--- name: "lag2" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/lag2" --- # lag2(3) lag2: 2x2 eig ## NAME lag2 - lag2: 2x2 eig ## SYNOPSIS ### Functions subroutine **dlag2** (a, lda, b, ldb, safmin, scale1, scale2, wr1, wr2, wi)\ **DLAG2** computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. subroutine **slag2** (a, lda, b, ldb, safmin, scale1, scale2, wr1, wr2, wi)\ **SLAG2** computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. ## Detailed Description ## Function Documentation ### subroutine dlag2 (double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldb, \* ) b, integer ldb, double precision safmin, double precision scale1, double precision scale2, double precision wr1, double precision wr2, double precision wi) **DLAG2** computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. **Purpose:** ``` !> !> DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue !> problem A - w B, with scaling as necessary to avoid over-/underflow. !> !> The scaling factor results in a modified eigenvalue equation !> !> s A - w B !> !> where s is a non-negative scaling factor chosen so that w, w B, !> and s A do not overflow and, if possible, do not underflow, either. !> ``` **Parameters** *A* ``` !> A is DOUBLE PRECISION array, dimension (LDA, 2) !> On entry, the 2 x 2 matrix A. It is assumed that its 1-norm !> is less than 1/SAFMIN. Entries less than !> sqrt(SAFMIN)*norm(A) are subject to being treated as zero. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= 2. !> ``` *B* ``` !> B is DOUBLE PRECISION array, dimension (LDB, 2) !> On entry, the 2 x 2 upper triangular matrix B. It is !> assumed that the one-norm of B is less than 1/SAFMIN. The !> diagonals should be at least sqrt(SAFMIN) times the largest !> element of B (in absolute value); if a diagonal is smaller !> than that, then +/- sqrt(SAFMIN) will be used instead of !> that diagonal. !> ``` *LDB* ``` !> LDB is INTEGER !> The leading dimension of the array B. LDB >= 2. !> ``` *SAFMIN* ``` !> SAFMIN is DOUBLE PRECISION !> The smallest positive number s.t. 1/SAFMIN does not !> overflow. (This should always be DLAMCH('S') -- it is an !> argument in order to avoid having to call DLAMCH frequently.) !> ``` *SCALE1* ``` !> SCALE1 is DOUBLE PRECISION !> A scaling factor used to avoid over-/underflow in the !> eigenvalue equation which defines the first eigenvalue. If !> the eigenvalues are complex, then the eigenvalues are !> ( WR1 +/- WI i ) / SCALE1 (which may lie outside the !> exponent range of the machine), SCALE1=SCALE2, and SCALE1 !> will always be positive. If the eigenvalues are real, then !> the first (real) eigenvalue is WR1 / SCALE1 , but this may !> overflow or underflow, and in fact, SCALE1 may be zero or !> less than the underflow threshold if the exact eigenvalue !> is sufficiently large. !> ``` *SCALE2* ``` !> SCALE2 is DOUBLE PRECISION !> A scaling factor used to avoid over-/underflow in the !> eigenvalue equation which defines the second eigenvalue. If !> the eigenvalues are complex, then SCALE2=SCALE1. If the !> eigenvalues are real, then the second (real) eigenvalue is !> WR2 / SCALE2 , but this may overflow or underflow, and in !> fact, SCALE2 may be zero or less than the underflow !> threshold if the exact eigenvalue is sufficiently large. !> ``` *WR1* ``` !> WR1 is DOUBLE PRECISION !> If the eigenvalue is real, then WR1 is SCALE1 times the !> eigenvalue closest to the (2,2) element of A B**(-1). If the !> eigenvalue is complex, then WR1=WR2 is SCALE1 times the real !> part of the eigenvalues. !> ``` *WR2* ``` !> WR2 is DOUBLE PRECISION !> If the eigenvalue is real, then WR2 is SCALE2 times the !> other eigenvalue. If the eigenvalue is complex, then !> WR1=WR2 is SCALE1 times the real part of the eigenvalues. !