?latps

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?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^T denotes the transpose of A, A^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 slatpsDOUBLE 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

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?latps