dlasv2.f.html

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      SUBROUTINE <a name="DLASV2.1"></a><a href="dlasv2.f.html#DLASV2.1">DLASV2</a>( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
<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>      DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
<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="DLASV2.14"></a><a href="dlasv2.f.html#DLASV2.1">DLASV2</a> computes the singular value decomposition of a 2-by-2
</span><span class="comment">*</span><span class="comment">  triangular matrix
</span><span class="comment">*</span><span class="comment">     [  F   G  ]
</span><span class="comment">*</span><span class="comment">     [  0   H  ].
</span><span class="comment">*</span><span class="comment">  On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the
</span><span class="comment">*</span><span class="comment">  smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and
</span><span class="comment">*</span><span class="comment">  right singular vectors for abs(SSMAX), giving the decomposition
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
</span><span class="comment">*</span><span class="comment">     [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].
</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">  F       (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The (1,1) element of the 2-by-2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  G       (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The (1,2) element of the 2-by-2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  H       (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The (2,2) element of the 2-by-2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SSMIN   (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          abs(SSMIN) is the smaller singular value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SSMAX   (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          abs(SSMAX) is the larger singular value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SNL     (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">  CSL     (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The vector (CSL, SNL) is a unit left singular vector for the
</span><span class="comment">*</span><span class="comment">          singular value abs(SSMAX).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SNR     (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">  CSR     (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          The vector (CSR, SNR) is a unit right singular vector for the
</span><span class="comment">*</span><span class="comment">          singular value abs(SSMAX).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Any input parameter may be aliased with any output parameter.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Barring over/underflow and assuming a guard digit in subtraction, all
</span><span class="comment">*</span><span class="comment">  output quantities are correct to within a few units in the last
</span><span class="comment">*</span><span class="comment">  place (ulps).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  In IEEE arithmetic, the code works correctly if one matrix element is
</span><span class="comment">*</span><span class="comment">  infinite.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Overflow will not occur unless the largest singular value itself
</span><span class="comment">*</span><span class="comment">  overflows or is within a few ulps of overflow. (On machines with
</span><span class="comment">*</span><span class="comment">  partial overflow, like the Cray, overflow may occur if the largest
</span><span class="comment">*</span><span class="comment">  singular value is within a factor of 2 of overflow.)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Underflow is harmless if underflow is gradual. Otherwise, results
</span><span class="comment">*</span><span class="comment">  may correspond to a matrix modified by perturbations of size near
</span><span class="comment">*</span><span class="comment">  the underflow threshold.
</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>      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D0 )
      DOUBLE PRECISION   HALF
      PARAMETER          ( HALF = 0.5D0 )
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D0 )
      DOUBLE PRECISION   TWO
      PARAMETER          ( TWO = 2.0D0 )
      DOUBLE PRECISION   FOUR
      PARAMETER          ( FOUR = 4.0D0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            GASMAL, SWAP
      INTEGER            PMAX
      DOUBLE PRECISION   A, CLT, CRT, D, FA, FT, GA, GT, HA, HT, L, M,
     $                   MM, R, S, SLT, SRT, T, TEMP, TSIGN, TT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, SIGN, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      DOUBLE PRECISION   <a name="DLAMCH.98"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
      EXTERNAL           <a name="DLAMCH.99"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<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>      FT = F
      FA = ABS( FT )
      HT = H
      HA = ABS( H )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     PMAX points to the maximum absolute element of matrix
</span><span class="comment">*</span><span class="comment">       PMAX = 1 if F largest in absolute values
</span><span class="comment">*</span><span class="comment">       PMAX = 2 if G largest in absolute values
</span><span class="comment">*</span><span class="comment">       PMAX = 3 if H largest in absolute values
</span><span class="comment">*</span><span class="comment">
</span>      PMAX = 1
      SWAP = ( HA.GT.FA )
      IF( SWAP ) THEN
         PMAX = 3
         TEMP = FT
         FT = HT
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