> ``` *WI* ``` !> WI is DOUBLE PRECISION !> If the eigenvalue is real, then WI is zero. If the !> eigenvalue is complex, then WI is SCALE1 times the imaginary !> part of the eigenvalues. WI will always be non-negative. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **154** of file **dlag2.f**. ### subroutine slag2 (real, dimension( lda, \* ) a, integer lda, real, dimension( ldb, \* ) b, integer ldb, real safmin, real scale1, real scale2, real wr1, real wr2, real wi) **SLAG2** computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. **Purpose:** ``` !> !> SLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue !> problem A - w B, with scaling as necessary to avoid over-/underflow. !> !> The scaling factor results in a modified eigenvalue equation !> !> s A - w B !> !> where s is a non-negative scaling factor chosen so that w, w B, !> and s A do not overflow and, if possible, do not underflow, either. !> ``` **Parameters** *A* ``` !> A is REAL array, dimension (LDA, 2) !> On entry, the 2 x 2 matrix A. It is assumed that its 1-norm !> is less than 1/SAFMIN. Entries less than !> sqrt(SAFMIN)*norm(A) are subject to being treated as zero. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= 2. !> ``` *B* ``` !> B is REAL array, dimension (LDB, 2) !> On entry, the 2 x 2 upper triangular matrix B. It is !> assumed that the one-norm of B is less than 1/SAFMIN. The !> diagonals should be at least sqrt(SAFMIN) times the largest !> element of B (in absolute value); if a diagonal is smaller !> than that, then +/- sqrt(SAFMIN) will be used instead of !> that diagonal. !> ``` *LDB* ``` !> LDB is INTEGER !> The leading dimension of the array B. LDB >= 2. !> ``` *SAFMIN* ``` !> SAFMIN is REAL !> The smallest positive number s.t. 1/SAFMIN does not !> overflow. (This should always be SLAMCH('S') -- it is an !> argument in order to avoid having to call SLAMCH frequently.) !> ``` *SCALE1* ``` !> SCALE1 is REAL !> A scaling factor used to avoid over-/underflow in the !> eigenvalue equation which defines the first eigenvalue. If !> the eigenvalues are complex, then the eigenvalues are !> ( WR1 +/- WI i ) / SCALE1 (which may lie outside the !> exponent range of the machine), SCALE1=SCALE2, and SCALE1 !> will always be positive. If the eigenvalues are real, then !> the first (real) eigenvalue is WR1 / SCALE1 , but this may !> overflow or underflow, and in fact, SCALE1 may be zero or !> less than the underflow threshold if the exact eigenvalue !> is sufficiently large. !> ``` *SCALE2* ``` !> SCALE2 is REAL !> A scaling factor used to avoid over-/underflow in the !> eigenvalue equation which defines the second eigenvalue. If !> the eigenvalues are complex, then SCALE2=SCALE1. If the !> eigenvalues are real, then the second (real) eigenvalue is !> WR2 / SCALE2 , but this may overflow or underflow, and in !> fact, SCALE2 may be zero or less than the underflow !> threshold if the exact eigenvalue is sufficiently large. !> ``` *WR1* ``` !> WR1 is REAL !> If the eigenvalue is real, then WR1 is SCALE1 times the !> eigenvalue closest to the (2,2) element of A B**(-1). If the !> eigenvalue is complex, then WR1=WR2 is SCALE1 times the real !> part of the eigenvalues. !> ``` *WR2* ``` !> WR2 is REAL !> If the eigenvalue is real, then WR2 is SCALE2 times the !> other eigenvalue. If the eigenvalue is complex, then !> WR1=WR2 is SCALE1 times the real part of the eigenvalues. !> ``` *WI* ``` !> WI is REAL !> If the eigenvalue is real, then WI is zero. If the !> eigenvalue is complex, then WI is SCALE1 times the imaginary !> part of the eigenvalues. WI will always be non-negative. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **154** of file **slag2.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.