hetrd_hb2st#

chetrd_hb2st

Functions

void chetrd_hb2st(
    const char* stage1,
    const char* vect,
    const char* uplo,
    const INT   n,
    const INT   kd,
          c64*  AB,
    const INT   ldab,
          f32*  D,
          f32*  E,
          c64*  hous,
    const INT   lhous,
          c64*  work,
    const INT   lwork,
          INT*  info
);

void chetrd_hb2st(const char *stage1, const char *vect, const char *uplo, const INT n, const INT kd, c64 *AB, const INT ldab, f32 *D, f32 *E, c64 *hous, const INT lhous, c64 *work, const INT lwork, INT *info)#

CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.

Parameters

in

stage1

= ‘N’: the stage 1 of the reduction from dense to band using the chetrd_he2hb routine was not called before this routine to reproduce AB. In other term this routine is called as standalone. = ‘Y’: the stage 1 of the reduction from dense to band using the chetrd_he2hb routine has been called to produce AB (e.g., AB is the output of chetrd_he2hb).

in

vect

= ‘N’: No need for the Householder representation, and thus LHOUS is of size 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).

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The order of the matrix A. N >= 0.

in

kd

The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.

inout

AB

Single complex array, dimension (LDAB,N). On entry, the upper or lower triangle of the Hermitian 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+i-j,j) = A(i,j) for max(0,j-kd)<=i<=j; if UPLO = ‘L’, AB(i-j,j) = A(i,j) for j<=i<=min(n-1,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.

in

ldab

The leading dimension of the array AB. LDAB >= KD+1.

out

D

Single precision array, dimension (N). The diagonal elements of the tridiagonal matrix T.

out

E

Single precision 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’.

out

hous

Single complex array, dimension (MAX(1,LHOUS)). Stores the Householder representation.

in

lhous

The dimension of the array HOUS. If N = 0 or KD <= 1, LHOUS >= 1, else LHOUS = MAX(1, dimension) where dimension = 4*N if VECT=’N’.

out

work

Single complex array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

in

lwork

The dimension of the array WORK. If N = 0 or KD <= 1, LWORK >= 1, else LWORK = MAX(1, dimension) where dimension = (2KD+1)*N + KD*NTHREADS where NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value.

zhetrd_hb2st

Functions

void zhetrd_hb2st(
    const char* stage1,
    const char* vect,
    const char* uplo,
    const INT   n,
    const INT   kd,
          c128* AB,
    const INT   ldab,
          f64*  D,
          f64*  E,
          c128* hous,
    const INT   lhous,
          c128* work,
    const INT   lwork,
          INT*  info
);

void zhetrd_hb2st(const char *stage1, const char *vect, const char *uplo, const INT n, const INT kd, c128 *AB, const INT ldab, f64 *D, f64 *E, c128 *hous, const INT lhous, c128 *work, const INT lwork, INT *info)#

ZHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.

Parameters

in

stage1

= ‘N’: the stage 1 of the reduction from dense to band using the zhetrd_he2hb routine was not called before this routine to reproduce AB. In other term this routine is called as standalone. = ‘Y’: the stage 1 of the reduction from dense to band using the zhetrd_he2hb routine has been called to produce AB (e.g., AB is the output of zhetrd_he2hb).

in

vect

= ‘N’: No need for the Householder representation, and thus LHOUS is of size 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).

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The order of the matrix A. N >= 0.

in

kd

The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.

inout

AB

Double complex array, dimension (LDAB,N). On entry, the upper or lower triangle of the Hermitian 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+i-j,j) = A(i,j) for max(0,j-kd)<=i<=j; if UPLO = ‘L’, AB(i-j,j) = A(i,j) for j<=i<=min(n-1,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.

in

ldab

The leading dimension of the array AB. LDAB >= KD+1.

out

D

Double precision array, dimension (N). The diagonal elements of the tridiagonal matrix T.

out

E

Double precision 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’.

out

hous

Double complex array, dimension (MAX(1,LHOUS)). Stores the Householder representation.

in

lhous

The dimension of the array HOUS. If N = 0 or KD <= 1, LHOUS >= 1, else LHOUS = MAX(1, dimension) where dimension = 4*N if VECT=’N’.

out

work

Double complex array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

in

lwork

The dimension of the array WORK. If N = 0 or KD <= 1, LWORK >= 1, else LWORK = MAX(1, dimension) where dimension = (2KD+1)*N + KD*NTHREADS where NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value.

hetrd_hb2st#

This Page