MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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stedx: Eigenvalues & vectors of tridiagonal using D&C

Functions

magma_int_t magma_cstedx (magma_range_t range, magma_int_t n, float vl, float vu, magma_int_t il, magma_int_t iu, float *d, float *e, magmaFloatComplex *Z, magma_int_t ldz, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magmaFloat_ptr dwork, magma_int_t *info)
 CSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_cstedx_m (magma_int_t ngpu, magma_range_t range, magma_int_t n, float vl, float vu, magma_int_t il, magma_int_t iu, float *d, float *e, magmaFloatComplex *Z, magma_int_t ldz, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
 CSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_dstedx (magma_range_t range, magma_int_t n, double vl, double vu, magma_int_t il, magma_int_t iu, double *d, double *e, double *Z, magma_int_t ldz, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magmaDouble_ptr dwork, magma_int_t *info)
 DSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_dstedx_m (magma_int_t ngpu, magma_range_t range, magma_int_t n, double vl, double vu, magma_int_t il, magma_int_t iu, double *d, double *e, double *Z, magma_int_t ldz, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
 DSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_sstedx (magma_range_t range, magma_int_t n, float vl, float vu, magma_int_t il, magma_int_t iu, float *d, float *e, float *Z, magma_int_t ldz, float *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magmaFloat_ptr dwork, magma_int_t *info)
 SSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_sstedx_m (magma_int_t ngpu, magma_range_t range, magma_int_t n, float vl, float vu, magma_int_t il, magma_int_t iu, float *d, float *e, float *Z, magma_int_t ldz, float *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
 SSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_zstedx (magma_range_t range, magma_int_t n, double vl, double vu, magma_int_t il, magma_int_t iu, double *d, double *e, magmaDoubleComplex *Z, magma_int_t ldz, double *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magmaDouble_ptr dwork, magma_int_t *info)
 ZSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 
magma_int_t magma_zstedx_m (magma_int_t ngpu, magma_range_t range, magma_int_t n, double vl, double vu, magma_int_t il, magma_int_t iu, double *d, double *e, magmaDoubleComplex *Z, magma_int_t ldz, double *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
 ZSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. More...
 

Detailed Description

Function Documentation

magma_int_t magma_cstedx ( magma_range_t  range,
magma_int_t  n,
float  vl,
float  vu,
magma_int_t  il,
magma_int_t  iu,
float *  d,
float *  e,
magmaFloatComplex *  Z,
magma_int_t  ldz,
float *  rwork,
magma_int_t  lrwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magmaFloat_ptr  dwork,
magma_int_t *  info 
)

CSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See SLAEX3 for details.

Parameters
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlREAL
[in]vuREAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dREAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eREAL array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[out]ZCOMPLEX array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]rwork(workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
[in]lrworkINTEGER The dimension of the array RWORK. LRWORK >= 1 + 4*N + 2*N**2. Note that if N is less than or equal to the minimum divide size, usually 25, then LRWORK need only be max(1,2*(N-1)).
If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= 3 + 5*N . Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
dwork(workspace) REAL array, dimension (3*N*N/2+3*N)
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

magma_int_t magma_cstedx_m ( magma_int_t  ngpu,
magma_range_t  range,
magma_int_t  n,
float  vl,
float  vu,
magma_int_t  il,
magma_int_t  iu,
float *  d,
float *  e,
magmaFloatComplex *  Z,
magma_int_t  ldz,
float *  rwork,
magma_int_t  lrwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magma_int_t *  info 
)

CSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See SLAEX3 for details.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlREAL
[in]vuREAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dREAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eREAL array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[out]ZCOMPLEX array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]rwork(workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
[in]lrworkINTEGER The dimension of the array RWORK. LRWORK >= 1 + 4*N + 2*N**2 . Note that if N is less than or equal to the minimum divide size, usually 25, then LRWORK need only be max(1,2*(N-1)).
If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= 3 + 5*N . Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

magma_int_t magma_dstedx ( magma_range_t  range,
magma_int_t  n,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double *  d,
double *  e,
double *  Z,
magma_int_t  ldz,
double *  work,
magma_int_t  lwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magmaDouble_ptr  dwork,
magma_int_t *  info 
)

DSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLAEX3 for details.

