Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?latps
Solves a triangular system of equations with the matrix held in packed storage.
Syntax
call slatps ( uplo , trans , diag , normin , n , ap , x , scale , cnorm , info )
call dlatps ( uplo , trans , diag , normin , n , ap , x , scale , cnorm , info )
call clatps ( uplo , trans , diag , normin , n , ap , x , scale , cnorm , info )
call zlatps ( uplo , trans , diag , normin , n , ap , x , scale , cnorm , info )
Include Files
mkl.fi
Description
The routine ?latps solves one of the triangular systems
A*x = s*b , or A^{T}*x = s*b, or A^{H}*x = s*b (for complex flavors)
with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here A:code:`T` denotes the transpose of A , A:code:`H` denotes the conjugate transpose of A , x and b are n -element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem does not cause overflow, the Level 2 BLAS routine ?tpsv is called. If the matrix A is singular ( A(j, j) = 0 for some j ), then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
Input Parameters
- uplo
-
CHARACTER*1 . Specifies whether the matrix A is upper or lower triangular. = ‘U’ : upper triangular = ‘L’ : uower triangular
- trans
-
CHARACTER*1 . Specifies the operation applied to A . = ‘N’ : solve A*x = s*b (no transpose) = ‘T’ : solve A^{T}*x = s*b (transpose) = ‘C’ : solve A^{H}*x = s*b (conjugate transpose)
- diag
-
CHARACTER*1 . Specifies whether the matrix A is unit triangular. = 'N ‘: non-unit triangular = ‘U’ : unit triangular
- normin
-
CHARACTER*1 . Specifies whether cnorm is set. = ‘Y’ : cnorm contains the column norms on entry; = ‘N’ : cnorm is not set on entry. On exit, the norms will be computed and stored in cnorm.
- n
-
INTEGER . The order of the matrix A . n≥ 0 .
- ap
-
REAL for slatps DOUBLE PRECISION for dlatps COMPLEX for clatps DOUBLE COMPLEX for zlatps . Array, DIMENSION ( n(n+1)/2). The upper or lower triangular matrix A , packed columnwise in a linear array. The j -th column of A is stored in the array ap as follows: if uplo = 'U' , ap(i + (j-1)j/2) = A(i,j) for 1≤ i ≤ j ; if uplo = 'L' , ap(i + (j-1)(2n-j)/2) = A(i, j) for j≤i≤n .
- x
-
REAL for slatps DOUBLE PRECISION for dlatps COMPLEX for clatps DOUBLE COMPLEX for zlatps . Array, DIMENSION ( n ) On entry, the right hand side b of the triangular system.
- cnorm
-
REAL for slatps / clatps DOUBLE PRECISION for dlatps / zlatps . Array, DIMENSION ( n ). If normin = 'Y' , cnorm is an input argument and cnorm(j) contains the norm of the off-diagonal part of the j -th column of A . If trans = 'N' , cnorm(j) must be greater than or equal to the infinity-norm, and if trans = 'T' or ‘C’ , cnorm(j) must be greater than or equal to the 1-norm.
Output Parameters
- x
-
On exit, x is overwritten by the solution vector x .
- scale
-
REAL for slatps / clatps DOUBLE PRECISION for dlatps / zlatps . The scaling factor s for the triangular system as described above. If scale = 0 , the matrix A is singular or badly scaled, and the vector x is an exact or approximate solution to A*x = 0 .
- cnorm
-
If normin = 'N' , cnorm is an output argument and cnorm(j) returns the 1-norm of the off-diagonal part of the j -th column of A .
info
INTEGER .
= 0: successful exit
< 0: if info = -k , the k -th argument had an illegal value