i, then i eigenvectors failed to converge in MAXITS iterations. Their indices are stored in array ifail.

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