MAGMA 2.9.0
Matrix Algebra for GPU and Multicore Architectures
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Functions
or/ungtr: Generate Q from tridiagonal reduction
Dense LA » Eigenvalues » Symmetric/Hermitian eigenvalues

Functions

magma_int_t magma_cungtr (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magmaFloatComplex *dT, magma_int_t nb, magma_int_t *info)
 CUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD:
 
magma_int_t magma_dorgtr (magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, double *tau, double *work, magma_int_t lwork, double *dT, magma_int_t nb, magma_int_t *info)
 DORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD:
 
magma_int_t magma_sorgtr (magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *tau, float *work, magma_int_t lwork, float *dT, magma_int_t nb, magma_int_t *info)
 SORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD:
 
magma_int_t magma_zungtr (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, magmaDoubleComplex *dT, magma_int_t nb, magma_int_t *info)
 ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD:
 

Detailed Description

Function Documentation

◆ magma_cungtr()

magma_int_t magma_cungtr ( magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex * A,
magma_int_t lda,
magmaFloatComplex * tau,
magmaFloatComplex * work,
magma_int_t lwork,
magmaFloatComplex * dT,
magma_int_t nb,
magma_int_t * info )

CUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD:

if UPLO = MagmaUpper, Q = H(n-1) . . . H(2) H(1),

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(n-1).

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD.
[in]nINTEGER The order of the matrix Q. N >= 0.
[in,out]ACOMPLEX array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by CHETRD. On exit, the N-by-N unitary matrix Q.
[in]ldaINTEGER The leading dimension of the array A. LDA >= N.
[in]tauCOMPLEX array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD.
[out]work(workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= N-1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.
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.
[in]dTCOMPLEX array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i) as returned by magma_chetrd.
[in]nbINTEGER This is the block size used in CHETRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_dorgtr()

magma_int_t magma_dorgtr ( magma_uplo_t uplo,
magma_int_t n,
double * A,
magma_int_t lda,
double * tau,
double * work,
magma_int_t lwork,
double * dT,
magma_int_t nb,
magma_int_t * info )

DORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD:

if UPLO = MagmaUpper, Q = H(n-1) . . . H(2) H(1),

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(n-1).

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD.
[in]nINTEGER The order of the matrix Q. N >= 0.
[in,out]ADOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DSYTRD. On exit, the N-by-N orthogonal matrix Q.
[in]ldaINTEGER The leading dimension of the array A. LDA >= N.
[in]tauDOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.
[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. LWORK >= N-1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.
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.
[in]dTDOUBLE PRECISION array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i) as returned by magma_dsytrd.
[in]nbINTEGER This is the block size used in DSYTRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_sorgtr()

magma_int_t magma_sorgtr ( magma_uplo_t uplo,
magma_int_t n,
float * A,
magma_int_t lda,
float * tau,
float * work,
magma_int_t lwork,
float * dT,
magma_int_t nb,
magma_int_t * info )

SORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD:

if UPLO = MagmaUpper, Q = H(n-1) . . . H(2) H(1),

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(n-1).

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD.
[in]nINTEGER The order of the matrix Q. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by SSYTRD. On exit, the N-by-N orthogonal matrix Q.
[in]ldaINTEGER The leading dimension of the array A. LDA >= N.
[in]tauREAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.
[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. LWORK >= N-1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.
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.
[in]dTREAL array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i) as returned by magma_ssytrd.
[in]nbINTEGER This is the block size used in SSYTRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_zungtr()

magma_int_t magma_zungtr ( magma_uplo_t uplo,
magma_int_t n,
magmaDoubleComplex * A,
magma_int_t lda,
magmaDoubleComplex * tau,
magmaDoubleComplex * work,
magma_int_t lwork,
magmaDoubleComplex * dT,
magma_int_t nb,
magma_int_t * info )

ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD:

if UPLO = MagmaUpper, Q = H(n-1) . . . H(2) H(1),

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(n-1).

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD.
[in]nINTEGER The order of the matrix Q. N >= 0.
[in,out]ACOMPLEX_16 array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by ZHETRD. On exit, the N-by-N unitary matrix Q.
[in]ldaINTEGER The leading dimension of the array A. LDA >= N.
[in]tauCOMPLEX_16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.
[out]work(workspace) COMPLEX_16 array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= N-1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.
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.
[in]dTCOMPLEX_16 array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i) as returned by magma_zhetrd.
[in]nbINTEGER This is the block size used in ZHETRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value