Move LAPACK trunk into position.

1 files changed, 137 insertions, 0 deletions

diff --git a/SRC/cpoequ.f b/SRC/cpoequ.f
new file mode 100644
index 00000000..f08acd3e
--- /dev/null
+++ b/SRC/cpoequ.f
@@ -0,0 +1,137 @@
+      SUBROUTINE CPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
+*
+*  -- LAPACK routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LDA, N
+      REAL               AMAX, SCOND
+*     ..
+*     .. Array Arguments ..
+      REAL               S( * )
+      COMPLEX            A( LDA, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  CPOEQU computes row and column scalings intended to equilibrate a
+*  Hermitian positive definite matrix A and reduce its condition number
+*  (with respect to the two-norm).  S contains the scale factors,
+*  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
+*  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
+*  choice of S puts the condition number of B within a factor N of the
+*  smallest possible condition number over all possible diagonal
+*  scalings.
+*
+*  Arguments
+*  =========
+*
+*  N       (input) INTEGER
+*          The order of the matrix A.  N >= 0.
+*
+*  A       (input) COMPLEX array, dimension (LDA,N)
+*          The N-by-N Hermitian positive definite matrix whose scaling
+*          factors are to be computed.  Only the diagonal elements of A
+*          are referenced.
+*
+*  LDA     (input) INTEGER
+*          The leading dimension of the array A.  LDA >= max(1,N).
+*
+*  S       (output) REAL array, dimension (N)
+*          If INFO = 0, S contains the scale factors for A.
+*
+*  SCOND   (output) REAL
+*          If INFO = 0, S contains the ratio of the smallest S(i) to
+*          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
+*          large nor too small, it is not worth scaling by S.
+*
+*  AMAX    (output) REAL
+*          Absolute value of largest matrix element.  If AMAX is very
+*          close to overflow or very close to underflow, the matrix
+*          should be scaled.
+*
+*  INFO    (output) INTEGER
+*          = 0:  successful exit
+*          < 0:  if INFO = -i, the i-th argument had an illegal value
+*          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO, ONE
+      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I
+      REAL               SMIN
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX, MIN, REAL, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      IF( N.LT.0 ) THEN
+         INFO = -1
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -3
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CPOEQU', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 ) THEN
+         SCOND = ONE
+         AMAX = ZERO
+         RETURN
+      END IF
+*
+*     Find the minimum and maximum diagonal elements.
+*
+      S( 1 ) = REAL( A( 1, 1 ) )
+      SMIN = S( 1 )
+      AMAX = S( 1 )
+      DO 10 I = 2, N
+         S( I ) = REAL( A( I, I ) )
+         SMIN = MIN( SMIN, S( I ) )
+         AMAX = MAX( AMAX, S( I ) )
+   10 CONTINUE
+*
+      IF( SMIN.LE.ZERO ) THEN
+*
+*        Find the first non-positive diagonal element and return.
+*
+         DO 20 I = 1, N
+            IF( S( I ).LE.ZERO ) THEN
+               INFO = I
+               RETURN
+            END IF
+   20    CONTINUE
+      ELSE
+*
+*        Set the scale factors to the reciprocals
+*        of the diagonal elements.
+*
+         DO 30 I = 1, N
+            S( I ) = ONE / SQRT( S( I ) )
+   30    CONTINUE
+*
+*        Compute SCOND = min(S(I)) / max(S(I))
+*
+         SCOND = SQRT( SMIN ) / SQRT( AMAX )
+      END IF
+      RETURN
+*
+*     End of CPOEQU
+*
+      END