*> \brief \b ALAHDG
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ALAHDG( IOUNIT, PATH )
*
* .. Scalar Arguments ..
* CHARACTER*3 PATH
* INTEGER IOUNIT
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ALAHDG prints header information for the different test paths.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] IOUNIT
*> \verbatim
*> IOUNIT is INTEGER
*> The unit number to which the header information should be
*> printed.
*> \endverbatim
*>
*> \param[in] PATH
*> \verbatim
*> PATH is CHARACTER*3
*> The name of the path for which the header information is to
*> be printed. Current paths are
*> GQR: GQR (general matrices)
*> GRQ: GRQ (general matrices)
*> LSE: LSE Problem
*> GLM: GLM Problem
*> GSV: Generalized Singular Value Decomposition
*> CSD: CS Decomposition
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup aux_eig
*
* =====================================================================
SUBROUTINE ALAHDG( IOUNIT, PATH )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER*3 PATH
INTEGER IOUNIT
* ..
*
* =====================================================================
*
* .. Local Scalars ..
CHARACTER*3 C2
INTEGER ITYPE
* ..
* .. External Functions ..
LOGICAL LSAMEN
EXTERNAL LSAMEN
* ..
* .. Executable Statements ..
*
IF( IOUNIT.LE.0 )
$ RETURN
C2 = PATH( 1: 3 )
*
* First line describing matrices in this path
*
IF( LSAMEN( 3, C2, 'GQR' ) ) THEN
ITYPE = 1
WRITE( IOUNIT, FMT = 9991 )PATH
ELSE IF( LSAMEN( 3, C2, 'GRQ' ) ) THEN
ITYPE = 2
WRITE( IOUNIT, FMT = 9992 )PATH
ELSE IF( LSAMEN( 3, C2, 'LSE' ) ) THEN
ITYPE = 3
WRITE( IOUNIT, FMT = 9993 )PATH
ELSE IF( LSAMEN( 3, C2, 'GLM' ) ) THEN
ITYPE = 4
WRITE( IOUNIT, FMT = 9994 )PATH
ELSE IF( LSAMEN( 3, C2, 'GSV' ) ) THEN
ITYPE = 5
WRITE( IOUNIT, FMT = 9995 )PATH
ELSE IF( LSAMEN( 3, C2, 'CSD' ) ) THEN
ITYPE = 6
WRITE( IOUNIT, FMT = 9996 )PATH
END IF
*
* Matrix types
*
WRITE( IOUNIT, FMT = 9999 )'Matrix types: '
*
IF( ITYPE.EQ.1 )THEN
WRITE( IOUNIT, FMT = 9950 )1
WRITE( IOUNIT, FMT = 9952 )2
WRITE( IOUNIT, FMT = 9954 )3
WRITE( IOUNIT, FMT = 9955 )4
WRITE( IOUNIT, FMT = 9956 )5
WRITE( IOUNIT, FMT = 9957 )6
WRITE( IOUNIT, FMT = 9961 )7
WRITE( IOUNIT, FMT = 9962 )8
ELSE IF( ITYPE.EQ.2 )THEN
WRITE( IOUNIT, FMT = 9951 )1
WRITE( IOUNIT, FMT = 9953 )2
WRITE( IOUNIT, FMT = 9954 )3
WRITE( IOUNIT, FMT = 9955 )4
WRITE( IOUNIT, FMT = 9956 )5
WRITE( IOUNIT, FMT = 9957 )6
WRITE( IOUNIT, FMT = 9961 )7
WRITE( IOUNIT, FMT = 9962 )8
ELSE IF( ITYPE.EQ.3 )THEN
WRITE( IOUNIT, FMT = 9950 )1
WRITE( IOUNIT, FMT = 9952 )2
WRITE( IOUNIT, FMT = 9954 )3
WRITE( IOUNIT, FMT = 9955 )4
WRITE( IOUNIT, FMT = 9955 )5
WRITE( IOUNIT, FMT = 9955 )6
WRITE( IOUNIT, FMT = 9955 )7
WRITE( IOUNIT, FMT = 9955 )8
ELSE IF( ITYPE.EQ.4 )THEN
WRITE( IOUNIT, FMT = 9951 )1
WRITE( IOUNIT, FMT = 9953 )2
WRITE( IOUNIT, FMT = 9954 )3
WRITE( IOUNIT, FMT = 9955 )4
WRITE( IOUNIT, FMT = 9955 )5
WRITE( IOUNIT, FMT = 9955 )6
WRITE( IOUNIT, FMT = 9955 )7
