dorcsd2by1 (3) Linux Manual Page

dorcsd2by1.f –

Synopsis

Functions/Subroutines

subroutine dorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO)
DORCSD2BY1

Function/Subroutine Documentation

subroutine dorcsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T, integerM, integerP, integerQ, double precision, dimension(ldx11,*)X11, integerLDX11, double precision, dimension(ldx21,*)X21, integerLDX21, double precision, dimension(*)THETA, double precision, dimension(ldu1,*)U1, integerLDU1, double precision, dimension(ldu2,*)U2, integerLDU2, double precision, dimension(ldv1t,*)V1T, integerLDV1T, double precision, dimension(*)WORK, integerLWORK, integer, dimension(*)IWORK, integerINFO)

DORCSD2BY1 .SH "Purpose:"

 Purpose:

 ========

 DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with

 orthonormal columns that has been partitioned into a 2-by-1 block

 structure:

 [ I 0 0 ]

 [ 0 C 0 ]

 [ X11 ] [ U1 | ] [ 0 0 0 ]

 X = [—–] = [———] [———-] V1**T .

 [ X21 ] [ | U2 ] [ 0 0 0 ]

 [ 0 S 0 ]

 [ 0 0 I ]

 X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,

 (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are

 R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in

 which R = MIN(P,M-P,Q,M-Q)..fi
Parameters:

JOBU1

 JOBU1 is CHARACTER

 = ‘Y’: U1 is computed;

 otherwise: U1 is not computed.

JOBU2

 JOBU2 is CHARACTER

 = ‘Y’: U2 is computed;

 otherwise: U2 is not computed.

JOBV1T

 JOBV1T is CHARACTER

 = ‘Y’: V1T is computed;

 otherwise: V1T is not computed.

M

 M is INTEGER

 The number of rows and columns in X.

P

 P is INTEGER

 The number of rows in X11 and X12. 0 <= P <= M.

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, part of the orthogonal matrix whose CSD is

 desired.

LDX11

 LDX11 is INTEGER

 The leading dimension of X11. LDX11 >= MAX(1,P).

X21

 X21 is DOUBLE PRECISION array, dimension (LDX21,Q)

 On entry, part of the orthogonal matrix whose CSD is

 desired.

LDX21

 LDX21 is INTEGER

 The leading dimension of X21. LDX21 >= MAX(1,M-P).

THETA

 THETA is DOUBLE PRECISION array, dimension (R), in which R =

 MIN(P,M-P,Q,M-Q).

 C = DIAG( COS(THETA(1)), … , COS(THETA(R)) ) and

 S = DIAG( SIN(THETA(1)), … , SIN(THETA(R)) ).

U1

 U1 is DOUBLE PRECISION array, dimension (P)

 If JOBU1 = ‘Y’, U1 contains the P-by-P orthogonal matrix U1.

LDU1

 LDU1 is INTEGER

 The leading dimension of U1. If JOBU1 = ‘Y’, LDU1 >=

 MAX(1,P).

U2

 U2 is DOUBLE PRECISION array, dimension (M-P)

 If JOBU2 = ‘Y’, U2 contains the (M-P)-by-(M-P) orthogonal

 matrix U2.

LDU2

 LDU2 is INTEGER

 The leading dimension of U2. If JOBU2 = ‘Y’, LDU2 >=

 MAX(1,M-P).

V1T

 V1T is DOUBLE PRECISION array, dimension (Q)

 If JOBV1T = ‘Y’, V1T contains the Q-by-Q matrix orthogonal

 matrix V1**T.

LDV1T

 LDV1T is INTEGER

 The leading dimension of V1T. If JOBV1T = ‘Y’, LDV1T >=

 MAX(1,Q).

WORK

 WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))

 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

 If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),

 …, PHI(R-1) that, together with THETA(1), …, THETA(R),

 define the matrix in intermediate bidiagonal-block form

 remaining after nonconvergence. INFO specifies the number

 of nonzero PHI’s.

LWORK

 LWORK is INTEGER

 The dimension of the array WORK.

 

 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.

 
IWORK

 IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))

INFO

 INFO is INTEGER

 = 0: successful exit.

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

 > 0: DBBCSD did not converge. See the description of WORK

 above for details.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

July 2012

References:

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

Definition at line 236 of file dorcsd2by1.f.

Author

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