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---
:name: dlagv2
:md5sum: 0213b40436ec590dd32628d8b5e77774
:category: :subroutine
:arguments:
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- "2"
- lda:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- "2"
- ldb:
:type: integer
:intent: input
- alphar:
:type: doublereal
:intent: output
:dims:
- "2"
- alphai:
:type: doublereal
:intent: output
:dims:
- "2"
- beta:
:type: doublereal
:intent: output
:dims:
- "2"
- csl:
:type: doublereal
:intent: output
- snl:
:type: doublereal
:intent: output
- csr:
:type: doublereal
:intent: output
- snr:
:type: doublereal
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAGV2 computes the Generalized Schur factorization of a real 2-by-2\n\
* matrix pencil (A,B) where B is upper triangular. This routine\n\
* computes orthogonal (rotation) matrices given by CSL, SNL and CSR,\n\
* SNR such that\n\
*\n\
* 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0\n\
* types), then\n\
*\n\
* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]\n\
* [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]\n\
*\n\
* [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]\n\
* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],\n\
*\n\
* 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,\n\
* then\n\
*\n\
* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]\n\
* [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]\n\
*\n\
* [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]\n\
* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]\n\
*\n\
* where b11 >= b22 > 0.\n\
*\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA, 2)\n\
* On entry, the 2 x 2 matrix A.\n\
* On exit, A is overwritten by the ``A-part'' of the\n\
* generalized Schur form.\n\
*\n\
* LDA (input) INTEGER\n\
* THe leading dimension of the array A. LDA >= 2.\n\
*\n\
* B (input/output) DOUBLE PRECISION array, dimension (LDB, 2)\n\
* On entry, the upper triangular 2 x 2 matrix B.\n\
* On exit, B is overwritten by the ``B-part'' of the\n\
* generalized Schur form.\n\
*\n\
* LDB (input) INTEGER\n\
* THe leading dimension of the array B. LDB >= 2.\n\
*\n\
* ALPHAR (output) DOUBLE PRECISION array, dimension (2)\n\
* ALPHAI (output) DOUBLE PRECISION array, dimension (2)\n\
* BETA (output) DOUBLE PRECISION array, dimension (2)\n\
* (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the\n\
* pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may\n\
* be zero.\n\
*\n\
* CSL (output) DOUBLE PRECISION\n\
* The cosine of the left rotation matrix.\n\
*\n\
* SNL (output) DOUBLE PRECISION\n\
* The sine of the left rotation matrix.\n\
*\n\
* CSR (output) DOUBLE PRECISION\n\
* The cosine of the right rotation matrix.\n\
*\n\
* SNR (output) DOUBLE PRECISION\n\
* The sine of the right rotation matrix.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA\n\
*\n\
* =====================================================================\n\
*\n"
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