Man page - unbdb2(3)

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Manual

unbdb2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cunbdb2 (integer m, integer p, integer q, complex,dimension(ldx11,*) x11, integer ldx11, complex, dimension(ldx21,*) x21,integer ldx21, real, dimension(*) theta, real, dimension(*) phi,complex, dimension(*) taup1, complex, dimension(*) taup2, complex,dimension(*) tauq1, complex, dimension(*) work, integer lwork, integerinfo)
subroutine dorbdb2 (integer m, integer p, integer q, double precision,dimension(ldx11,*) x11, integer ldx11, double precision,dimension(ldx21,*) x21, integer ldx21, double precision, dimension(*)theta, double precision, dimension(*) phi, double precision,dimension(*) taup1, double precision, dimension(*) taup2, doubleprecision, dimension(*) tauq1, double precision, dimension(*) work,integer lwork, integer info)
subroutine sorbdb2 (integer m, integer p, integer q, real,dimension(ldx11,*) x11, integer ldx11, real, dimension(ldx21,*) x21,integer ldx21, real, dimension(*) theta, real, dimension(*) phi, real,dimension(*) taup1, real, dimension(*) taup2, real, dimension(*) tauq1,real, dimension(*) work, integer lwork, integer info)
subroutine zunbdb2 (integer m, integer p, integer q, complex*16,dimension(ldx11,*) x11, integer ldx11, complex*16, dimension(ldx21,*)x21, integer ldx21, double precision, dimension(*) theta, doubleprecision, dimension(*) phi, complex*16, dimension(*) taup1,complex*16, dimension(*) taup2, complex*16, dimension(*) tauq1,complex*16, dimension(*) work, integer lwork, integer info)
Author

NAME

unbdb2 - {un,or}bdb2: step in uncsd2by1

SYNOPSIS

Functions

subroutine cunbdb2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
CUNBDB2
subroutine dorbdb2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
DORBDB2
subroutine sorbdb2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
SORBDB2
subroutine zunbdb2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
ZUNBDB2

Detailed Description

Function Documentation

subroutine cunbdb2 (integer m, integer p, integer q, complex,dimension(ldx11,*) x11, integer ldx11, complex, dimension(ldx21,*) x21,integer ldx21, real, dimension(*) theta, real, dimension(*) phi,complex, dimension(*) taup1, complex, dimension(*) taup2, complex,dimension(*) tauq1, complex, dimension(*) work, integer lwork, integerinfo)

CUNBDB2

Purpose:

CUNBDB2 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. P must be no larger than M-P,
Q, or M-Q. Routines CUNBDB1, CUNBDB3, and CUNBDB4 handle cases in
which 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 P-by-P bidiagonal matrices represented implicitly by
angles THETA, PHI.

Parameters

M

M is INTEGER
The number of rows X11 plus the number of rows in X21.

P

P is INTEGER
The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q).

Q

Q is INTEGER
The number of columns in X11 and X21. 0 <= Q <= M.

X11

X11 is 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.

LDX11

LDX11 is INTEGER
The leading dimension of X11. LDX11 >= P.

X21

X21 is 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.

LDX21

LDX21 is INTEGER
The leading dimension of X21. LDX21 >= M-P.

THETA

THETA is REAL array, dimension (Q)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

PHI

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

TAUP1

TAUP1 is COMPLEX array, dimension (P-1)
The scalar factors of the elementary reflectors that define
P1.

TAUP2

TAUP2 is COMPLEX array, dimension (Q)
The scalar factors of the elementary reflectors that define
P2.

TAUQ1

TAUQ1 is COMPLEX array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.

WORK

WORK is COMPLEX array, dimension (LWORK)

LWORK

LWORK is INTEGER
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.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The upper-bidiagonal blocks B11, B21 are represented implicitly by
angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
in each bidiagonal band is a product of a sine or cosine of a THETA
with a sine or cosine of a PHI. See [1] or CUNCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors.
See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
and CUNGLQ.

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

subroutine dorbdb2 (integer m, integer p, integer q, double precision,dimension(ldx11,*) x11, integer ldx11, double precision,dimension(ldx21,*) x21, integer ldx21, double precision, dimension(*)theta, double precision, dimension(*) phi, double precision,dimension(*) taup1, double precision, dimension(*) taup2, doubleprecision, dimension(*) tauq1, double precision, dimension(*) work,integer lwork, integer info)

DORBDB2

Purpose:

DORBDB2 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. P must be no larger than M-P,
Q, or M-Q. Routines DORBDB1, DORBDB3, and DORBDB4 handle cases in
which P is not the minimum dimension.

The orthogonal 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 P-by-P bidiagonal matrices represented implicitly by
angles THETA, PHI.

Parameters

M

M is INTEGER
The number of rows X11 plus the number of rows in X21.

P

P is INTEGER
The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q).

Q

Q is INTEGER
The number of columns in X11 and X21. 0 <= Q <= M.

X11

X11 is 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.

LDX11

LDX11 is INTEGER
The leading dimension of X11. LDX11 >= P.

X21

X21 is 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.

