hetrd#

Functions

void chetrd(
    const char* uplo,
    const INT   n,
          c64*  A,
    const INT   lda,
          f32*  D,
          f32*  E,
          c64*  tau,
          c64*  work,
    const INT   lwork,
          INT*  info
);
void chetrd(const char *uplo, const INT n, c64 *A, const INT lda, f32 *D, f32 *E, c64 *tau, c64 *work, const INT lwork, INT *info)#

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

Parameters

in
uplo

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

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

inout
A

Complex*16 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.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
D

Single precision array, dimension (n). The diagonal elements of the tridiagonal matrix T: D[i] = A[i + i*lda].

out
E

Single precision array, dimension (n-1). The off-diagonal elements of the tridiagonal matrix T: E[i] = A[i + (i+1)*lda] if uplo = ‘U’, E[i] = A[(i+1) + i*lda] if uplo = ‘L’.

out
tau

Complex*16 array, dimension (n-1). The scalar factors of the elementary reflectors.

out
work

Complex*16 array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of the array work. lwork >= 1. For optimum performance lwork >= n*nb, where nb is the optimal blocksize. If lwork = -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.

out
info

  • = 0: successful exit

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

Functions

void zhetrd(
    const char* uplo,
    const INT   n,
          c128* A,
    const INT   lda,
          f64*  D,
          f64*  E,
          c128* tau,
          c128* work,
    const INT   lwork,
          INT*  info
);
void zhetrd(const char *uplo, const INT n, c128 *A, const INT lda, f64 *D, f64 *E, c128 *tau, c128 *work, const INT lwork, INT *info)#

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

Parameters

in
uplo

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

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

inout
A

Complex*16 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.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
D

Double precision array, dimension (n). The diagonal elements of the tridiagonal matrix T: D[i] = A[i + i*lda].

out
E

Double precision array, dimension (n-1). The off-diagonal elements of the tridiagonal matrix T: E[i] = A[i + (i+1)*lda] if uplo = ‘U’, E[i] = A[(i+1) + i*lda] if uplo = ‘L’.

out
tau

Complex*16 array, dimension (n-1). The scalar factors of the elementary reflectors.

out
work

Complex*16 array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of the array work. lwork >= 1. For optimum performance lwork >= n*nb, where nb is the optimal blocksize. If lwork = -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.

out
info

  • = 0: successful exit

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

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