WRITE( IOUNIT, FMT = 9955 )8
ELSE IF( ITYPE.EQ.5 )THEN
WRITE( IOUNIT, FMT = 9950 )1
WRITE( IOUNIT, FMT = 9952 )2
WRITE( IOUNIT, FMT = 9954 )3
WRITE( IOUNIT, FMT = 9955 )4
WRITE( IOUNIT, FMT = 9956 )5
WRITE( IOUNIT, FMT = 9957 )6
WRITE( IOUNIT, FMT = 9959 )7
WRITE( IOUNIT, FMT = 9960 )8
ELSE IF( ITYPE.EQ.6 )THEN
WRITE( IOUNIT, FMT = 9963 )1
WRITE( IOUNIT, FMT = 9964 )2
WRITE( IOUNIT, FMT = 9965 )3
END IF
*
* Tests performed
*
WRITE( IOUNIT, FMT = 9999 )'Test ratios: '
*
IF( ITYPE.EQ.1 ) THEN
*
* GQR decomposition of rectangular matrices
*
WRITE( IOUNIT, FMT = 9930 )1
WRITE( IOUNIT, FMT = 9931 )2
WRITE( IOUNIT, FMT = 9932 )3
WRITE( IOUNIT, FMT = 9933 )4
ELSE IF( ITYPE.EQ.2 ) THEN
*
* GRQ decomposition of rectangular matrices
*
WRITE( IOUNIT, FMT = 9934 )1
WRITE( IOUNIT, FMT = 9935 )2
WRITE( IOUNIT, FMT = 9932 )3
WRITE( IOUNIT, FMT = 9933 )4
ELSE IF( ITYPE.EQ.3 ) THEN
*
* LSE Problem
*
WRITE( IOUNIT, FMT = 9937 )1
WRITE( IOUNIT, FMT = 9938 )2
ELSE IF( ITYPE.EQ.4 ) THEN
*
* GLM Problem
*
WRITE( IOUNIT, FMT = 9939 )1
ELSE IF( ITYPE.EQ.5 ) THEN
*
* GSVD
*
WRITE( IOUNIT, FMT = 9940 )1
WRITE( IOUNIT, FMT = 9941 )2
WRITE( IOUNIT, FMT = 9942 )3
WRITE( IOUNIT, FMT = 9943 )4
WRITE( IOUNIT, FMT = 9944 )5
ELSE IF( ITYPE.EQ.6 ) THEN
*
* CSD
*
WRITE( IOUNIT, FMT = 9910 )
WRITE( IOUNIT, FMT = 9911 )1
WRITE( IOUNIT, FMT = 9912 )2
WRITE( IOUNIT, FMT = 9913 )3
WRITE( IOUNIT, FMT = 9914 )4
WRITE( IOUNIT, FMT = 9915 )5
WRITE( IOUNIT, FMT = 9916 )6
WRITE( IOUNIT, FMT = 9917 )7
WRITE( IOUNIT, FMT = 9918 )8
WRITE( IOUNIT, FMT = 9919 )9
WRITE( IOUNIT, FMT = 9920 )
WRITE( IOUNIT, FMT = 9921 )10
WRITE( IOUNIT, FMT = 9922 )11
WRITE( IOUNIT, FMT = 9923 )12
WRITE( IOUNIT, FMT = 9924 )13
WRITE( IOUNIT, FMT = 9925 )14
WRITE( IOUNIT, FMT = 9926 )15
END IF
*
9999 FORMAT( 1X, A )
9991 FORMAT( / 1X, A3, ': GQR factorization of general matrices' )
9992 FORMAT( / 1X, A3, ': GRQ factorization of general matrices' )
9993 FORMAT( / 1X, A3, ': LSE Problem' )
9994 FORMAT( / 1X, A3, ': GLM Problem' )
9995 FORMAT( / 1X, A3, ': Generalized Singular Value Decomposition' )
9996 FORMAT( / 1X, A3, ': CS Decomposition' )
*
9950 FORMAT( 3X, I2, ': A-diagonal matrix B-upper triangular' )
9951 FORMAT( 3X, I2, ': A-diagonal matrix B-lower triangular' )
9952 FORMAT( 3X, I2, ': A-upper triangular B-upper triangular' )
9953 FORMAT( 3X, I2, ': A-lower triangular B-diagonal triangular' )
9954 FORMAT( 3X, I2, ': A-lower triangular B-upper triangular' )
*
9955 FORMAT( 3X, I2, ': Random matrices cond(A)=100, cond(B)=10,' )
*
9956 FORMAT( 3X, I2, ': Random matrices cond(A)= sqrt( 0.1/EPS ) ',
$ 'cond(B)= sqrt( 0.1/EPS )' )
9957 FORMAT( 3X, I2, ': Random matrices cond(A)= 0.1/EPS ',
$ 'cond(B)= 0.1/EPS' )
9959 FORMAT( 3X, I2, ': Random matrices cond(A)= sqrt( 0.1/EPS ) ',
$ 'cond(B)= 0.1/EPS ' )
9960 FORMAT( 3X, I2, ': Random matrices cond(A)= 0.1/EPS ',
$ 'cond(B)= sqrt( 0.1/EPS )' )
*
