From baba851215b44ac3b60b9248eb02bcce7eb76247 Mon Sep 17 00:00:00 2001 From: jason Date: Tue, 28 Oct 2008 01:38:50 +0000 Subject: Move LAPACK trunk into position. --- SRC/slaed7.f | 287 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 287 insertions(+) create mode 100644 SRC/slaed7.f (limited to 'SRC/slaed7.f') diff --git a/SRC/slaed7.f b/SRC/slaed7.f new file mode 100644 index 00000000..f8979c80 --- /dev/null +++ b/SRC/slaed7.f @@ -0,0 +1,287 @@ + SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, + $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, + $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, + $ INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, + $ QSIZ, TLVLS + REAL RHO +* .. +* .. Array Arguments .. + INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), + $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) + REAL D( * ), GIVNUM( 2, * ), Q( LDQ, * ), + $ QSTORE( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* SLAED7 computes the updated eigensystem of a diagonal +* matrix after modification by a rank-one symmetric matrix. This +* routine is used only for the eigenproblem which requires all +* eigenvalues and optionally eigenvectors of a dense symmetric matrix +* that has been reduced to tridiagonal form. SLAED1 handles +* the case in which all eigenvalues and eigenvectors of a symmetric +* tridiagonal matrix are desired. +* +* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) +* +* where Z = Q'u, u is a vector of length N with ones in the +* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. +* +* The eigenvectors of the original matrix are stored in Q, and the +* eigenvalues are in D. The algorithm consists of three stages: +* +* The first stage consists of deflating the size of the problem +* when there are multiple eigenvalues or if there is a zero in +* the Z vector. For each such occurence the dimension of the +* secular equation problem is reduced by one. This stage is +* performed by the routine SLAED8. +* +* The second stage consists of calculating the updated +* eigenvalues. This is done by finding the roots of the secular +* equation via the routine SLAED4 (as called by SLAED9). +* This routine also calculates the eigenvectors of the current +* problem. +* +* The final stage consists of computing the updated eigenvectors +* directly using the updated eigenvalues. The eigenvectors for +* the current problem are multiplied with the eigenvectors from +* the overall problem. +* +* Arguments +* ========= +* +* ICOMPQ (input) INTEGER +* = 0: Compute eigenvalues only. +* = 1: Compute eigenvectors of original dense symmetric matrix +* also. On entry, Q contains the orthogonal matrix used +* to reduce the original matrix to tridiagonal form. +* +* N (input) INTEGER +* The dimension of the symmetric tridiagonal matrix. N >= 0. +* +* QSIZ (input) INTEGER +* The dimension of the orthogonal matrix used to reduce +* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. +* +* TLVLS (input) INTEGER +* The total number of merging levels in the overall divide and +* conquer tree. +* +* CURLVL (input) INTEGER +* The current level in the overall merge routine, +* 0 <= CURLVL <= TLVLS. +* +* CURPBM (input) INTEGER +* The current problem in the current level in the overall +* merge routine (counting from upper left to lower right). +* +* D (input/output) REAL array, dimension (N) +* On entry, the eigenvalues of the rank-1-perturbed matrix. +* On exit, the eigenvalues of the repaired matrix. +* +* Q (input/output) REAL array, dimension (LDQ, N) +* On entry, the eigenvectors of the rank-1-perturbed matrix. +* On exit, the eigenvectors of the repaired tridiagonal matrix. +* +* LDQ (input) INTEGER +* The leading dimension of the array Q. LDQ >= max(1,N). +* +* INDXQ (output) INTEGER array, dimension (N) +* The permutation which will reintegrate the subproblem just +* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) +* will be in ascending order. +* +* RHO (input) REAL +* The subdiagonal element used to create the rank-1 +* modification. +* +* CUTPNT (input) INTEGER +* Contains the location of the last eigenvalue in the leading +* sub-matrix. min(1,N) <= CUTPNT <= N. +* +* QSTORE (input/output) REAL array, dimension (N**2+1) +* Stores eigenvectors of submatrices encountered during +* divide and conquer, packed together. QPTR points to +* beginning of the submatrices. +* +* QPTR (input/output) INTEGER array, dimension (N+2) +* List of indices pointing to beginning of submatrices stored +* in QSTORE. The submatrices are numbered starting at the +* bottom left of the divide and conquer tree, from left to +* right and bottom to top. +* +* PRMPTR (input) INTEGER array, dimension (N lg N) +* Contains a list of pointers which indicate where in PERM a +* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) +* indicates the size of the permutation and also the size of +* the full, non-deflated problem. +* +* PERM (input) INTEGER array, dimension (N lg N) +* Contains the permutations (from deflation and sorting) to be +* applied to each eigenblock. +* +* GIVPTR (input) INTEGER array, dimension (N lg N) +* Contains a list of pointers which indicate where in GIVCOL a +* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) +* indicates the number of Givens rotations. +* +* GIVCOL (input) INTEGER array, dimension (2, N lg N) +* Each pair of numbers indicates a pair of columns to take place +* in a Givens rotation. +* +* GIVNUM (input) REAL array, dimension (2, N lg N) +* Each number indicates the S value to be used in the +* corresponding Givens rotation. +* +* WORK (workspace) REAL array, dimension (3*N+QSIZ*N) +* +* IWORK (workspace) INTEGER array, dimension (4*N) +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* > 0: if INFO = 1, an eigenvalue did not converge +* +* Further Details +* =============== +* +* Based on contributions by +* Jeff Rutter, Computer Science Division, University of California +* at Berkeley, USA +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 ) +* .. +* .. Local Scalars .. + INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP, + $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR +* .. +* .. External Subroutines .. + EXTERNAL SGEMM, SLAED8, SLAED9, SLAEDA, SLAMRG, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 +* + IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN + INFO = -4 + ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN + INFO = -9 + ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN + INFO = -12 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SLAED7', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* The following values are for bookkeeping purposes only. They are +* integer pointers which indicate the portion of the workspace +* used by a particular array in SLAED8 and SLAED9. +* + IF( ICOMPQ.EQ.1 ) THEN + LDQ2 = QSIZ + ELSE + LDQ2 = N + END IF +* + IZ = 1 + IDLMDA = IZ + N + IW = IDLMDA + N + IQ2 = IW + N + IS = IQ2 + N*LDQ2 +* + INDX = 1 + INDXC = INDX + N + COLTYP = INDXC + N + INDXP = COLTYP + N +* +* Form the z-vector which consists of the last row of Q_1 and the +* first row of Q_2. +* + PTR = 1 + 2**TLVLS + DO 10 I = 1, CURLVL - 1 + PTR = PTR + 2**( TLVLS-I ) + 10 CONTINUE + CURR = PTR + CURPBM + CALL SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, + $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ), + $ WORK( IZ+N ), INFO ) +* +* When solving the final problem, we no longer need the stored data, +* so we will overwrite the data from this level onto the previously +* used storage space. +* + IF( CURLVL.EQ.TLVLS ) THEN + QPTR( CURR ) = 1 + PRMPTR( CURR ) = 1 + GIVPTR( CURR ) = 1 + END IF +* +* Sort and Deflate eigenvalues. +* + CALL SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, + $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2, + $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), + $ GIVCOL( 1, GIVPTR( CURR ) ), + $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ), + $ IWORK( INDX ), INFO ) + PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N + GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) +* +* Solve Secular Equation. +* + IF( K.NE.0 ) THEN + CALL SLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ), + $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO ) + IF( INFO.NE.0 ) + $ GO TO 30 + IF( ICOMPQ.EQ.1 ) THEN + CALL SGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2, + $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ ) + END IF + QPTR( CURR+1 ) = QPTR( CURR ) + K**2 +* +* Prepare the INDXQ sorting permutation. +* + N1 = K + N2 = N - K + CALL SLAMRG( N1, N2, D, 1, -1, INDXQ ) + ELSE + QPTR( CURR+1 ) = QPTR( CURR ) + DO 20 I = 1, N + INDXQ( I ) = I + 20 CONTINUE + END IF +* + 30 CONTINUE + RETURN +* +* End of SLAED7 +* + END -- cgit v1.2.3