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template<typename T>
void sytrd_sb2st(char *stage1, char *vect, char *uplo, integer *n, integer *kd, T *ab, integer *ldab, T *d, T *e, T *hous, integer *lhous, T *work, integer *lwork, integer *info)# SYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T.
Purpose:
SYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T by a orthogonal similarity transformation: Q**T * A * Q = T.
- Parameters:
STAGE1 – [in]
STAGE1 is CHARACTER*1
= ‘N’: “No”: to mention that the stage 1 of the reduction from dense to band using the ssytrd_sy2sb routine was not called before this routine to reproduce AB. In other term this routine is called as standalone.
= ‘Y’: “Yes”: to mention that the stage 1 of the reduction from dense to band using the ssytrd_sy2sb routine has been called to produce AB (e.g., AB is the output of ssytrd_sy2sb.VECT – [in]
VECT is CHARACTER*1
= ‘N’: No need for the Housholder representation, and thus LHOUS is of size fla_max(1, 4*N);
= ‘V’: the Householder representation is needed to either generate or to apply Q later on, then LHOUS is to be queried and computed. (NOT AVAILABLE IN THIS RELEASE).UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangle of A is stored;
= ‘L’: Lower triangle of A is stored.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
KD – [in]
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.
AB – [inout]
AB is REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = ‘U’, AB(kd+1+i-j,j) = A(i,j) for fla_max(1,j-kd)<=i<=j;
if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = ‘U’) or the first subdiagonal (if UPLO = ‘L’) are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction.LDAB – [in]
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
D – [out]
D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.
E – [out]
E is REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = T(i,i+1) if UPLO = ‘U’; E(i) = T(i+1,i) if UPLO = ‘L’.HOUS – [out] HOUS is REAL array, dimension LHOUS, that store the Householder representation.
LHOUS – [in]
LHOUS is INTEGER
The dimension of the array HOUS. LHOUS = MAX(1, dimension)
If LWORK = -1, or LHOUS=-1, then a query is assumed; the routine only calculates the optimal size of the HOUS array, returns this value as the first entry of the HOUS array, and no error message related to LHOUS is issued by XERBLA.
LHOUS = MAX(1, dimension) where
dimension = 4*N if VECT=’N’
not available now if VECT=’H’
WORK – [out] WORK is REAL array, dimension LWORK.
LWORK – [in]
LWORK is INTEGER
The dimension of the array WORK. LWORK = MAX(1, dimension)
If LWORK = -1, or LHOUS=-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.
LWORK = MAX(1, dimension) where dimension = (2KD+1)*N + KD*NTHREADS
where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1.INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value