hetrd_he2hb#

Functions

void chetrd_he2hb(
    const char* uplo,
    const INT   n,
    const INT   kd,
          c64*  A,
    const INT   lda,
          c64*  AB,
    const INT   ldab,
          c64*  tau,
          c64*  work,
    const INT   lwork,
          INT*  info
);
void chetrd_he2hb(const char *uplo, const INT n, const INT kd, c64 *A, const INT lda, c64 *AB, const INT ldab, c64 *tau, c64 *work, const INT lwork, INT *info)#

CHETRD_HE2HB reduces a complex Hermitian matrix A to complex Hermitian band-diagonal form AB by a unitary similarity transformation: Q**H * A * Q = AB.

Parameters

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 reduced matrix if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0. The reduced matrix is stored in the array AB.

inout
A

Single complex array, dimension (LDA,N). On entry, the Hermitian matrix A. If UPLO = ‘U’, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = ‘L’, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = ‘U’, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors; if UPLO = ‘L’, the diagonal and first subdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details.

in
lda

The leading dimension of the array A. LDA >= max(1,N).

out
AB

Single complex array, dimension (LDAB,N). On exit, 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).

in
ldab

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

out
tau

Single complex array, dimension (N-KD). The scalar factors of the elementary reflectors (see Further Details).

out
work

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

in
lwork

The dimension of the array WORK. If N <= KD+1, LWORK >= 1, else LWORK = MAX(1, LWORK_QUERY). LWORK_QUERY = N*KD + N*max(KD,FACTOPTNB) + 2*KD*KD where FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice otherwise putting LWORK=-1 will provide the size of WORK.

out
info

  • = 0: successful exit

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

Functions

void zhetrd_he2hb(
    const char* uplo,
    const INT   n,
    const INT   kd,
          c128* A,
    const INT   lda,
          c128* AB,
    const INT   ldab,
          c128* tau,
          c128* work,
    const INT   lwork,
          INT*  info
);
void zhetrd_he2hb(const char *uplo, const INT n, const INT kd, c128 *A, const INT lda, c128 *AB, const INT ldab, c128 *tau, c128 *work, const INT lwork, INT *info)#

ZHETRD_HE2HB reduces a complex Hermitian matrix A to complex Hermitian band-diagonal form AB by a unitary similarity transformation: Q**H * A * Q = AB.

Parameters

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 reduced matrix if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0. The reduced matrix is stored in the array AB.

inout
A

Double complex array, dimension (LDA,N). On entry, the Hermitian matrix A. If UPLO = ‘U’, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = ‘L’, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = ‘U’, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors; if UPLO = ‘L’, the diagonal and first subdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details.

in
lda

The leading dimension of the array A. LDA >= max(1,N).

out
AB

Double complex array, dimension (LDAB,N). On exit, 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).

in
ldab

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

out
tau

Double complex array, dimension (N-KD). The scalar factors of the elementary reflectors (see Further Details).

out
work

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

in
lwork

The dimension of the array WORK. If N <= KD+1, LWORK >= 1, else LWORK = MAX(1, LWORK_QUERY). LWORK_QUERY = N*KD + N*max(KD,FACTOPTNB) + 2*KD*KD where FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice otherwise putting LWORK=-1 will provide the size of WORK.

out
info

  • = 0: successful exit

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

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