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---
:name: spteqr
:md5sum: 602a7d1d94751729b99e8b4b6eb7a9b3
:category: :subroutine
:arguments:
- compz:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- e:
:type: real
:intent: input/output
:dims:
- n-1
- z:
:type: real
:intent: input/output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- work:
:type: real
:intent: workspace
:dims:
- 4*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SPTEQR computes all eigenvalues and, optionally, eigenvectors of a\n\
* symmetric positive definite tridiagonal matrix by first factoring the\n\
* matrix using SPTTRF, and then calling SBDSQR to compute the singular\n\
* values of the bidiagonal factor.\n\
*\n\
* This routine computes the eigenvalues of the positive definite\n\
* tridiagonal matrix to high relative accuracy. This means that if the\n\
* eigenvalues range over many orders of magnitude in size, then the\n\
* small eigenvalues and corresponding eigenvectors will be computed\n\
* more accurately than, for example, with the standard QR method.\n\
*\n\
* The eigenvectors of a full or band symmetric positive definite matrix\n\
* can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to\n\
* reduce this matrix to tridiagonal form. (The reduction to tridiagonal\n\
* form, however, may preclude the possibility of obtaining high\n\
* relative accuracy in the small eigenvalues of the original matrix, if\n\
* these eigenvalues range over many orders of magnitude.)\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* COMPZ (input) CHARACTER*1\n\
* = 'N': Compute eigenvalues only.\n\
* = 'V': Compute eigenvectors of original symmetric\n\
* matrix also. Array Z contains the orthogonal\n\
* matrix used to reduce the original matrix to\n\
* tridiagonal form.\n\
* = 'I': Compute eigenvectors of tridiagonal matrix also.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix. N >= 0.\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry, the n diagonal elements of the tridiagonal\n\
* matrix.\n\
* On normal exit, D contains the eigenvalues, in descending\n\
* order.\n\
*\n\
* E (input/output) REAL array, dimension (N-1)\n\
* On entry, the (n-1) subdiagonal elements of the tridiagonal\n\
* matrix.\n\
* On exit, E has been destroyed.\n\
*\n\
* Z (input/output) REAL array, dimension (LDZ, N)\n\
* On entry, if COMPZ = 'V', the orthogonal matrix used in the\n\
* reduction to tridiagonal form.\n\
* On exit, if COMPZ = 'V', the orthonormal eigenvectors of the\n\
* original symmetric matrix;\n\
* if COMPZ = 'I', the orthonormal eigenvectors of the\n\
* tridiagonal matrix.\n\
* If INFO > 0 on exit, Z contains the eigenvectors associated\n\
* with only the stored eigenvalues.\n\
* If COMPZ = 'N', then Z is not referenced.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1, and if\n\
* COMPZ = 'V' or 'I', LDZ >= max(1,N).\n\
*\n\
* WORK (workspace) REAL 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 = i, and i is:\n\
* <= N the Cholesky factorization of the matrix could\n\
* not be performed because the i-th principal minor\n\
* was not positive definite.\n\
* > N the SVD algorithm failed to converge;\n\
* if INFO = N+i, i off-diagonal elements of the\n\
* bidiagonal factor did not converge to zero.\n\
*\n\n\
* =====================================================================\n\
*\n"
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