unbdb3#

Functions

void cunbdb3(
    const INT           m,
    const INT           p,
    const INT           q,
          c64* restrict X11,
    const INT           ldx11,
          c64* restrict X21,
    const INT           ldx21,
          f32* restrict theta,
          f32* restrict phi,
          c64* restrict taup1,
          c64* restrict taup2,
          c64* restrict tauq1,
          c64* restrict work,
    const INT           lwork,
          INT*          info
);
void cunbdb3(const INT m, const INT p, const INT q, c64 *restrict X11, const INT ldx11, c64 *restrict X21, const INT ldx21, f32 *restrict theta, f32 *restrict phi, c64 *restrict taup1, c64 *restrict taup2, c64 *restrict tauq1, c64 *restrict work, const INT lwork, INT *info)#

CUNBDB3 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. Routines CUNBDB1, CUNBDB2, and CUNBDB4 handle cases in which M-P is not the minimum dimension.

The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), and (M-Q)-by-(M-Q), respectively. They are represented implicitly by Householder vectors.

B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented implicitly by angles THETA, PHI.

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

Complex 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

Complex 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

Single precision array, dimension (q). The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.

out
phi

Single precision array, dimension (q-1). The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.

out
taup1

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

out
taup2

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

out
tauq1

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

out
work

Complex array, dimension (lwork).

in
lwork

The dimension of the array WORK. lwork >= M-Q. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to lwork is issued by XERBLA.

out
info

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

Functions

void zunbdb3(
    const INT            m,
    const INT            p,
    const INT            q,
          c128* restrict X11,
    const INT            ldx11,
          c128* restrict X21,
    const INT            ldx21,
          f64*  restrict theta,
          f64*  restrict phi,
          c128* restrict taup1,
          c128* restrict taup2,
          c128* restrict tauq1,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zunbdb3(const INT m, const INT p, const INT q, c128 *restrict X11, const INT ldx11, c128 *restrict X21, const INT ldx21, f64 *restrict theta, f64 *restrict phi, c128 *restrict taup1, c128 *restrict taup2, c128 *restrict tauq1, c128 *restrict work, const INT lwork, INT *info)#

ZUNBDB3 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. Routines ZUNBDB1, ZUNBDB2, and ZUNBDB4 handle cases in which M-P is not the minimum dimension.

The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), and (M-Q)-by-(M-Q), respectively. They are represented implicitly by Householder vectors.

B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented implicitly by angles THETA, PHI.

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

Complex 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

Complex 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. See Further Details.

out
phi

Double precision array, dimension (q-1). The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details.

out
taup1

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

out
taup2

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

out
tauq1

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

out
work

Complex array, dimension (lwork).

in
lwork

The dimension of the array WORK. lwork >= M-Q. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to lwork is issued by XERBLA.

out
info

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

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