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SUBROUTINE <a name="SLAGS2.1"></a><a href="slags2.f.html#SLAGS2.1">SLAGS2</a>( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
$ SNV, CSQ, SNQ )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> LOGICAL UPPER
REAL A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV, SNQ,
$ SNU, SNV
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SLAGS2.17"></a><a href="slags2.f.html#SLAGS2.1">SLAGS2</a> computes 2-by-2 orthogonal matrices U, V and Q, such
</span><span class="comment">*</span><span class="comment"> that if ( UPPER ) then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U'*A*Q = U'*( A1 A2 )*Q = ( x 0 )
</span><span class="comment">*</span><span class="comment"> ( 0 A3 ) ( x x )
</span><span class="comment">*</span><span class="comment"> and
</span><span class="comment">*</span><span class="comment"> V'*B*Q = V'*( B1 B2 )*Q = ( x 0 )
</span><span class="comment">*</span><span class="comment"> ( 0 B3 ) ( x x )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> or if ( .NOT.UPPER ) then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U'*A*Q = U'*( A1 0 )*Q = ( x x )
</span><span class="comment">*</span><span class="comment"> ( A2 A3 ) ( 0 x )
</span><span class="comment">*</span><span class="comment"> and
</span><span class="comment">*</span><span class="comment"> V'*B*Q = V'*( B1 0 )*Q = ( x x )
</span><span class="comment">*</span><span class="comment"> ( B2 B3 ) ( 0 x )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The rows of the transformed A and B are parallel, where
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ )
</span><span class="comment">*</span><span class="comment"> ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z' denotes the transpose of Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPPER (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> = .TRUE.: the input matrices A and B are upper triangular.
</span><span class="comment">*</span><span class="comment"> = .FALSE.: the input matrices A and B are lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A1 (input) REAL
</span><span class="comment">*</span><span class="comment"> A2 (input) REAL
</span><span class="comment">*</span><span class="comment"> A3 (input) REAL
</span><span class="comment">*</span><span class="comment"> On entry, A1, A2 and A3 are elements of the input 2-by-2
</span><span class="comment">*</span><span class="comment"> upper (lower) triangular matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B1 (input) REAL
</span><span class="comment">*</span><span class="comment"> B2 (input) REAL
</span><span class="comment">*</span><span class="comment"> B3 (input) REAL
</span><span class="comment">*</span><span class="comment"> On entry, B1, B2 and B3 are elements of the input 2-by-2
</span><span class="comment">*</span><span class="comment"> upper (lower) triangular matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CSU (output) REAL
</span><span class="comment">*</span><span class="comment"> SNU (output) REAL
</span><span class="comment">*</span><span class="comment"> The desired orthogonal matrix U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CSV (output) REAL
</span><span class="comment">*</span><span class="comment"> SNV (output) REAL
</span><span class="comment">*</span><span class="comment"> The desired orthogonal matrix V.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CSQ (output) REAL
</span><span class="comment">*</span><span class="comment"> SNQ (output) REAL
</span><span class="comment">*</span><span class="comment"> The desired orthogonal matrix Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> REAL A, AUA11, AUA12, AUA21, AUA22, AVB11, AVB12,
$ AVB21, AVB22, CSL, CSR, D, S1, S2, SNL,
$ SNR, UA11R, UA22R, VB11R, VB22R, B, C, R, UA11,
$ UA12, UA21, UA22, VB11, VB12, VB21, VB22
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SLARTG.86"></a><a href="slartg.f.html#SLARTG.1">SLARTG</a>, <a name="SLASV2.86"></a><a href="slasv2.f.html#SLASV2.1">SLASV2</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Input matrices A and B are upper triangular matrices
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Form matrix C = A*adj(B) = ( a b )
</span><span class="comment">*</span><span class="comment"> ( 0 d )
</span><span class="comment">*</span><span class="comment">
</span> A = A1*B3
D = A3*B1
B = A2*B1 - A1*B2
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The SVD of real 2-by-2 triangular C
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 )
</span><span class="comment">*</span><span class="comment"> ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T )
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="SLASV2.109"></a><a href="slasv2.f.html#SLASV2.1">SLASV2</a>( A, B, D, S1, S2, SNR, CSR, SNL, CSL )
<span class="comment">*</span><span class="comment">
</span> IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
$ THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the (1,1) and (1,2) elements of U'*A and V'*B,
</span><span class="comment">*</span><span class="comment"> and (1,2) element of |U|'*|A| and |V|'*|B|.
</span><span class="comment">*</span><span class="comment">
</span> UA11R = CSL*A1
UA12 = CSL*A2 + SNL*A3
<span class="comment">*</span><span class="comment">
</span> VB11R = CSR*B1
VB12 = CSR*B2 + SNR*B3
<span class="comment">*</span><span class="comment">
</span> AUA12 = ABS( CSL )*ABS( A2 ) + ABS( SNL )*ABS( A3 )
AVB12 = ABS( CSR )*ABS( B2 ) + ABS( SNR )*ABS( B3 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> zero (1,2) elements of U'*A and V'*B
</span><span class="comment">*</span><span class="comment">
</span> IF( ( ABS( UA11R )+ABS( UA12 ) ).NE.ZERO ) THEN
IF( AUA12 / ( ABS( UA11R )+ABS( UA12 ) ).LE.AVB12 /
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