unbdb1#

cunbdb1

Functions

void cunbdb1(
    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 cunbdb1(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)#

CUNBDB1 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. Q must be no larger than P, M-P, or M-Q. Routines CUNBDB2, CUNBDB3, and CUNBDB4 handle cases in which Q 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 Q-by-Q 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.

in

q

The number of columns in X11 and X21. 0 <= Q <= MIN(P,M-P,M-Q).

inout

X11

Complex*16 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*16 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*16 array, dimension (P). The scalar factors of the elementary reflectors that define P1.

out

taup2

Complex*16 array, dimension (M-P). The scalar factors of the elementary reflectors that define P2.

out

tauq1

Complex*16 array, dimension (Q). The scalar factors of the elementary reflectors that define Q1.

out

work

Complex*16 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.

zunbdb1

Functions

void zunbdb1(
    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 zunbdb1(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)#

ZUNBDB1 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. Q must be no larger than P, M-P, or M-Q. Routines ZUNBDB2, ZUNBDB3, and ZUNBDB4 handle cases in which Q 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 Q-by-Q 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.

in

q

The number of columns in X11 and X21. 0 <= Q <= MIN(P,M-P,M-Q).

inout

X11

Complex*16 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*16 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*16 array, dimension (P). The scalar factors of the elementary reflectors that define P1.

out

taup2

Complex*16 array, dimension (M-P). The scalar factors of the elementary reflectors that define P2.

out

tauq1

Complex*16 array, dimension (Q). The scalar factors of the elementary reflectors that define Q1.

out

work

Complex*16 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.

unbdb1#

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