sorcsd (3) - Linux Manuals

NAME

sorcsd.f -

SYNOPSIS


Functions/Subroutines


recursive subroutine sorcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO)
SORCSD

Function/Subroutine Documentation

recursive subroutine sorcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, characterSIGNS, integerM, integerP, integerQ, real, dimension( ldx11, * )X11, integerLDX11, real, dimension( ldx12, * )X12, integerLDX12, real, dimension( ldx21, * )X21, integerLDX21, real, dimension( ldx22, * )X22, integerLDX22, real, dimension( * )THETA, real, dimension( ldu1, * )U1, integerLDU1, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldv1t, * )V1T, integerLDV1T, real, dimension( ldv2t, * )V2T, integerLDV2T, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)

SORCSD

Purpose: 

 SORCSD computes the CS decomposition of an M-by-M partitioned
 orthogonal matrix X:

                                 [  I  0  0 |  0  0  0 ]
                                 [  0  C  0 |  0 -S  0 ]
     [ X11 | X12 ]   [ U1 |    ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**T
 X = [-----------] = [---------] [---------------------] [---------]   .
     [ X21 | X22 ]   [    | U2 ] [  0  0  0 |  I  0  0 ] [    | V2 ]
                                 [  0  S  0 |  0  C  0 ]
                                 [  0  0  I |  0  0  0 ]

 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).


 

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.


JOBV2T 

          JOBV2T is CHARACTER
          = 'Y':      V2T is computed;
          otherwise:  V2T is not computed.


TRANS 

          TRANS is CHARACTER
          = 'T':      X, U1, U2, V1T, and V2T are stored in row-major
                      order;
          otherwise:  X, U1, U2, V1T, and V2T are stored in column-
                      major order.


SIGNS 

          SIGNS is CHARACTER
          = 'O':      The lower-left block is made nonpositive (the
                      "other" convention);
          otherwise:  The upper-right block is made nonpositive (the
                      "default" convention).


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 REAL 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).


X12 

          X12 is REAL array, dimension (LDX12,M-Q)
          On entry, part of the orthogonal matrix whose CSD is desired.


LDX12 

          LDX12 is INTEGER
          The leading dimension of X12. LDX12 >= MAX(1,P).


X21 

          X21 is REAL array, dimension (LDX21,Q)
          On entry, part of the orthogonal matrix whose CSD is desired.


LDX21 

          LDX21 is INTEGER
          The leading dimension of X11. LDX21 >= MAX(1,M-P).


X22 

          X22 is REAL array, dimension (LDX22,M-Q)
          On entry, part of the orthogonal matrix whose CSD is desired.


LDX22 

          LDX22 is INTEGER
          The leading dimension of X11. LDX22 >= MAX(1,M-P).


THETA 

          THETA is REAL 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 REAL 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 REAL 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 REAL 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).


V2T 

          V2T is REAL array, dimension (M-Q)
          If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
          matrix V2**T.


LDV2T 

          LDV2T is INTEGER
          The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
          MAX(1,M-Q).


WORK 

          WORK is REAL 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:  SBBCSD 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:

November 2013

Definition at line 297 of file sorcsd.f.

Author

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