orbdb3#

Functions

void sorbdb3(
    const INT           m,
    const INT           p,
    const INT           q,
          f32* restrict X11,
    const INT           ldx11,
          f32* restrict X21,
    const INT           ldx21,
          f32* restrict theta,
          f32* restrict phi,
          f32* restrict taup1,
          f32* restrict taup2,
          f32* restrict tauq1,
          f32* restrict work,
    const INT           lwork,
          INT*          info
);
void sorbdb3(const INT m, const INT p, const INT q, f32 *restrict X11, const INT ldx11, f32 *restrict X21, const INT ldx21, f32 *restrict theta, f32 *restrict phi, f32 *restrict taup1, f32 *restrict taup2, f32 *restrict tauq1, f32 *restrict work, const INT lwork, INT *info)#

SORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny matrix X with orthonormal columns: 

                       [ B11 ]
 [ X11 ]   [ P1 |    ] [  0  ]
 [-----] = [---------] [-----] Q1**T .
 [ X21 ]   [    | P2 ] [ B21 ]
                       [  0  ]
X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P, Q, or M-Q.

Parameters

in
m

The number of rows X11 plus the number of rows in X21.

in
p

The number of rows in X11. 0 <= p <= m. m-p <= min(p, q, m-q).

in
q

The number of columns in X11 and X21. 0 <= q <= m.

inout
X11

Double precision array, dimension (ldx11, q). On entry, the top block of the matrix X to be reduced. On exit, the columns of tril(X11) specify reflectors for P1 and the rows of triu(X11,1) specify reflectors for Q1.

in
ldx11

The leading dimension of X11. ldx11 >= p.

inout
X21

Double precision array, dimension (ldx21, q). On entry, the bottom block of the matrix X to be reduced. On exit, the columns of tril(X21) specify reflectors for P2.

in
ldx21

The leading dimension of X21. ldx21 >= m-p.

out
theta

Double precision array, dimension (q). The entries of the bidiagonal blocks B11, B21 are defined by theta and phi.

out
phi

Double precision array, dimension (q-1). The entries of the bidiagonal blocks B11, B21 are defined by theta and phi.

out
taup1

Double precision array, dimension (p). The scalar factors of the elementary reflectors that define P1.

out
taup2

Double precision array, dimension (m-p). The scalar factors of the elementary reflectors that define P2.

out
tauq1

Double precision array, dimension (q). The scalar factors of the elementary reflectors that define Q1.

out
work

Double precision array, dimension (lwork).

in
lwork

The dimension of the array work. lwork >= m-q. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void dorbdb3(
    const INT           m,
    const INT           p,
    const INT           q,
          f64* restrict X11,
    const INT           ldx11,
          f64* restrict X21,
    const INT           ldx21,
          f64* restrict theta,
          f64* restrict phi,
          f64* restrict taup1,
          f64* restrict taup2,
          f64* restrict tauq1,
          f64* restrict work,
    const INT           lwork,
          INT*          info
);
void dorbdb3(const INT m, const INT p, const INT q, f64 *restrict X11, const INT ldx11, f64 *restrict X21, const INT ldx21, f64 *restrict theta, f64 *restrict phi, f64 *restrict taup1, f64 *restrict taup2, f64 *restrict tauq1, f64 *restrict work, const INT lwork, INT *info)#

DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny matrix X with orthonormal columns: 

                       [ B11 ]
 [ X11 ]   [ P1 |    ] [  0  ]
 [-----] = [---------] [-----] Q1**T .
 [ X21 ]   [    | P2 ] [ B21 ]
                       [  0  ]
X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P, Q, or M-Q.

Parameters

in
m

The number of rows X11 plus the number of rows in X21.

in
p

The number of rows in X11. 0 <= p <= m. m-p <= min(p, q, m-q).

in
q

The number of columns in X11 and X21. 0 <= q <= m.

inout
X11

Double precision array, dimension (ldx11, q). On entry, the top block of the matrix X to be reduced. On exit, the columns of tril(X11) specify reflectors for P1 and the rows of triu(X11,1) specify reflectors for Q1.

in
ldx11

The leading dimension of X11. ldx11 >= p.

inout
X21

Double precision array, dimension (ldx21, q). On entry, the bottom block of the matrix X to be reduced. On exit, the columns of tril(X21) specify reflectors for P2.

in
ldx21

The leading dimension of X21. ldx21 >= m-p.

out
theta

Double precision array, dimension (q). The entries of the bidiagonal blocks B11, B21 are defined by theta and phi.

out
phi

Double precision array, dimension (q-1). The entries of the bidiagonal blocks B11, B21 are defined by theta and phi.

out
taup1

Double precision array, dimension (p). The scalar factors of the elementary reflectors that define P1.

out
taup2

Double precision array, dimension (m-p). The scalar factors of the elementary reflectors that define P2.

out
tauq1

Double precision array, dimension (q). The scalar factors of the elementary reflectors that define Q1.

out
work

Double precision array, dimension (lwork).

in
lwork

The dimension of the array work. lwork >= m-q. If lwork = -1, then 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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