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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/claqsb.f | |
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Move LAPACK trunk into position.
Diffstat (limited to 'SRC/claqsb.f')
-rw-r--r-- | SRC/claqsb.f | 149 |
1 files changed, 149 insertions, 0 deletions
diff --git a/SRC/claqsb.f b/SRC/claqsb.f new file mode 100644 index 00000000..0ac7e6a4 --- /dev/null +++ b/SRC/claqsb.f @@ -0,0 +1,149 @@ + SUBROUTINE CLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER EQUED, UPLO + INTEGER KD, LDAB, N + REAL AMAX, SCOND +* .. +* .. Array Arguments .. + REAL S( * ) + COMPLEX AB( LDAB, * ) +* .. +* +* Purpose +* ======= +* +* CLAQSB equilibrates a symmetric band matrix A using the scaling +* factors in the vector S. +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* symmetric matrix A is stored. +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* KD (input) INTEGER +* The number of super-diagonals of the matrix A if UPLO = 'U', +* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. +* +* AB (input/output) COMPLEX array, dimension (LDAB,N) +* On entry, the upper or lower triangle of the symmetric band +* matrix A, stored in the first KD+1 rows of the array. The +* j-th column of A is stored in the j-th column of the array AB +* as follows: +* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; +* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). +* +* On exit, if INFO = 0, the triangular factor U or L from the +* Cholesky factorization A = U'*U or A = L*L' of the band +* matrix A, in the same storage format as A. +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= KD+1. +* +* S (input) REAL array, dimension (N) +* The scale factors for A. +* +* SCOND (input) REAL +* Ratio of the smallest S(i) to the largest S(i). +* +* AMAX (input) REAL +* Absolute value of largest matrix entry. +* +* EQUED (output) CHARACTER*1 +* Specifies whether or not equilibration was done. +* = 'N': No equilibration. +* = 'Y': Equilibration was done, i.e., A has been replaced by +* diag(S) * A * diag(S). +* +* Internal Parameters +* =================== +* +* THRESH is a threshold value used to decide if scaling should be done +* based on the ratio of the scaling factors. If SCOND < THRESH, +* scaling is done. +* +* LARGE and SMALL are threshold values used to decide if scaling should +* be done based on the absolute size of the largest matrix element. +* If AMAX > LARGE or AMAX < SMALL, scaling is done. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, THRESH + PARAMETER ( ONE = 1.0E+0, THRESH = 0.1E+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J + REAL CJ, LARGE, SMALL +* .. +* .. External Functions .. + LOGICAL LSAME + REAL SLAMCH + EXTERNAL LSAME, SLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.LE.0 ) THEN + EQUED = 'N' + RETURN + END IF +* +* Initialize LARGE and SMALL. +* + SMALL = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' ) + LARGE = ONE / SMALL +* + IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN +* +* No equilibration +* + EQUED = 'N' + ELSE +* +* Replace A by diag(S) * A * diag(S). +* + IF( LSAME( UPLO, 'U' ) ) THEN +* +* Upper triangle of A is stored in band format. +* + DO 20 J = 1, N + CJ = S( J ) + DO 10 I = MAX( 1, J-KD ), J + AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J ) + 10 CONTINUE + 20 CONTINUE + ELSE +* +* Lower triangle of A is stored. +* + DO 40 J = 1, N + CJ = S( J ) + DO 30 I = J, MIN( N, J+KD ) + AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J ) + 30 CONTINUE + 40 CONTINUE + END IF + EQUED = 'Y' + END IF +* + RETURN +* +* End of CLAQSB +* + END |