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---
:name: slaed1
:md5sum: d07835f50a422bece671635ac839355a
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- q:
:type: real
:intent: input/output
:dims:
- ldq
- n
- ldq:
:type: integer
:intent: input
- indxq:
:type: integer
:intent: input/output
:dims:
- n
- rho:
:type: real
:intent: input
- cutpnt:
:type: integer
:intent: input
- work:
:type: real
:intent: workspace
:dims:
- 4*n + pow(n,2)
- iwork:
:type: integer
:intent: workspace
:dims:
- 4*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SLAED1 computes the updated eigensystem of a diagonal\n\
* matrix after modification by a rank-one symmetric matrix. This\n\
* routine is used only for the eigenproblem which requires all\n\
* eigenvalues and eigenvectors of a tridiagonal matrix. SLAED7 handles\n\
* the case in which eigenvalues only or eigenvalues and eigenvectors\n\
* of a full symmetric matrix (which was reduced to tridiagonal form)\n\
* are desired.\n\
*\n\
* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)\n\
*\n\
* where Z = Q'u, u is a vector of length N with ones in the\n\
* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.\n\
*\n\
* The eigenvectors of the original matrix are stored in Q, and the\n\
* eigenvalues are in D. The algorithm consists of three stages:\n\
*\n\
* The first stage consists of deflating the size of the problem\n\
* when there are multiple eigenvalues or if there is a zero in\n\
* the Z vector. For each such occurrence the dimension of the\n\
* secular equation problem is reduced by one. This stage is\n\
* performed by the routine SLAED2.\n\
*\n\
* The second stage consists of calculating the updated\n\
* eigenvalues. This is done by finding the roots of the secular\n\
* equation via the routine SLAED4 (as called by SLAED3).\n\
* This routine also calculates the eigenvectors of the current\n\
* problem.\n\
*\n\
* The final stage consists of computing the updated eigenvectors\n\
* directly using the updated eigenvalues. The eigenvectors for\n\
* the current problem are multiplied with the eigenvectors from\n\
* the overall problem.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The dimension of the symmetric tridiagonal matrix. N >= 0.\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry, the eigenvalues of the rank-1-perturbed matrix.\n\
* On exit, the eigenvalues of the repaired matrix.\n\
*\n\
* Q (input/output) REAL array, dimension (LDQ,N)\n\
* On entry, the eigenvectors of the rank-1-perturbed matrix.\n\
* On exit, the eigenvectors of the repaired tridiagonal matrix.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= max(1,N).\n\
*\n\
* INDXQ (input/output) INTEGER array, dimension (N)\n\
* On entry, the permutation which separately sorts the two\n\
* subproblems in D into ascending order.\n\
* On exit, the permutation which will reintegrate the\n\
* subproblems back into sorted order,\n\
* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.\n\
*\n\
* RHO (input) REAL\n\
* The subdiagonal entry used to create the rank-1 modification.\n\
*\n\
* CUTPNT (input) INTEGER\n\
* The location of the last eigenvalue in the leading sub-matrix.\n\
* min(1,N) <= CUTPNT <= N/2.\n\
*\n\
* WORK (workspace) REAL array, dimension (4*N + N**2)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (4*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: if INFO = 1, an eigenvalue did not converge\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Jeff Rutter, Computer Science Division, University of California\n\
* at Berkeley, USA\n\
* Modified by Francoise Tisseur, University of Tennessee.\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n INTEGER COLTYP, CPP1, I, IDLMDA, INDX, INDXC, INDXP,\n $ IQ2, IS, IW, IZ, K, N1, N2\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL SCOPY, SLAED2, SLAED3, SLAMRG, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX, MIN\n\
* ..\n"
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