MAGMA  2.7.1
Matrix Algebra for GPU and Multicore Architectures
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Functions
sy/heevx: Solves using QR iteration (expert)
Symmetric/Hermitian eigenvalues

Functions

magma_int_t magma_cheevx (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
 CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More...
 
magma_int_t magma_cheevx_gpu (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex_ptr dZ, magma_int_t lddz, magmaFloatComplex *wA, magma_int_t ldwa, magmaFloatComplex *wZ, magma_int_t ldwz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
 CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More...
 
magma_int_t magma_zheevx (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, double vl, double vu, magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m, double *w, magmaDoubleComplex *Z, magma_int_t ldz, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
 ZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More...
 
magma_int_t magma_zheevx_gpu (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, double vl, double vu, magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m, double *w, magmaDoubleComplex_ptr dZ, magma_int_t lddz, magmaDoubleComplex *wA, magma_int_t ldwa, magmaDoubleComplex *wZ, magma_int_t ldwz, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
 ZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More...
 

Detailed Description

Function Documentation

magma_int_t magma_cheevx ( magma_vec_t  jobz,
magma_range_t  range,
magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
float  vl,
float  vu,
magma_int_t  il,
magma_int_t  iu,
float  abstol,
magma_int_t *  m,
float *  w,
magmaFloatComplex *  Z,
magma_int_t  ldz,
magmaFloatComplex *  work,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  iwork,
magma_int_t *  ifail,
magma_int_t *  info 
)

CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters
[in]jobzmagma_vec_t
  • = MagmaNoVec: Compute eigenvalues only;
  • = MagmaVec: Compute eigenvalues and eigenvectors.
[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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[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]abstolREAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to 
    ABSTOL + EPS * max( |a|,|b| ),

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.
[out]mINTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
[out]wREAL array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order.
[out]ZCOMPLEX array, dimension (LDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N).
[out]work(workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the max of the blocksize for CHETRD and for CUNMTR as returned by ILAENV.
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.
rwork(workspace) REAL array, dimension (7*N)
iwork(workspace) INTEGER array, dimension (5*N)
[out]ifailINTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced.
[out]infoINTEGER
  • = 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. Their indices are stored in array IFAIL.
magma_int_t magma_cheevx_gpu ( magma_vec_t  jobz,
magma_range_t  range,
magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex_ptr  dA,
magma_int_t  ldda,
float  vl,
float  vu,
magma_int_t  il,
magma_int_t  iu,
float  abstol,
magma_int_t *  m,
float *  w,
magmaFloatComplex_ptr  dZ,
magma_int_t  lddz,
magmaFloatComplex *  wA,
magma_int_t  ldwa,
magmaFloatComplex *  wZ,
magma_int_t  ldwz,
magmaFloatComplex *  work,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  iwork,
magma_int_t *  ifail,
magma_int_t *  info 
)

CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters
[in]jobzmagma_vec_t
  • = MagmaNoVec: Compute eigenvalues only;
  • = MagmaVec: Compute eigenvalues and eigenvectors.
[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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dACOMPLEX array, dimension (LDDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed.
[in]lddaINTEGER The leading dimension of the array DA. LDDA >= max(1,N).
[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]abstolREAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to 
    ABSTOL + EPS * max( |a|,|b| ),

