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435 lines
13 KiB
435 lines
13 KiB
/* slaed0.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__9 = 9; |
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static integer c__0 = 0; |
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static integer c__2 = 2; |
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static real c_b23 = 1.f; |
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static real c_b24 = 0.f; |
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static integer c__1 = 1; |
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/* Subroutine */ int slaed0_(integer *icompq, integer *qsiz, integer *n, real |
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*d__, real *e, real *q, integer *ldq, real *qstore, integer *ldqs, |
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real *work, integer *iwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; |
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real r__1; |
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/* Builtin functions */ |
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double log(doublereal); |
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integer pow_ii(integer *, integer *); |
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/* Local variables */ |
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integer i__, j, k, iq, lgn, msd2, smm1, spm1, spm2; |
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real temp; |
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integer curr; |
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extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, |
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integer *, real *, real *, integer *, real *, integer *, real *, |
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real *, integer *); |
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integer iperm, indxq, iwrem; |
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, |
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integer *); |
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integer iqptr, tlvls; |
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extern /* Subroutine */ int slaed1_(integer *, real *, real *, integer *, |
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integer *, real *, integer *, real *, integer *, integer *), |
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slaed7_(integer *, integer *, integer *, integer *, integer *, |
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integer *, real *, real *, integer *, integer *, real *, integer * |
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, real *, integer *, integer *, integer *, integer *, integer *, |
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real *, real *, integer *, integer *); |
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integer igivcl; |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *); |
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integer igivnm, submat; |
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extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, |
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integer *, real *, integer *); |
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integer curprb, subpbs, igivpt, curlvl, matsiz, iprmpt, smlsiz; |
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extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *, |
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real *, integer *, real *, integer *); |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* SLAED0 computes all eigenvalues and corresponding eigenvectors of a */ |
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/* symmetric tridiagonal matrix using the divide and conquer method. */ |
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/* Arguments */ |
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/* ========= */ |
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/* ICOMPQ (input) INTEGER */ |
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/* = 0: Compute eigenvalues only. */ |
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/* = 1: Compute eigenvectors of original dense symmetric matrix */ |
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/* also. On entry, Q contains the orthogonal matrix used */ |
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/* to reduce the original matrix to tridiagonal form. */ |
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/* = 2: Compute eigenvalues and eigenvectors of tridiagonal */ |
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/* matrix. */ |
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/* QSIZ (input) INTEGER */ |
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/* The dimension of the orthogonal matrix used to reduce */ |
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/* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ |
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/* N (input) INTEGER */ |
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/* The dimension of the symmetric tridiagonal matrix. N >= 0. */ |
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/* D (input/output) REAL array, dimension (N) */ |
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/* On entry, the main diagonal of the tridiagonal matrix. */ |
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/* On exit, its eigenvalues. */ |
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/* E (input) REAL array, dimension (N-1) */ |
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/* The off-diagonal elements of the tridiagonal matrix. */ |
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/* On exit, E has been destroyed. */ |
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/* Q (input/output) REAL array, dimension (LDQ, N) */ |
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/* On entry, Q must contain an N-by-N orthogonal matrix. */ |
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/* If ICOMPQ = 0 Q is not referenced. */ |
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/* If ICOMPQ = 1 On entry, Q is a subset of the columns of the */ |
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/* orthogonal matrix used to reduce the full */ |
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/* matrix to tridiagonal form corresponding to */ |
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/* the subset of the full matrix which is being */ |
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/* decomposed at this time. */ |
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/* If ICOMPQ = 2 On entry, Q will be the identity matrix. */ |
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/* On exit, Q contains the eigenvectors of the */ |
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/* tridiagonal matrix. */ |
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/* LDQ (input) INTEGER */ |
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/* The leading dimension of the array Q. If eigenvectors are */ |
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/* desired, then LDQ >= max(1,N). In any case, LDQ >= 1. */ |
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/* QSTORE (workspace) REAL array, dimension (LDQS, N) */ |
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/* Referenced only when ICOMPQ = 1. Used to store parts of */ |
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/* the eigenvector matrix when the updating matrix multiplies */ |
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/* take place. */ |
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/* LDQS (input) INTEGER */ |
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/* The leading dimension of the array QSTORE. If ICOMPQ = 1, */ |
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/* then LDQS >= max(1,N). In any case, LDQS >= 1. */ |
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/* WORK (workspace) REAL array, */ |
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/* If ICOMPQ = 0 or 1, the dimension of WORK must be at least */ |
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/* 1 + 3*N + 2*N*lg N + 2*N**2 */ |
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/* ( lg( N ) = smallest integer k */ |
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/* such that 2^k >= N ) */ |
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/* If ICOMPQ = 2, the dimension of WORK must be at least */ |
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/* 4*N + N**2. */ |
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/* IWORK (workspace) INTEGER array, */ |
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/* If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */ |
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/* 6 + 6*N + 5*N*lg N. */ |
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/* ( lg( N ) = smallest integer k */ |
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/* such that 2^k >= N ) */ |
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/* If ICOMPQ = 2, the dimension of IWORK must be at least */ |
