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---
:name: dlag2
:md5sum: cb3cffe0121d3cdef959429272b11c8d
:category: :subroutine
:arguments:
- a:
:type: doublereal
:intent: input
:dims:
- lda
- "2"
- lda:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input
:dims:
- ldb
- "2"
- ldb:
:type: integer
:intent: input
- safmin:
:type: doublereal
:intent: input
- scale1:
:type: doublereal
:intent: output
- scale2:
:type: doublereal
:intent: output
- wr1:
:type: doublereal
:intent: output
- wr2:
:type: doublereal
:intent: output
- wi:
:type: doublereal
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue\n\
* problem A - w B, with scaling as necessary to avoid over-/underflow.\n\
*\n\
* The scaling factor \"s\" results in a modified eigenvalue equation\n\
*\n\
* s A - w B\n\
*\n\
* where s is a non-negative scaling factor chosen so that w, w B,\n\
* and s A do not overflow and, if possible, do not underflow, either.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* A (input) DOUBLE PRECISION array, dimension (LDA, 2)\n\
* On entry, the 2 x 2 matrix A. It is assumed that its 1-norm\n\
* is less than 1/SAFMIN. Entries less than\n\
* sqrt(SAFMIN)*norm(A) are subject to being treated as zero.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= 2.\n\
*\n\
* B (input) DOUBLE PRECISION array, dimension (LDB, 2)\n\
* On entry, the 2 x 2 upper triangular matrix B. It is\n\
* assumed that the one-norm of B is less than 1/SAFMIN. The\n\
* diagonals should be at least sqrt(SAFMIN) times the largest\n\
* element of B (in absolute value); if a diagonal is smaller\n\
* than that, then +/- sqrt(SAFMIN) will be used instead of\n\
* that diagonal.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= 2.\n\
*\n\
* SAFMIN (input) DOUBLE PRECISION\n\
* The smallest positive number s.t. 1/SAFMIN does not\n\
* overflow. (This should always be DLAMCH('S') -- it is an\n\
* argument in order to avoid having to call DLAMCH frequently.)\n\
*\n\
* SCALE1 (output) DOUBLE PRECISION\n\
* A scaling factor used to avoid over-/underflow in the\n\
* eigenvalue equation which defines the first eigenvalue. If\n\
* the eigenvalues are complex, then the eigenvalues are\n\
* ( WR1 +/- WI i ) / SCALE1 (which may lie outside the\n\
* exponent range of the machine), SCALE1=SCALE2, and SCALE1\n\
* will always be positive. If the eigenvalues are real, then\n\
* the first (real) eigenvalue is WR1 / SCALE1 , but this may\n\
* overflow or underflow, and in fact, SCALE1 may be zero or\n\
* less than the underflow threshold if the exact eigenvalue\n\
* is sufficiently large.\n\
*\n\
* SCALE2 (output) DOUBLE PRECISION\n\
* A scaling factor used to avoid over-/underflow in the\n\
* eigenvalue equation which defines the second eigenvalue. If\n\
* the eigenvalues are complex, then SCALE2=SCALE1. If the\n\
* eigenvalues are real, then the second (real) eigenvalue is\n\
* WR2 / SCALE2 , but this may overflow or underflow, and in\n\
* fact, SCALE2 may be zero or less than the underflow\n\
* threshold if the exact eigenvalue is sufficiently large.\n\
*\n\
* WR1 (output) DOUBLE PRECISION\n\
* If the eigenvalue is real, then WR1 is SCALE1 times the\n\
* eigenvalue closest to the (2,2) element of A B**(-1). If the\n\
* eigenvalue is complex, then WR1=WR2 is SCALE1 times the real\n\
* part of the eigenvalues.\n\
*\n\
* WR2 (output) DOUBLE PRECISION\n\
* If the eigenvalue is real, then WR2 is SCALE2 times the\n\
* other eigenvalue. If the eigenvalue is complex, then\n\
* WR1=WR2 is SCALE1 times the real part of the eigenvalues.\n\
*\n\
* WI (output) DOUBLE PRECISION\n\
* If the eigenvalue is real, then WI is zero. If the\n\
* eigenvalue is complex, then WI is SCALE1 times the imaginary\n\
* part of the eigenvalues. WI will always be non-negative.\n\
*\n\n\
* =====================================================================\n\
*\n"
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