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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine stpt03 | ( | character | UPLO, |
| character | TRANS, | ||
| character | DIAG, | ||
| integer | N, | ||
| integer | NRHS, | ||
| real, dimension( * ) | AP, | ||
| real | SCALE, | ||
| real, dimension( * ) | CNORM, | ||
| real | TSCAL, | ||
| real, dimension( ldx, * ) | X, | ||
| integer | LDX, | ||
| real, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| real, dimension( * ) | WORK, | ||
| real | RESID | ||
| ) |
STPT03
STPT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b or A'*x = s*b when the triangular
matrix A is stored in packed format. Here A' is the transpose of A,
s is a scalar, and x and b are N by NRHS matrices. The test ratio is
the maximum over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon. | [in] | UPLO | UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular |
| [in] | TRANS | TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = s*b (No transpose)
= 'T': A'*x = s*b (Transpose)
= 'C': A'*x = s*b (Conjugate transpose = Transpose) |
| [in] | DIAG | DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 0. |
| [in] | NRHS | NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0. |
| [in] | AP | AP is REAL 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. |
| [in] | SCALE | SCALE is REAL
The scaling factor s used in solving the triangular system. |
| [in] | CNORM | CNORM is REAL array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal. |
| [in] | TSCAL | TSCAL is REAL
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A. |
| [in] | X | X is REAL array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations. |
| [in] | LDX | LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N). |
| [in] | B | B is REAL array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N). |
| [out] | WORK | WORK is REAL array, dimension (N) |
| [out] | RESID | RESID is REAL
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). |
1.9.4