.TH "TESTING/EIG/scsdts.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/scsdts.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBscsdts\fP (m, p, q, x, xf, ldx, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, theta, iwork, work, lwork, rwork, result)"
.br
.RI "\fBSCSDTS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine scsdts (integer m, integer p, integer q, real, dimension( ldx, * ) x, real, dimension( ldx, * ) xf, integer ldx, real, dimension( ldu1, * ) u1, integer ldu1, real, dimension( ldu2, * ) u2, integer ldu2, real, dimension( ldv1t, * ) v1t, integer ldv1t, real, dimension( ldv2t, * ) v2t, integer ldv2t, real, dimension( * ) theta, integer, dimension( * ) iwork, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 15 ) result)"

.PP
\fBSCSDTS\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SCSDTS tests SORCSD, which, given an M-by-M partitioned orthogonal
!> matrix X,
!>              Q  M-Q
!>       X = [ X11 X12 ] P   ,
!>           [ X21 X22 ] M-P
!>
!> computes the CSD
!>
!>       [ U1    ]**T * [ X11 X12 ] * [ V1    ]
!>       [    U2 ]      [ X21 X22 ]   [    V2 ]
!>
!>                             [  I  0  0 |  0  0  0 ]
!>                             [  0  C  0 |  0 -S  0 ]
!>                             [  0  0  0 |  0  0 -I ]
!>                           = [---------------------] = [ D11 D12 ] \&.
!>                             [  0  0  0 |  I  0  0 ]   [ D21 D22 ]
!>                             [  0  S  0 |  0  C  0 ]
!>                             [  0  0  I |  0  0  0 ]
!>
!> and also SORCSD2BY1, which, given
!>          Q
!>       [ X11 ] P   ,
!>       [ X21 ] M-P
!>
!> computes the 2-by-1 CSD
!>
!>                                     [  I  0  0 ]
!>                                     [  0  C  0 ]
!>                                     [  0  0  0 ]
!>       [ U1    ]**T * [ X11 ] * V1 = [----------] = [ D11 ] ,
!>       [    U2 ]      [ X21 ]        [  0  0  0 ]   [ D21 ]
!>                                     [  0  S  0 ]
!>                                     [  0  0  I ]
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix X\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of rows of the matrix X11\&.  P >= 0\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is INTEGER
!>          The number of columns of the matrix X11\&.  Q >= 0\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is REAL array, dimension (LDX,M)
!>          The M-by-M matrix X\&.
!> 
.fi
.PP
.br
\fIXF\fP 
.PP
.nf
!>          XF is REAL array, dimension (LDX,M)
!>          Details of the CSD of X, as returned by SORCSD;
!>          see SORCSD for further details\&.
!> 
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
!>          LDX is INTEGER
!>          The leading dimension of the arrays X and XF\&.
!>          LDX >= max( 1,M )\&.
!> 
.fi
.PP
.br
\fIU1\fP 
.PP
.nf
!>          U1 is REAL array, dimension(LDU1,P)
!>          The P-by-P orthogonal matrix U1\&.
!> 
.fi
.PP
.br
\fILDU1\fP 
.PP
.nf
!>          LDU1 is INTEGER
!>          The leading dimension of the array U1\&. LDU >= max(1,P)\&.
!> 
.fi
.PP
.br
\fIU2\fP 
.PP
.nf
!>          U2 is REAL array, dimension(LDU2,M-P)
!>          The (M-P)-by-(M-P) orthogonal matrix U2\&.
!> 
.fi
.PP
.br
\fILDU2\fP 
.PP
.nf
!>          LDU2 is INTEGER
!>          The leading dimension of the array U2\&. LDU >= max(1,M-P)\&.
!> 
.fi
.PP
.br
\fIV1T\fP 
.PP
.nf
!>          V1T is REAL array, dimension(LDV1T,Q)
!>          The Q-by-Q orthogonal matrix V1T\&.
!> 
.fi
.PP
.br
\fILDV1T\fP 
.PP
.nf
!>          LDV1T is INTEGER
!>          The leading dimension of the array V1T\&. LDV1T >=
!>          max(1,Q)\&.
!> 
.fi
.PP
.br
\fIV2T\fP 
.PP
.nf
!>          V2T is REAL array, dimension(LDV2T,M-Q)
!>          The (M-Q)-by-(M-Q) orthogonal matrix V2T\&.
!> 
.fi
.PP
.br
\fILDV2T\fP 
.PP
.nf
!>          LDV2T is INTEGER
!>          The leading dimension of the array V2T\&. LDV2T >=
!>          max(1,M-Q)\&.
!> 
.fi
.PP
.br
\fITHETA\fP 
.PP
.nf
!>          THETA is REAL array, dimension MIN(P,M-P,Q,M-Q)
!>          The CS values of X; the essentially diagonal matrices C and
!>          S are constructed from THETA; see subroutine SORCSD for
!>          details\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (M)
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          RWORK is REAL array
!> 
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
!>          RESULT is REAL array, dimension (15)
!>          The test ratios:
!>          First, the 2-by-2 CSD:
!>          RESULT(1) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
!>          RESULT(2) = norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 )
!>          RESULT(3) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
!>          RESULT(4) = norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 )
!>          RESULT(5) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
!>          RESULT(6) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
!>          RESULT(7) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
!>          RESULT(8) = norm( I - V2T'*V2T ) / ( MAX(1,M-Q)*ULP )
!>          RESULT(9) = 0        if THETA is in increasing order and
!>                               all angles are in [0,pi/2] 

!>                    = ULPINV   otherwise\&.
!>          Then, the 2-by-1 CSD:
!>          RESULT(10) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
!>          RESULT(11) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
!>          RESULT(12) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
!>          RESULT(13) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
!>          RESULT(14) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
!>          RESULT(15) = 0        if THETA is in increasing order and
!>                                all angles are in [0,pi/2] 

!>                     = ULPINV   otherwise\&.
!>          ( EPS2 = MAX( norm( I - X'*X ) / M, ULP )\&. )
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB226\fP of file \fBscsdts\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.