9961 FORMAT( 3X, I2, ': Matrix scaled near underflow limit' )
9962 FORMAT( 3X, I2, ': Matrix scaled near overflow limit' )
9963 FORMAT( 3X, I2, ': Random orthogonal matrix (Haar measure)' )
9964 FORMAT( 3X, I2, ': Nearly orthogonal matrix with uniformly ',
$ 'distributed angles atan2( S, C ) in CS decomposition' )
9965 FORMAT( 3X, I2, ': Random orthogonal matrix with clustered ',
$ 'angles atan2( S, C ) in CS decomposition' )
*
*
* GQR test ratio
*
9930 FORMAT( 3X, I2, ': norm( R - Q'' * A ) / ( min( N, M )*norm( A )',
$ '* EPS )' )
9931 FORMAT( 3X, I2, ': norm( T * Z - Q'' * B ) / ( min(P,N)*norm(B)',
$ '* EPS )' )
9932 FORMAT( 3X, I2, ': norm( I - Q''*Q ) / ( N * EPS )' )
9933 FORMAT( 3X, I2, ': norm( I - Z''*Z ) / ( P * EPS )' )
*
* GRQ test ratio
*
9934 FORMAT( 3X, I2, ': norm( R - A * Q'' ) / ( min( N,M )*norm(A) * ',
$ 'EPS )' )
9935 FORMAT( 3X, I2, ': norm( T * Q - Z'' * B ) / ( min( P,N ) * nor',
$ 'm(B)*EPS )' )
*
* LSE test ratio
*
9937 FORMAT( 3X, I2, ': norm( A*x - c ) / ( norm(A)*norm(x) * EPS )' )
9938 FORMAT( 3X, I2, ': norm( B*x - d ) / ( norm(B)*norm(x) * EPS )' )
*
* GLM test ratio
*
9939 FORMAT( 3X, I2, ': norm( d - A*x - B*y ) / ( (norm(A)+norm(B) )*',
$ '(norm(x)+norm(y))*EPS )' )
*
* GSVD test ratio
*
9940 FORMAT( 3X, I2, ': norm( U'' * A * Q - D1 * R ) / ( min( M, N )*',
$ 'norm( A ) * EPS )' )
9941 FORMAT( 3X, I2, ': norm( V'' * B * Q - D2 * R ) / ( min( P, N )*',
$ 'norm( B ) * EPS )' )
9942 FORMAT( 3X, I2, ': norm( I - U''*U ) / ( M * EPS )' )
9943 FORMAT( 3X, I2, ': norm( I - V''*V ) / ( P * EPS )' )
9944 FORMAT( 3X, I2, ': norm( I - Q''*Q ) / ( N * EPS )' )
*
* CSD test ratio
*
9910 FORMAT( 3X, '2-by-2 CSD' )
9911 FORMAT( 3X, I2, ': norm( U1'' * X11 * V1 - C ) / ( max( P, Q)',
$ ' * max(norm(I-X''*X),EPS) )' )
9912 FORMAT( 3X, I2, ': norm( U1'' * X12 * V2-(-S)) / ( max( P,',
$ 'M-Q) * max(norm(I-X''*X),EPS) )' )
9913 FORMAT( 3X, I2, ': norm( U2'' * X21 * V1 - S ) / ( max(M-P,',
$ ' Q) * max(norm(I-X''*X),EPS) )' )
9914 FORMAT( 3X, I2, ': norm( U2'' * X22 * V2 - C ) / ( max(M-P,',
$ 'M-Q) * max(norm(I-X''*X),EPS) )' )
9915 FORMAT( 3X, I2, ': norm( I - U1''*U1 ) / ( P * EPS )' )
9916 FORMAT( 3X, I2, ': norm( I - U2''*U2 ) / ( (M-P) * EPS )' )
9917 FORMAT( 3X, I2, ': norm( I - V1''*V1 ) / ( Q * EPS )' )
9918 FORMAT( 3X, I2, ': norm( I - V2''*V2 ) / ( (M-Q) * EPS )' )
9919 FORMAT( 3X, I2, ': principal angle ordering ( 0 or ULP )' )
9920 FORMAT( 3X, '2-by-1 CSD' )
9921 FORMAT( 3X, I2, ': norm( U1'' * X11 * V1 - C ) / ( max( P, Q)',
$ ' * max(norm(I-X''*X),EPS) )' )
9922 FORMAT( 3X, I2, ': norm( U2'' * X21 * V1 - S ) / ( max( M-P,',
$ 'Q) * max(norm(I-X''*X),EPS) )' )
9923 FORMAT( 3X, I2, ': norm( I - U1''*U1 ) / ( P * EPS )' )
9924 FORMAT( 3X, I2, ': norm( I - U2''*U2 ) / ( (M-P) * EPS )' )
9925 FORMAT( 3X, I2, ': norm( I - V1''*V1 ) / ( Q * EPS )' )
9926 FORMAT( 3X, I2, ': principal angle ordering ( 0 or ULP )' )
RETURN
*
* End of ALAHDG
*
END