gelq2#

Functions

void sgelq2(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict tau,
          f32* restrict work,
          INT*          info
);
void sgelq2(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict tau, f32 *restrict work, INT *info)#

SGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * Q.

The matrix Q is represented as a product of elementary reflectors Q = H(k) … H(2) H(1), where k = min(m, n).

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-1) = 0 and v(i) = 1; v(i+1:n-1) is stored on exit in A(i, i+1:n-1), and tau in TAU(i).

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and below the diagonal contain the m-by-min(m,n) lower trapezoidal matrix L; the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors.

in
lda

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

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (m).

out
info

  • = 0: successful exit

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

Functions

void dgelq2(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict tau,
          f64* restrict work,
          INT*          info
);
void dgelq2(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict tau, f64 *restrict work, INT *info)#

DGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * Q.

The matrix Q is represented as a product of elementary reflectors Q = H(k) … H(2) H(1), where k = min(m, n).

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-1) = 0 and v(i) = 1; v(i+1:n-1) is stored on exit in A(i, i+1:n-1), and tau in TAU(i).

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and below the diagonal contain the m-by-min(m,n) lower trapezoidal matrix L; the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors.

in
lda

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

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (m).

out
info

  • = 0: successful exit

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

Functions

void cgelq2(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          c64* restrict tau,
          c64* restrict work,
          INT*          info
);
void cgelq2(const INT m, const INT n, c64 *restrict A, const INT lda, c64 *restrict tau, c64 *restrict work, INT *info)#

CGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q.

The matrix Q is represented as a product of elementary reflectors Q = H(k)**H … H(2)**H H(1)**H, where k = min(m, n).

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-1) = 0 and v(i) = 1; conjg(v(i+1:n-1)) is stored on exit in A(i, i+1:n-1), and tau in TAU(i).

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and below the diagonal contain the m-by-min(m,n) lower trapezoidal matrix L; the elements above the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors.

in
lda

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

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (m).

out
info

  • = 0: successful exit

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

Functions

void zgelq2(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict tau,
          c128* restrict work,
          INT*           info
);
void zgelq2(const INT m, const INT n, c128 *restrict A, const INT lda, c128 *restrict tau, c128 *restrict work, INT *info)#

ZGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q.

The matrix Q is represented as a product of elementary reflectors Q = H(k)**H … H(2)**H H(1)**H, where k = min(m, n).

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-1) = 0 and v(i) = 1; conjg(v(i+1:n-1)) is stored on exit in A(i, i+1:n-1), and tau in TAU(i).

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and below the diagonal contain the m-by-min(m,n) lower trapezoidal matrix L; the elements above the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors.

in
lda

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

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (m).

out
info

  • = 0: successful exit

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

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