?laqtr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

Solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

call slaqtr(ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
call dlaqtr(ltran, lreal, n, t, ldt, b, w, scale, x, work, info)

The routine ?laqtr solves the real quasi-triangular system

op(T) * p = scale*c , if lreal = .TRUE.

or the complex quasi-triangular systems

op(T + iB)*(p+iq) = scale*(c+id) , if lreal = .FALSE.

in real arithmetic, where T is upper quasi-triangular.

If lreal = .FALSE. , then the first diagonal block of T must be 1-by-1, B is the specially structured matrix

op(A) = A or A^T , A^T denotes the transpose of matrix A .

On input,

This routine is designed for the condition number estimation in routine ?trsna .

ltran: LOGICAL . On entry, ltran specifies the option of conjugate transpose: = .FALSE. , op(T + iB) = T + iB , = .TRUE. , op(T + iB) = (T + iB)^{T} .
lreal: LOGICAL . On entry, lreal specifies the input matrix structure: = .FALSE. , the input is complex = .TRUE. , the input is real.
n: INTEGER . On entry, n specifies the order of T + iB . n≥ 0 .
t: REAL for slaqtr DOUBLE PRECISION for dlaqtr Array, dimension ( ldt , n ). On entry, t contains a matrix in Schur canonical form. If lreal = .FALSE. , then the first diagonal block of t must be 1-by-1.
ldt: INTEGER . The leading dimension of the matrix T . ldt≥ max(1,n) .
b: REAL for slaqtr DOUBLE PRECISION for dlaqtr Array, dimension ( n ). On entry, b contains the elements to form the matrix B as described above. If lreal = .TRUE. , b is not referenced.
w: REAL for slaqtr DOUBLE PRECISION for dlaqtr On entry, w is the diagonal element of the matrix B . If lreal = .TRUE. , w is not referenced.
x: REAL for slaqtr DOUBLE PRECISION for dlaqtr Array, dimension (2 n ). On entry, x contains the right hand side of the system.
work: REAL for slaqtr DOUBLE PRECISION for dlaqtr Workspace array, dimension ( n ).

scale: REAL for slaqtr DOUBLE PRECISION for dlaqtr On exit, scale is the scale factor.
x: On exit, X is overwritten by the solution.

info

INTEGER .

If info = 0 : successful exit.
If info = 1 : the some diagonal 1-by-1 block has been perturbed by a small number smin to keep nonsingularity.
If info = 2 : the some diagonal 2-by-2 block has been perturbed by a small number in ?laln2 (Solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.) to keep nonsingularity.

NOTE:

For higher speed, this routine does not check the inputs for errors.