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/* 3 + 5*N. */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit. */ |
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */ |
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/* > 0: The algorithm failed to compute an eigenvalue while */ |
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/* working on the submatrix lying in rows and columns */ |
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/* INFO/(N+1) through mod(INFO,N+1). */ |
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/* Further Details */ |
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/* =============== */ |
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/* Based on contributions by */ |
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/* Jeff Rutter, Computer Science Division, University of California */ |
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/* at Berkeley, USA */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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--d__; |
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--e; |
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q_dim1 = *ldq; |
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q_offset = 1 + q_dim1; |
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q -= q_offset; |
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qstore_dim1 = *ldqs; |
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qstore_offset = 1 + qstore_dim1; |
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qstore -= qstore_offset; |
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--work; |
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--iwork; |
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/* Function Body */ |
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*info = 0; |
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if (*icompq < 0 || *icompq > 2) { |
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*info = -1; |
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} else if (*icompq == 1 && *qsiz < max(0,*n)) { |
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*info = -2; |
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} else if (*n < 0) { |
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*info = -3; |
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} else if (*ldq < max(1,*n)) { |
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*info = -7; |
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} else if (*ldqs < max(1,*n)) { |
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*info = -9; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLAED0", &i__1); |
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return 0; |
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} |
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/* Quick return if possible */ |
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if (*n == 0) { |
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return 0; |
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} |
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smlsiz = ilaenv_(&c__9, "SLAED0", " ", &c__0, &c__0, &c__0, &c__0); |
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/* Determine the size and placement of the submatrices, and save in */ |
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/* the leading elements of IWORK. */ |
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iwork[1] = *n; |
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subpbs = 1; |
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tlvls = 0; |
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L10: |
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if (iwork[subpbs] > smlsiz) { |
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for (j = subpbs; j >= 1; --j) { |
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iwork[j * 2] = (iwork[j] + 1) / 2; |
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iwork[(j << 1) - 1] = iwork[j] / 2; |
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/* L20: */ |
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} |
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++tlvls; |
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subpbs <<= 1; |
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goto L10; |
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} |
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i__1 = subpbs; |
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for (j = 2; j <= i__1; ++j) { |
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iwork[j] += iwork[j - 1]; |
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/* L30: */ |
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} |
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/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ |
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/* using rank-1 modifications (cuts). */ |
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spm1 = subpbs - 1; |
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i__1 = spm1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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submat = iwork[i__] + 1; |
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smm1 = submat - 1; |
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d__[smm1] -= (r__1 = e[smm1], dabs(r__1)); |
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d__[submat] -= (r__1 = e[smm1], dabs(r__1)); |
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/* L40: */ |
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} |
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indxq = (*n << 2) + 3; |
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if (*icompq != 2) { |
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/* Set up workspaces for eigenvalues only/accumulate new vectors */ |
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/* routine */ |
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temp = log((real) (*n)) / log(2.f); |
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lgn = (integer) temp; |
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if (pow_ii(&c__2, &lgn) < *n) { |
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++lgn; |
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} |
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if (pow_ii(&c__2, &lgn) < *n) { |
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++lgn; |
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} |
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iprmpt = indxq + *n + 1; |
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iperm = iprmpt + *n * lgn; |
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iqptr = iperm + *n * lgn; |
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igivpt = iqptr + *n + 2; |
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igivcl = igivpt + *n * lgn; |
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igivnm = 1; |
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iq = igivnm + (*n << 1) * lgn; |
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/* Computing 2nd power */ |
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i__1 = *n; |
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iwrem = iq + i__1 * i__1 + 1; |
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/* Initialize pointers */ |
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i__1 = subpbs; |
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for (i__ = 0; i__ <= i__1; ++i__) { |
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iwork[iprmpt + i__] = 1; |
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iwork[igivpt + i__] = 1; |
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/* L50: */ |
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} |
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iwork[iqptr] = 1; |
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} |
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/* Solve each submatrix eigenproblem at the bottom of the divide and */ |
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/* conquer tree. */ |
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curr = 0; |
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i__1 = spm1; |
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for (i__ = 0; i__ <= i__1; ++i__) { |
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if (i__ == 0) { |
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submat = 1; |
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matsiz = iwork[1]; |
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} else { |
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submat = iwork[i__] + 1; |
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matsiz = iwork[i__ + 1] - iwork[i__]; |
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} |
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if (*icompq == 2) { |
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ssteqr_("I", &matsiz, &d__[submat], &e[submat], &q[submat + |
