![]() |
LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
|
subroutine dcsdts | ( | integer | M, |
integer | P, | ||
integer | Q, | ||
double precision, dimension( ldx, * ) | X, | ||
double precision, dimension( ldx, * ) | XF, | ||
integer | LDX, | ||
double precision, dimension( ldu1, * ) | U1, | ||
integer | LDU1, | ||
double precision, dimension( ldu2, * ) | U2, | ||
integer | LDU2, | ||
double precision, dimension( ldv1t, * ) | V1T, | ||
integer | LDV1T, | ||
double precision, dimension( ldv2t, * ) | V2T, | ||
integer | LDV2T, | ||
double precision, dimension( * ) | THETA, | ||
integer, dimension( * ) | IWORK, | ||
double precision, dimension( lwork ) | WORK, | ||
integer | LWORK, | ||
double precision, dimension( * ) | RWORK, | ||
double precision, dimension( 15 ) | RESULT | ||
) |
DCSDTS
DCSDTS tests DORCSD, 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 DORCSD2BY1, 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 ]
[in] | M | M is INTEGER The number of rows of the matrix X. M >= 0. |
[in] | P | P is INTEGER The number of rows of the matrix X11. P >= 0. |
[in] | Q | Q is INTEGER The number of columns of the matrix X11. Q >= 0. |
[in] | X | X is DOUBLE PRECISION array, dimension (LDX,M) The M-by-M matrix X. |
[out] | XF | XF is DOUBLE PRECISION array, dimension (LDX,M) Details of the CSD of X, as returned by DORCSD; see DORCSD for further details. |
[in] | LDX | LDX is INTEGER The leading dimension of the arrays X and XF. LDX >= max( 1,M ). |
[out] | U1 | U1 is DOUBLE PRECISION array, dimension(LDU1,P) The P-by-P orthogonal matrix U1. |
[in] | LDU1 | LDU1 is INTEGER The leading dimension of the array U1. LDU >= max(1,P). |
[out] | U2 | U2 is DOUBLE PRECISION array, dimension(LDU2,M-P) The (M-P)-by-(M-P) orthogonal matrix U2. |
[in] | LDU2 | LDU2 is INTEGER The leading dimension of the array U2. LDU >= max(1,M-P). |
[out] | V1T | V1T is DOUBLE PRECISION array, dimension(LDV1T,Q) The Q-by-Q orthogonal matrix V1T. |
[in] | LDV1T | LDV1T is INTEGER The leading dimension of the array V1T. LDV1T >= max(1,Q). |
[out] | V2T | V2T is DOUBLE PRECISION array, dimension(LDV2T,M-Q) The (M-Q)-by-(M-Q) orthogonal matrix V2T. |
[in] | LDV2T | LDV2T is INTEGER The leading dimension of the array V2T. LDV2T >= max(1,M-Q). |
[out] | THETA | THETA is DOUBLE PRECISION 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 DORCSD for details. |
[out] | IWORK | IWORK is INTEGER array, dimension (M) |
[out] | WORK | WORK is DOUBLE PRECISION array, dimension (LWORK) |
[in] | LWORK | LWORK is INTEGER The dimension of the array WORK |
[out] | RWORK | RWORK is DOUBLE PRECISION array |
[out] | RESULT | RESULT is DOUBLE PRECISION 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 ). ) |
Definition at line 231 of file dcsdts.f.