Functions
magma_int_t	magma_dlaqtrsd (magma_trans_t trans, magma_int_t n, const double T, magma_int_t ldt, double x, magma_int_t ldx, const double cnorm, magma_int_t info)
	DLAQTRSD is used by DTREVC to solve one of the (singular) quasi-triangular systems with modified diagonal (T - lambdaI) x = 0 or (T - lambdaI)T x = 0 with scaling to prevent overflow.

magma_int_t	magma_slaqtrsd (magma_trans_t trans, magma_int_t n, const float T, magma_int_t ldt, float x, magma_int_t ldx, const float cnorm, magma_int_t info)
	SLAQTRSD is used by STREVC to solve one of the (singular) quasi-triangular systems with modified diagonal (T - lambdaI) x = 0 or (T - lambdaI)T x = 0 with scaling to prevent overflow.

Detailed Description

Function Documentation

◆ magma_dlaqtrsd()

magma_int_t magma_dlaqtrsd	(	magma_trans_t	trans,
		magma_int_t	n,
		const double *	T,
		magma_int_t	ldt,
		double *	x,
		magma_int_t	ldx,
		const double *	cnorm,
		magma_int_t *	info )

DLAQTRSD is used by DTREVC to solve one of the (singular) quasi-triangular systems with modified diagonal (T - lambda*I) * x = 0 or (T - lambda*I)**T * x = 0 with scaling to prevent overflow.

Here T is an upper quasi-triangular matrix with 1x1 or 2x2 diagonal blocks, A**T denotes the transpose of A, and x is an n-element real or complex vector. The eigenvalue lambda is computed from the block diagonal of T. It does not modify T during the computation.

If trans = MagmaNoTrans, lambda is an eigenvalue for the lower 1x1 or 2x2 block, and it solves ( [ That u ] - lambda*I ) * x = 0, ( [ 0 lambda ] ) which becomes (That - lambda*I) * w = -s*u, with x = [ w; 1 ] and scaling s. If the lower block is 1x1, lambda and x are real; if the lower block is 2x2, lambda and x are complex.

If trans = MagmaTrans, lambda is an eigenvalue for the upper 1x1 or 2x2 block, and it solves ( [ lambda v^T ] - lambda I )**T * x = 0, ( [ 0 That ] ) which becomes (That - lambda*I)**T * w = -s*v, with x = [ 1; w ] and scaling s. If the upper block is 1x1, lambda and x are real; if the upper block is 2x2, lambda and x are complex.

Parameters

[in]	trans	magma_trans_t Specifies the operation applied to T. = MagmaNoTrans: Solve (T - lambdaI) x = 0 (No transpose) = MagmaTrans: Solve (T - lambdaI)T x = 0 (Transpose)
[in]	n	INTEGER The order of the matrix T. N >= 0.
[in]	T	DOUBLE PRECISION array, dimension (LDT,N) The triangular matrix T. The leading n by n upper triangular part of the array T contains the upper triangular matrix, and the strictly lower triangular part of T is not referenced.
[in]	ldt	INTEGER The leading dimension of the array T. LDT >= max (1,N).
[out]	x	DOUBLE PRECISION array, dimension (LDX,1) or (LDX,2). On exit, X is overwritten by the solution vector x. If LAMBDAI .EQ. 0, X is real and has dimension (LDX,1). If LAMBDAI .NE. 0, X is complex and has dimension (LDX,2); the real part is in X(:,0), the imaginary part in X(:,1).
[in]	ldx	INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	cnorm	(input) DOUBLE PRECISION array, dimension (N) CNORM(j) contains the norm of the off-diagonal part of the j-th column of T. If TRANS = MagmaNoTrans, CNORM(j) must be greater than or equal to the infinity-norm, and if TRANS = MagmaTrans or MagmaConjTrans, CNORM(j) must be greater than or equal to the 1-norm.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

◆ magma_slaqtrsd()

magma_int_t magma_slaqtrsd	(	magma_trans_t	trans,
		magma_int_t	n,
		const float *	T,
		magma_int_t	ldt,
		float *	x,
		magma_int_t	ldx,
		const float *	cnorm,
		magma_int_t *	info )

SLAQTRSD is used by STREVC to solve one of the (singular) quasi-triangular systems with modified diagonal (T - lambda*I) * x = 0 or (T - lambda*I)**T * x = 0 with scaling to prevent overflow.