gebd2#

Functions

void sgebd2(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict D,
          f32* restrict E,
          f32* restrict tauq,
          f32* restrict taup,
          f32* restrict work,
          INT*          info
);
void sgebd2(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict D, f32 *restrict E, f32 *restrict tauq, f32 *restrict taup, f32 *restrict work, INT *info)#

SGEBD2 reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in
m

The number of rows in the matrix A. m >= 0.

in
n

The number of columns in the matrix A. n >= 0.

inout
A

Double precision array, dimension (lda, n). On entry, the m by n general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors.

in
lda

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

out
D

Double precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out
E

Double precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out
tauq

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix Q.

out
taup

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix P.

out
work

Double precision array, dimension (max(m,n)).

out
info

  • = 0: successful exit.

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

Functions

void dgebd2(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict D,
          f64* restrict E,
          f64* restrict tauq,
          f64* restrict taup,
          f64* restrict work,
          INT*          info
);
void dgebd2(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict D, f64 *restrict E, f64 *restrict tauq, f64 *restrict taup, f64 *restrict work, INT *info)#

DGEBD2 reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in
m

The number of rows in the matrix A. m >= 0.

in
n

The number of columns in the matrix A. n >= 0.

inout
A

Double precision array, dimension (lda, n). On entry, the m by n general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors.

in
lda

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

out
D

Double precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out
E

Double precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out
tauq

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix Q.

out
taup

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix P.

out
work

Double precision array, dimension (max(m,n)).

out
info

  • = 0: successful exit.

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

Functions

void cgebd2(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          f32* restrict D,
          f32* restrict E,
          c64* restrict tauq,
          c64* restrict taup,
          c64* restrict work,
          INT*          info
);
void cgebd2(const INT m, const INT n, c64 *restrict A, const INT lda, f32 *restrict D, f32 *restrict E, c64 *restrict tauq, c64 *restrict taup, c64 *restrict work, INT *info)#

CGEBD2 reduces a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation: Q**H * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in
m

The number of rows in the matrix A. m >= 0.

in
n

The number of columns in the matrix A. n >= 0.

inout
A

Complex*16 array, dimension (lda, n). On entry, the m by n general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors.

in
lda

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

out
D

Single precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out
E

Single precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out
tauq

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix Q.

out
taup

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix P.

out
work

Complex*16 array, dimension (max(m,n)).

out
info

  • = 0: successful exit.

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

Functions

void zgebd2(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          f64*  restrict D,
          f64*  restrict E,
          c128* restrict tauq,
          c128* restrict taup,
          c128* restrict work,
          INT*           info
);
void zgebd2(const INT m, const INT n, c128 *restrict A, const INT lda, f64 *restrict D, f64 *restrict E, c128 *restrict tauq, c128 *restrict taup, c128 *restrict work, INT *info)#

ZGEBD2 reduces a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation: Q**H * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in
m

The number of rows in the matrix A. m >= 0.

in
n

The number of columns in the matrix A. n >= 0.

inout
A

Complex*16 array, dimension (lda, n). On entry, the m by n general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors.

in
lda

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

out
D

Double precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out
E

Double precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out
tauq

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix Q.

out
taup

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix P.

out
work

Complex*16 array, dimension (max(m,n)).

out
info

  • = 0: successful exit.

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

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