summaryrefslogtreecommitdiff
path: root/SRC/cpoequb.f
diff options
context:
space:
mode:
authorjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
committerjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
commitff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch)
treea386cad907bcaefd6893535c31d67ec9468e693e /SRC/cpoequb.f
parente58b61578b55644f6391f3333262b72c1dc88437 (diff)
downloadlapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.gz
lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.bz2
lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.zip
Diffstat (limited to 'SRC/cpoequb.f')
-rw-r--r--SRC/cpoequb.f160
1 files changed, 160 insertions, 0 deletions
diff --git a/SRC/cpoequb.f b/SRC/cpoequb.f
new file mode 100644
index 00000000..88a87b71
--- /dev/null
+++ b/SRC/cpoequb.f
@@ -0,0 +1,160 @@
+ SUBROUTINE CPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
+*
+* -- LAPACK routine (version 3.2) --
+* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
+* -- Jason Riedy of Univ. of California Berkeley. --
+* -- November 2008 --
+*
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley and NAG Ltd. --
+*
+ IMPLICIT NONE
+* ..
+* .. Scalar Arguments ..
+ INTEGER INFO, LDA, N
+ REAL AMAX, SCOND
+* ..
+* .. Array Arguments ..
+ COMPLEX A( LDA, * )
+ REAL S( * )
+* ..
+*
+* Purpose
+* =======
+*
+* CPOEQUB computes row and column scalings intended to equilibrate a
+* symmetric 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 symmetric 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, BASE, TMP
+ COMPLEX ZDUM
+* ..
+* .. External Functions ..
+ REAL SLAMCH
+ EXTERNAL SLAMCH
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN, SQRT, LOG, INT, REAL, AIMAG
+* ..
+* .. Statement Functions ..
+ REAL CABS1
+* ..
+* .. Statement Function Definitions ..
+ CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+* Positive definite only performs 1 pass of equilibration.
+*
+ 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( 'CPOEQUB', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF( N.EQ.0 ) THEN
+ SCOND = ONE
+ AMAX = ZERO
+ RETURN
+ END IF
+
+ BASE = SLAMCH( 'B' )
+ TMP = -0.5 / LOG ( BASE )
+*
+* Find the minimum and maximum diagonal elements.
+*
+ S( 1 ) = A( 1, 1 )
+ SMIN = S( 1 )
+ AMAX = S( 1 )
+ DO 10 I = 2, N
+ S( I ) = 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 ) = BASE ** INT( TMP * LOG( S( I ) ) )
+ 30 CONTINUE
+*
+* Compute SCOND = min(S(I)) / max(S(I)).
+*
+ SCOND = SQRT( SMIN ) / SQRT( AMAX )
+ END IF
+*
+ RETURN
+*
+* End of CPOEQUB
+*
+ END