gehrd#

Functions

void sgehrd(
    const INT  n,
    const INT  ilo,
    const INT  ihi,
          f32* A,
    const INT  lda,
          f32* tau,
          f32* work,
    const INT  lwork,
          INT* info
);
void sgehrd(const INT n, const INT ilo, const INT ihi, f32 *A, const INT lda, f32 *tau, f32 *work, const INT lwork, INT *info)#

SGEHRD reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q**T * A * Q = H .

Parameters

in
n

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

in
ilo

It is assumed that A is already upper triangular in rows and columns 0:ilo-1 and ihi+1:n-1. ilo and ihi are normally set by a previous call to SGEBAL; otherwise they should be set to 0 and n-1 respectively. 0 <= ilo <= ihi <= n-1, if n > 0; ilo=0 and ihi=-1, if n=0. (0-based indexing)

in
ihi

See ilo. (0-based)

inout
A

On entry, the n by n general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the elements below the first subdiagonal, with the array tau, represent the orthogonal matrix Q as a product of elementary reflectors. Dimension (lda, n).

in
lda

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

out
tau

The scalar factors of the elementary reflectors. Dimension (n-1). Elements 0:ilo-1 and ihi:n-2 are set to zero.

out
work

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

in
lwork

The length of work. lwork >= max(1, n). For good performance, lwork should generally be larger. If lwork = -1, a workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void dgehrd(
    const INT  n,
    const INT  ilo,
    const INT  ihi,
          f64* A,
    const INT  lda,
          f64* tau,
          f64* work,
    const INT  lwork,
          INT* info
);
void dgehrd(const INT n, const INT ilo, const INT ihi, f64 *A, const INT lda, f64 *tau, f64 *work, const INT lwork, INT *info)#

DGEHRD reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q**T * A * Q = H .

Parameters

in
n

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

in
ilo

It is assumed that A is already upper triangular in rows and columns 0:ilo-1 and ihi+1:n-1. ilo and ihi are normally set by a previous call to DGEBAL; otherwise they should be set to 0 and n-1 respectively. 0 <= ilo <= ihi <= n-1, if n > 0; ilo=0 and ihi=-1, if n=0. (0-based indexing)

in
ihi

See ilo. (0-based)

inout
A

On entry, the n by n general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the elements below the first subdiagonal, with the array tau, represent the orthogonal matrix Q as a product of elementary reflectors. Dimension (lda, n).

in
lda

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

out
tau

The scalar factors of the elementary reflectors. Dimension (n-1). Elements 0:ilo-1 and ihi:n-2 are set to zero.

out
work

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

in
lwork

The length of work. lwork >= max(1, n). For good performance, lwork should generally be larger. If lwork = -1, a workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void cgehrd(
    const INT  n,
    const INT  ilo,
    const INT  ihi,
          c64* A,
    const INT  lda,
          c64* tau,
          c64* work,
    const INT  lwork,
          INT* info
);
void cgehrd(const INT n, const INT ilo, const INT ihi, c64 *A, const INT lda, c64 *tau, c64 *work, const INT lwork, INT *info)#

CGEHRD reduces a complex general matrix A to upper Hessenberg form H by an unitary similarity transformation: Q**H * A * Q = H .

Parameters

in
n

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

in
ilo

It is assumed that A is already upper triangular in rows and columns 0:ilo-1 and ihi+1:n-1. ilo and ihi are normally set by a previous call to CGEBAL; otherwise they should be set to 0 and n-1 respectively. 0 <= ilo <= ihi <= n-1, if n > 0; ilo=0 and ihi=-1, if n=0. (0-based indexing)

in
ihi

See ilo. (0-based)

inout
A

On entry, the n by n general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the elements below the first subdiagonal, with the array tau, represent the unitary matrix Q as a product of elementary reflectors. Dimension (lda, n).

in
lda

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

out
tau

The scalar factors of the elementary reflectors. Dimension (n-1). Elements 0:ilo-1 and ihi:n-2 are set to zero.

out
work

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

in
lwork

The length of work. lwork >= max(1, n). For good performance, lwork should generally be larger. If lwork = -1, a workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void zgehrd(
    const INT   n,
    const INT   ilo,
    const INT   ihi,
          c128* A,
    const INT   lda,
          c128* tau,
          c128* work,
    const INT   lwork,
          INT*  info
);
void zgehrd(const INT n, const INT ilo, const INT ihi, c128 *A, const INT lda, c128 *tau, c128 *work, const INT lwork, INT *info)#

ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by an unitary similarity transformation: Q**H * A * Q = H .

Parameters

in
n

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

in
ilo

It is assumed that A is already upper triangular in rows and columns 0:ilo-1 and ihi+1:n-1. ilo and ihi are normally set by a previous call to ZGEBAL; otherwise they should be set to 0 and n-1 respectively. 0 <= ilo <= ihi <= n-1, if n > 0; ilo=0 and ihi=-1, if n=0. (0-based indexing)

in
ihi

See ilo. (0-based)

inout
A

On entry, the n by n general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the elements below the first subdiagonal, with the array tau, represent the unitary matrix Q as a product of elementary reflectors. Dimension (lda, n).

in
lda

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

out
tau

The scalar factors of the elementary reflectors. Dimension (n-1). Elements 0:ilo-1 and ihi:n-2 are set to zero.

out
work

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

in
lwork

The length of work. lwork >= max(1, n). For good performance, lwork should generally be larger. If lwork = -1, a workspace query is assumed.

out
info

  • = 0: successful exit

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

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