cuncsd2by1 (3) Linux Manual Page

cuncsd2by1.f –

Synopsis

Functions/Subroutines

subroutine cuncsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CUNCSD2BY1

Function/Subroutine Documentation

subroutine cuncsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T, integerM, integerP, integerQ, complex, dimension(ldx11,*)X11, integerLDX11, complex, dimension(ldx21,*)X21, integerLDX21, real, dimension(*)THETA, complex, dimension(ldu1,*)U1, integerLDU1, complex, dimension(ldu2,*)U2, integerLDU2, complex, dimension(ldv1t,*)V1T, integerLDV1T, complex, dimension(*)WORK, integerLWORK, real, dimension(*)RWORK, integerLRWORK, integer, dimension(*)IWORK, integerINFO)

CUNCSD2BY1 .SH "Purpose:"

 CUNCSD2BY1 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 unitary 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 COMPLEX array, dimension (LDX11,Q)

 On entry, part of the unitary matrix whose CSD is

 desired.

LDX11

 LDX11 is INTEGER

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

X21

 X21 is COMPLEX array, dimension (LDX21,Q)

 On entry, part of the unitary matrix whose CSD is

 desired.

LDX21

 LDX21 is INTEGER

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

THETA

 THETA is COMPLEX 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 COMPLEX array, dimension (P)

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

LDU1

 LDU1 is INTEGER

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

 MAX(1,P).

U2

 U2 is COMPLEX array, dimension (M-P)

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

 matrix U2.

LDU2

 LDU2 is INTEGER

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

 MAX(1,M-P).

V1T

 V1T is COMPLEX array, dimension (Q)

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

 matrix V1**T.

LDV1T

 LDV1T is INTEGER

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

 MAX(1,Q).

WORK

 WORK is COMPLEX 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.

RWORK

 RWORK is REAL array, dimension (MAX(1,LRWORK))

 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

 If INFO > 0 on exit, RWORK(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.

LRWORK

 LRWORK is INTEGER

 The dimension of the array RWORK.

 If LRWORK = -1, then a workspace query is assumed; the routine

 only calculates the optimal size of the RWORK array, returns

 this value as the first entry of the work array, and no error

 message related to LRWORK is issued by XERBLA.

 


aram[out] IWORK

 nsion (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: CBBCSD did not converge. See the description of WORK

 above for details.

References:

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

July 2012

Definition at line 260 of file cuncsd2by1.f.

Author

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