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.
[out]mINTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
[out]wREAL array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order.
[out]dZCOMPLEX array, dimension (LDDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases.
[in]lddzINTEGER The leading dimension of the array DZ. LDDZ >= 1, and if JOBZ = MagmaVec, LDDZ >= max(1,N).
wA(workspace) COMPLEX array, dimension (LDWA, N)
[in]ldwaINTEGER The leading dimension of the array wA. LDWA >= max(1,N).
wZ(workspace) COMPLEX array, dimension (LDWZ, max(1,M))
[in]ldwzINTEGER The leading dimension of the array wZ. LDWZ >= 1, and if JOBZ = MagmaVec, LDWZ >= max(1,N).
[out]work(workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The length of the array WORK. LWORK >= (NB+1)*N, where NB is the max of the blocksize for CHETRD.
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.
rwork(workspace) REAL array, dimension (7*N)
iwork(workspace) INTEGER array, dimension (5*N)
[out]ifailINTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced.
[out]infoINTEGER
  • = 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. Their indices are stored in array IFAIL.
magma_int_t magma_zheevx ( magma_vec_t  jobz,
magma_range_t  range,
magma_uplo_t  uplo,
magma_int_t  n,
magmaDoubleComplex *  A,
magma_int_t  lda,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double  abstol,
magma_int_t *  m,
double *  w,
magmaDoubleComplex *  Z,
magma_int_t  ldz,
magmaDoubleComplex *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  iwork,
magma_int_t *  ifail,
magma_int_t *  info 
)

ZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters
[in]jobzmagma_vec_t
  • = MagmaNoVec: Compute eigenvalues only;
  • = MagmaVec: Compute eigenvalues and eigenvectors.
[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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX_16 array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[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]abstolDOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to 
    ABSTOL + EPS * max( |a|,|b| ),

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.
[out]mINTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
[out]wDOUBLE PRECISION array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order.
[out]ZCOMPLEX_16 array, dimension (LDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used.
[in]ldzINTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N).
[out]work(workspace) COMPLEX_16 array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the max of the blocksize for ZHETRD and for ZUNMTR as returned by ILAENV.
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.
rwork(workspace) DOUBLE PRECISION array, dimension (7*N)
iwork(workspace) INTEGER array, dimension (5*N)
[out]ifailINTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced.
[out]infoINTEGER
  • = 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. Their indices are stored in array IFAIL.
magma_int_t magma_zheevx_gpu ( magma_vec_t  jobz,
magma_range_t  range,
magma_uplo_t  uplo,
magma_int_t  n,
magmaDoubleComplex_ptr  dA,
magma_int_t  ldda,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double  abstol,
magma_int_t *  m,
double *  w,
magmaDoubleComplex_ptr  dZ,
magma_int_t  lddz,
magmaDoubleComplex *  wA,
magma_int_t  ldwa,
magmaDoubleComplex *  wZ,
magma_int_t  ldwz,
magmaDoubleComplex *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  iwork,
magma_int_t *  ifail,
magma_int_t *  info 
)

ZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters
[in]jobzmagma_vec_t
  • = MagmaNoVec: Compute eigenvalues only;
  • = MagmaVec: Compute eigenvalues and eigenvectors.
[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]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dACOMPLEX_16 array, dimension (LDDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed.
[in]lddaINTEGER The leading dimension of the array DA. LDDA >= max(1,N).
[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]abstolDOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to 
    ABSTOL + EPS * max( |a|,|b| ),

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.
[out]mINTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
[out]wDOUBLE PRECISION array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order.
[out]dZCOMPLEX_16 array, dimension (LDDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases.
[in]lddzINTEGER The leading dimension of the array DZ. LDDZ >= 1, and if JOBZ = MagmaVec, LDDZ >= max(1,N).
wA(workspace) COMPLEX_16 array, dimension (LDWA, N)
[in]ldwaINTEGER The leading dimension of the array wA. LDWA >= max(1,N).
wZ(workspace) COMPLEX_16 array, dimension (LDWZ, max(1,M))
[in]ldwzINTEGER The leading dimension of the array wZ. LDWZ >= 1, and if JOBZ = MagmaVec, LDWZ >= max(1,N).
[out]work(workspace) COMPLEX_16 array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The length of the array WORK. LWORK >= (NB+1)*N, where NB is the max of the blocksize for ZHETRD.
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.
rwork(workspace) DOUBLE PRECISION array, dimension (7*N)
iwork(workspace) INTEGER array, dimension (5*N)
[out]ifailINTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced.
[out]infoINTEGER
  • = 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. Their indices are stored in array IFAIL.