?laqtr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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 )

slaqtr dlaqtr

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^:code:`T` , A^:code:`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.