LDX21

LDX21 is INTEGER
The leading dimension of X21. LDX21 >= M-P.

THETA

THETA is DOUBLE PRECISION array, dimension (Q)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

PHI

PHI is DOUBLE PRECISION array, dimension (Q-1)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

TAUP1

TAUP1 is DOUBLE PRECISION array, dimension (P-1)
The scalar factors of the elementary reflectors that define
P1.

TAUP2

TAUP2 is DOUBLE PRECISION array, dimension (Q)
The scalar factors of the elementary reflectors that define
P2.

TAUQ1

TAUQ1 is DOUBLE PRECISION array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.

WORK

WORK is DOUBLE PRECISION array, dimension (LWORK)

LWORK

LWORK is INTEGER
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.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The upper-bidiagonal blocks B11, B21 are represented implicitly by
angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
in each bidiagonal band is a product of a sine or cosine of a THETA
with a sine or cosine of a PHI. See [1] or DORCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors.
See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
and DORGLQ.

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

subroutine sorbdb2 (integer m, integer p, integer q, real,dimension(ldx11,*) x11, integer ldx11, real, dimension(ldx21,*) x21,integer ldx21, real, dimension(*) theta, real, dimension(*) phi, real,dimension(*) taup1, real, dimension(*) taup2, real, dimension(*) tauq1,real, dimension(*) work, integer lwork, integer info)

SORBDB2

Purpose:

SORBDB2 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. P must be no larger than M-P,
Q, or M-Q. Routines SORBDB1, SORBDB3, and SORBDB4 handle cases in
which P is not the minimum dimension.

The orthogonal 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 P-by-P bidiagonal matrices represented implicitly by
angles THETA, PHI.

Parameters

M

M is INTEGER
The number of rows X11 plus the number of rows in X21.

P

P is INTEGER
The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q).

Q

Q is INTEGER
The number of columns in X11 and X21. 0 <= Q <= M.

X11

X11 is REAL 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.

LDX11

LDX11 is INTEGER
The leading dimension of X11. LDX11 >= P.

X21

X21 is REAL 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.

LDX21

LDX21 is INTEGER
The leading dimension of X21. LDX21 >= M-P.

THETA

THETA is REAL array, dimension (Q)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

PHI

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

TAUP1

TAUP1 is REAL array, dimension (P-1)
The scalar factors of the elementary reflectors that define
P1.

TAUP2

TAUP2 is REAL array, dimension (Q)
The scalar factors of the elementary reflectors that define
P2.

TAUQ1

TAUQ1 is REAL array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.

WORK

WORK is REAL array, dimension (LWORK)

LWORK

LWORK is INTEGER
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.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The upper-bidiagonal blocks B11, B21 are represented implicitly by
angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
in each bidiagonal band is a product of a sine or cosine of a THETA
with a sine or cosine of a PHI. See [1] or SORCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors.
See SORCSD2BY1 for details on generating P1, P2, and Q1 using SORGQR
and SORGLQ.

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

subroutine zunbdb2 (integer m, integer p, integer q, complex*16,dimension(ldx11,*) x11, integer ldx11, complex*16, dimension(ldx21,*)x21, integer ldx21, double precision, dimension(*) theta, doubleprecision, dimension(*) phi, complex*16, dimension(*) taup1,complex*16, dimension(*) taup2, complex*16, dimension(*) tauq1,complex*16, dimension(*) work, integer lwork, integer info)

ZUNBDB2

Purpose:

ZUNBDB2 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. P must be no larger than M-P,
Q, or M-Q. Routines ZUNBDB1, ZUNBDB3, and ZUNBDB4 handle cases in
which 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 P-by-P bidiagonal matrices represented implicitly by
angles THETA, PHI.

Parameters

M

M is INTEGER
The number of rows X11 plus the number of rows in X21.

P

P is INTEGER
The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q).

Q

Q is INTEGER
The number of columns in X11 and X21. 0 <= Q <= M.

X11

X11 is 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.

LDX11

LDX11 is INTEGER
The leading dimension of X11. LDX11 >= P.

X21

X21 is 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.

LDX21

LDX21 is INTEGER
The leading dimension of X21. LDX21 >= M-P.

THETA

THETA is DOUBLE PRECISION array, dimension (Q)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

PHI

PHI is DOUBLE PRECISION array, dimension (Q-1)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

TAUP1

TAUP1 is COMPLEX*16 array, dimension (P-1)
The scalar factors of the elementary reflectors that define
P1.

TAUP2

TAUP2 is COMPLEX*16 array, dimension (Q)
The scalar factors of the elementary reflectors that define
P2.

TAUQ1

TAUQ1 is COMPLEX*16 array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.

WORK

WORK is COMPLEX*16 array, dimension (LWORK)

LWORK

LWORK is INTEGER
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.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The upper-bidiagonal blocks B11, B21 are represented implicitly by
angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
in each bidiagonal band is a product of a sine or cosine of a THETA
with a sine or cosine of a PHI. See [1] or ZUNCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors.
See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR
and ZUNGLQ.

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Author

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