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submat * q_dim1], ldq, &work[1], info); |
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if (*info != 0) { |
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goto L130; |
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} |
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} else { |
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ssteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + |
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iwork[iqptr + curr]], &matsiz, &work[1], info); |
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if (*info != 0) { |
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goto L130; |
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} |
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if (*icompq == 1) { |
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sgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * |
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q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], |
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&matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], |
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ldqs); |
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} |
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/* Computing 2nd power */ |
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i__2 = matsiz; |
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iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; |
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++curr; |
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} |
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k = 1; |
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i__2 = iwork[i__ + 1]; |
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for (j = submat; j <= i__2; ++j) { |
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iwork[indxq + j] = k; |
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++k; |
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/* L60: */ |
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} |
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/* L70: */ |
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} |
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/* Successively merge eigensystems of adjacent submatrices */ |
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/* into eigensystem for the corresponding larger matrix. */ |
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/* while ( SUBPBS > 1 ) */ |
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curlvl = 1; |
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L80: |
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if (subpbs > 1) { |
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spm2 = subpbs - 2; |
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i__1 = spm2; |
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for (i__ = 0; i__ <= i__1; i__ += 2) { |
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if (i__ == 0) { |
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submat = 1; |
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matsiz = iwork[2]; |
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msd2 = iwork[1]; |
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curprb = 0; |
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} else { |
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submat = iwork[i__] + 1; |
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matsiz = iwork[i__ + 2] - iwork[i__]; |
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msd2 = matsiz / 2; |
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++curprb; |
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} |
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/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ |
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/* into an eigensystem of size MATSIZ. */ |
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/* SLAED1 is used only for the full eigensystem of a tridiagonal */ |
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/* matrix. */ |
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/* SLAED7 handles the cases in which eigenvalues only or eigenvalues */ |
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/* and eigenvectors of a full symmetric matrix (which was reduced to */ |
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/* tridiagonal form) are desired. */ |
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if (*icompq == 2) { |
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slaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], |
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ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & |
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msd2, &work[1], &iwork[subpbs + 1], info); |
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} else { |
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slaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ |
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submat], &qstore[submat * qstore_dim1 + 1], ldqs, & |
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iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & |
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work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] |
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, &iwork[igivpt], &iwork[igivcl], &work[igivnm], & |
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work[iwrem], &iwork[subpbs + 1], info); |
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} |
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if (*info != 0) { |
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goto L130; |
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} |
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iwork[i__ / 2 + 1] = iwork[i__ + 2]; |
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/* L90: */ |
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} |
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subpbs /= 2; |
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++curlvl; |
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goto L80; |
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} |
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/* end while */ |
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/* Re-merge the eigenvalues/vectors which were deflated at the final */ |
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/* merge step. */ |
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if (*icompq == 1) { |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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j = iwork[indxq + i__]; |
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work[i__] = d__[j]; |
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scopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 |
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+ 1], &c__1); |
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/* L100: */ |
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} |
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scopy_(n, &work[1], &c__1, &d__[1], &c__1); |
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} else if (*icompq == 2) { |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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j = iwork[indxq + i__]; |
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work[i__] = d__[j]; |
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scopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); |
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/* L110: */ |
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} |
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scopy_(n, &work[1], &c__1, &d__[1], &c__1); |
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slacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq); |
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} else { |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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j = iwork[indxq + i__]; |
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work[i__] = d__[j]; |
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/* L120: */ |
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} |
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scopy_(n, &work[1], &c__1, &d__[1], &c__1); |
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} |
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goto L140; |
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L130: |
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*info = submat * (*n + 1) + submat + matsiz - 1; |
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L140: |
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return 0; |
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/* End of SLAED0 */ |
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} /* slaed0_ */
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