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:
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:
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:
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:
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:
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:
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:
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:

Detailed Description

Function Documentation

magma_cunghr()

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_cunghr_m()

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_dorghr()

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_dorghr_m()

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_sorghr()

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_sorghr_m()

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_zunghr()

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_zunghr_m()

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