Parameters
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlDOUBLE PRECISION
[in]vuDOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dDOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eDOUBLE PRECISION array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[in,out]ZDOUBLE PRECISION array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]work(workspace) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If N > 1 then LWORK >= ( 1 + 4*N + N**2 ). Note that if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be max(1,2*(N-1)).
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= ( 3 + 5*N ). Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.
dwork(workspace) DOUBLE PRECISION array, dimension (3*N*N/2+3*N)
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee.

magma_int_t magma_dstedx_m ( magma_int_t  ngpu,
magma_range_t  range,
magma_int_t  n,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double *  d,
double *  e,
double *  Z,
magma_int_t  ldz,
double *  work,
magma_int_t  lwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magma_int_t *  info 
)

DSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLAEX3 for details.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlDOUBLE PRECISION
[in]vuDOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dDOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eDOUBLE PRECISION array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[in,out]ZDOUBLE PRECISION array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]work(workspace) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If N > 1 then LWORK >= ( 1 + 4*N + N**2 ). Note that if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be max(1,2*(N-1)).
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= ( 3 + 5*N ). Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee.

magma_int_t magma_sstedx ( magma_range_t  range,
magma_int_t  n,
float  vl,
float  vu,
magma_int_t  il,
magma_int_t  iu,
float *  d,
float *  e,
float *  Z,
magma_int_t  ldz,
float *  work,
magma_int_t  lwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magmaFloat_ptr  dwork,
magma_int_t *  info 
)

SSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See SLAEX3 for details.

Parameters
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlREAL
[in]vuREAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dREAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eREAL array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[in,out]ZREAL array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]work(workspace) REAL array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If N > 1 then LWORK >= ( 1 + 4*N + N**2 ). Note that if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be max(1,2*(N-1)).
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= ( 3 + 5*N ). Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.
dwork(workspace) REAL array, dimension (3*N*N/2+3*N)
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee.

magma_int_t magma_sstedx_m ( magma_int_t  ngpu,
magma_range_t  range,
magma_int_t  n,
float  vl,
float  vu,
magma_int_t  il,
magma_int_t  iu,
float *  d,
float *  e,
float *  Z,
magma_int_t  ldz,
float *  work,
magma_int_t  lwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magma_int_t *  info 
)

SSTEDX computes some eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See SLAEX3 for details.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlREAL
[in]vuREAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dREAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eREAL array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[in,out]ZREAL array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]work(workspace) REAL array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If N > 1 then LWORK >= ( 1 + 4*N + N**2 ). Note that if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be max(1,2*(N-1)).
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= ( 3 + 5*N ). Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee.

magma_int_t magma_zstedx ( magma_range_t  range,
magma_int_t  n,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double *  d,
double *  e,
magmaDoubleComplex *  Z,
magma_int_t  ldz,
double *  rwork,
magma_int_t  lrwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magmaDouble_ptr  dwork,
magma_int_t *  info 
)

ZSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLAEX3 for details.

Parameters
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlDOUBLE PRECISION
[in]vuDOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dDOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eDOUBLE PRECISION array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[out]ZCOMPLEX_16 array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]rwork(workspace) DOUBLE PRECISION array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
[in]lrworkINTEGER The dimension of the array RWORK. LRWORK >= 1 + 4*N + 2*N**2. Note that if N is less than or equal to the minimum divide size, usually 25, then LRWORK need only be max(1,2*(N-1)).
If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= 3 + 5*N . Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
dwork(workspace) DOUBLE PRECISION array, dimension (3*N*N/2+3*N)
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

magma_int_t magma_zstedx_m ( magma_int_t  ngpu,
magma_range_t  range,
magma_int_t  n,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double *  d,
double *  e,
magmaDoubleComplex *  Z,
magma_int_t  ldz,
double *  rwork,
magma_int_t  lrwork,
magma_int_t *  iwork,
magma_int_t  liwork,
magma_int_t *  info 
)

ZSTEDX computes some eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLAEX3 for details.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]rangemagma_range_t
  • = MagmaRangeAll: all eigenvalues will be found.
  • = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found.
  • = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
[in]nINTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]vlDOUBLE PRECISION
[in]vuDOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
[in]ilINTEGER
[in]iuINTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
[in,out]dDOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]eDOUBLE PRECISION array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
[out]ZCOMPLEX_16 array, dimension (LDZ,N) On exit, if INFO = 0, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[out]rwork(workspace) DOUBLE PRECISION array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
[in]lrworkINTEGER The dimension of the array RWORK. LRWORK >= 1 + 4*N + 2*N**2 . Note that if N is less than or equal to the minimum divide size, usually 25, then LRWORK need only be max(1,2*(N-1)).
If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
[out]iwork(workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
[in]liworkINTEGER The dimension of the array IWORK. LIWORK >= 3 + 5*N . Note that if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
[out]infoINTEGER
  • = 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).

Further Details

Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA