gehd2#

Functions

void sgehd2(
    const INT  n,
    const INT  ilo,
    const INT  ihi,
          f32* A,
    const INT  lda,
          f32* tau,
          f32* work,
          INT* info
);
void sgehd2(const INT n, const INT ilo, const INT ihi, f32 *A, const INT lda, f32 *tau, f32 *work, INT *info)#

SGEHD2 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 <= max(0,n-1). (0-based)

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).

out
work

Workspace array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value. The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) … H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(0:i) = 0, v(i+1) = 1 and v(ihi+1:n-1) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in tau(i).

Functions

void dgehd2(
    const INT  n,
    const INT  ilo,
    const INT  ihi,
          f64* A,
    const INT  lda,
          f64* tau,
          f64* work,
          INT* info
);
void dgehd2(const INT n, const INT ilo, const INT ihi, f64 *A, const INT lda, f64 *tau, f64 *work, INT *info)#

DGEHD2 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 <= max(0,n-1). (0-based)

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).

out
work

Workspace array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value. The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) … H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(0:i) = 0, v(i+1) = 1 and v(ihi+1:n-1) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in tau(i).

Functions

void cgehd2(
    const INT  n,
    const INT  ilo,
    const INT  ihi,
          c64* A,
    const INT  lda,
          c64* tau,
          c64* work,
          INT* info
);
void cgehd2(const INT n, const INT ilo, const INT ihi, c64 *A, const INT lda, c64 *tau, c64 *work, INT *info)#

CGEHD2 reduces a complex general matrix A to upper Hessenberg form H by a 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 <= max(0,n-1). (0-based)

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).

out
work

Workspace array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value. The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) … H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(0:i) = 0, v(i+1) = 1 and v(ihi+1:n-1) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in tau(i).

Functions

void zgehd2(
    const INT   n,
    const INT   ilo,
    const INT   ihi,
          c128* A,
    const INT   lda,
          c128* tau,
          c128* work,
          INT*  info
);
void zgehd2(const INT n, const INT ilo, const INT ihi, c128 *A, const INT lda, c128 *tau, c128 *work, INT *info)#

ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H by a 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 <= max(0,n-1). (0-based)

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).

out
work

Workspace array, dimension (n).

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value. The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) … H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(0:i) = 0, v(i+1) = 1 and v(ihi+1:n-1) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in tau(i).

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