Visible to Intel only — GUID: GUID-D08C8C84-C23C-40C9-90AB-9F751E886B5A
Visible to Intel only — GUID: GUID-D08C8C84-C23C-40C9-90AB-9F751E886B5A
?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 AT*x = s*b, or AH*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 AT denotes the transpose of A, AH 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 AT*x = s*b (transpose)
= 'C': solve AH*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