diff options
Diffstat (limited to 'SRC/slaqr4.f')
| -rw-r--r-- | SRC/slaqr4.f | 23 |
1 files changed, 14 insertions, 9 deletions
diff --git a/SRC/slaqr4.f b/SRC/slaqr4.f index 1a05898c..bd27750b 100644 --- a/SRC/slaqr4.f +++ b/SRC/slaqr4.f @@ -14,16 +14,16 @@ $ Z( LDZ, * ) * .. * -* This subroutine implements one level of recursion for SLAQR0. +* Purpose +* ======= +* +* SLAQR4 implements one level of recursion for SLAQR0. * It is a complete implementation of the small bulge multi-shift * QR algorithm. It may be called by SLAQR0 and, for large enough * deflation window size, it may be called by SLAQR3. This * subroutine is identical to SLAQR0 except that it calls SLAQR2 * instead of SLAQR3. * -* Purpose -* ======= -* * SLAQR4 computes the eigenvalues of a Hessenberg matrix H * and, optionally, the matrices T and Z from the Schur decomposition * H = Z T Z**T, where T is an upper quasi-triangular matrix (the @@ -34,8 +34,8 @@ * of a matrix A which has been reduced to the Hessenberg form H * by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T. * -* Arguments -* ========= +* Arguments +* ========= * * WANTT (input) LOGICAL * = .TRUE. : the full Schur form T is required; @@ -49,6 +49,7 @@ * The order of the matrix H. N .GE. 0. * * ILO (input) INTEGER +* * IHI (input) INTEGER * It is assumed that H is already upper triangular in rows * and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1, @@ -78,6 +79,7 @@ * The leading dimension of the array H. LDH .GE. max(1,N). * * WR (output) REAL array, dimension (IHI) +* * WI (output) REAL array, dimension (IHI) * The real and imaginary parts, respectively, of the computed * eigenvalues of H(ILO:IHI,ILO:IHI) are stored in WR(ILO:IHI) @@ -92,6 +94,7 @@ * WI(i+1) = -WI(i). * * ILOZ (input) INTEGER +* * IHIZ (input) INTEGER * Specify the rows of Z to which transformations must be * applied if WANTZ is .TRUE.. @@ -159,12 +162,13 @@ * If INFO .GT. 0 and WANTZ is .FALSE., then Z is not * accessed. * -* ================================================================ +* Further Details +* =============== +* * Based on contributions by * Karen Braman and Ralph Byers, Department of Mathematics, * University of Kansas, USA * -* ================================================================ * References: * K. Braman, R. Byers and R. Mathias, The Multi-Shift QR * Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 @@ -175,7 +179,8 @@ * Algorithm Part II: Aggressive Early Deflation, SIAM Journal * of Matrix Analysis, volume 23, pages 948--973, 2002. * -* ================================================================ +* ================================================================ +* * .. Parameters .. * * ==== Matrices of order NTINY or smaller must be processed by |