MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
or/unghr: Generate Q from Hessenberg reduction

## Functions

magma_int_t magma_cunghr (magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex_ptr dT, magma_int_t nb, magma_int_t *info)
CUNGHR generates a COMPLEX unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD: More...

magma_int_t magma_cunghr_m (magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *T, magma_int_t nb, magma_int_t *info)
CUNGHR generates a COMPLEX unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD: More...

magma_int_t magma_dorghr (magma_int_t n, magma_int_t ilo, magma_int_t ihi, double *A, magma_int_t lda, double *tau, magmaDouble_ptr dT, magma_int_t nb, magma_int_t *info)
DORGHR generates a DOUBLE PRECISION orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD: More...

magma_int_t magma_dorghr_m (magma_int_t n, magma_int_t ilo, magma_int_t ihi, double *A, magma_int_t lda, double *tau, double *T, magma_int_t nb, magma_int_t *info)
DORGHR generates a DOUBLE PRECISION orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD: More...

magma_int_t magma_sorghr (magma_int_t n, magma_int_t ilo, magma_int_t ihi, float *A, magma_int_t lda, float *tau, magmaFloat_ptr dT, magma_int_t nb, magma_int_t *info)
SORGHR generates a REAL orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD: More...

magma_int_t magma_sorghr_m (magma_int_t n, magma_int_t ilo, magma_int_t ihi, float *A, magma_int_t lda, float *tau, float *T, magma_int_t nb, magma_int_t *info)
SORGHR generates a REAL orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD: More...

magma_int_t magma_zunghr (magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex_ptr dT, magma_int_t nb, magma_int_t *info)
ZUNGHR generates a COMPLEX_16 unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD: More...

magma_int_t magma_zunghr_m (magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *T, magma_int_t nb, magma_int_t *info)
ZUNGHR generates a COMPLEX_16 unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD: More...

## Function Documentation

 magma_int_t magma_cunghr ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex * A, magma_int_t lda, magmaFloatComplex * tau, magmaFloatComplex_ptr dT, magma_int_t nb, magma_int_t * info )

CUNGHR generates a COMPLEX unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of CGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A COMPLEX array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by CGEHRD. On exit, the N-by-N unitary matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau COMPLEX array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEHRD. [in] dT COMPLEX array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_cgehrd. [in] nb INTEGER This is the block size used in CGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_cunghr_m ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex * A, magma_int_t lda, magmaFloatComplex * tau, magmaFloatComplex * T, magma_int_t nb, magma_int_t * info )

CUNGHR generates a COMPLEX unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of CGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A COMPLEX array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by CGEHRD. On exit, the N-by-N unitary matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau COMPLEX array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEHRD. [in] T COMPLEX array on the GPU device. T contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_cgehrd. [in] nb INTEGER This is the block size used in CGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in T. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_dorghr ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, double * A, magma_int_t lda, double * tau, magmaDouble_ptr dT, magma_int_t nb, magma_int_t * info )

DORGHR generates a DOUBLE PRECISION orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of DGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A DOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DGEHRD. On exit, the N-by-N orthogonal matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEHRD. [in] dT DOUBLE PRECISION array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_dgehrd. [in] nb INTEGER This is the block size used in DGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_dorghr_m ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, double * A, magma_int_t lda, double * tau, double * T, magma_int_t nb, magma_int_t * info )

DORGHR generates a DOUBLE PRECISION orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of DGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A DOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DGEHRD. On exit, the N-by-N orthogonal matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEHRD. [in] T DOUBLE PRECISION array on the GPU device. T contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_dgehrd. [in] nb INTEGER This is the block size used in DGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in T. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_sorghr ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, float * A, magma_int_t lda, float * tau, magmaFloat_ptr dT, magma_int_t nb, magma_int_t * info )

SORGHR generates a REAL orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of SGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A REAL array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by SGEHRD. On exit, the N-by-N orthogonal matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau REAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEHRD. [in] dT REAL array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_sgehrd. [in] nb INTEGER This is the block size used in SGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_sorghr_m ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, float * A, magma_int_t lda, float * tau, float * T, magma_int_t nb, magma_int_t * info )

SORGHR generates a REAL orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of SGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A REAL array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by SGEHRD. On exit, the N-by-N orthogonal matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau REAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEHRD. [in] T REAL array on the GPU device. T contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_sgehrd. [in] nb INTEGER This is the block size used in SGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in T. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_zunghr ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaDoubleComplex * A, magma_int_t lda, magmaDoubleComplex * tau, magmaDoubleComplex_ptr dT, magma_int_t nb, magma_int_t * info )

ZUNGHR generates a COMPLEX_16 unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of ZGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A COMPLEX_16 array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by ZGEHRD. On exit, the N-by-N unitary matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau COMPLEX_16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEHRD. [in] dT COMPLEX_16 array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_zgehrd. [in] nb INTEGER This is the block size used in ZGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in DT. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_zunghr_m ( magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaDoubleComplex * A, magma_int_t lda, magmaDoubleComplex * tau, magmaDoubleComplex * T, magma_int_t nb, magma_int_t * info )

ZUNGHR generates a COMPLEX_16 unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters
 [in] n INTEGER The order of the matrix Q. N >= 0. [in] ilo INTEGER [in] ihi INTEGER ILO and IHI must have the same values as in the previous call of ZGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. [in,out] A COMPLEX_16 array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by ZGEHRD. On exit, the N-by-N unitary matrix Q. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in] tau COMPLEX_16 array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEHRD. [in] T COMPLEX_16 array on the GPU device. T contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 9th argument of magma_zgehrd. [in] nb INTEGER This is the block size used in ZGEHRD, and correspondingly the size of the T matrices, used in the factorization, and stored in T. [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value