|
|
complib/CPODI(3) -- CPODI computes the determinant and inverse of a certain complex Hermitian positive definite matrix (see below)
|
|
On Entry A COMPLEX(LDA, N) the output A from CPOCO or CPOFA or the output X from CQRDC. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . JOB INTEGER = 11 both determinant and inverse. = 01 inverse only. = 10 determinant only. On Return A If CPOCO or CPOFA was used to factor A then CPODI produces the upper half of INVERSE(A) . If CQRDC was used to decompose X then CPODI produces the upper half of INVERSE(CTRANS(X)*X) where CTRANS(X) is the conjugate transpo... |
|
complib/cpoequ(3) -- compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its
|
|
CPOEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.... |
|
complib/CPOFA(3) -- CPOFA factors a complex Hermitian positive definite matrix. CPOFA is usually called by CPOCO, but it can be ca
|
|
On Entry A COMPLEX(LDA, N) the Hermitian matrix to be factored. Only the diagonal and upper triangle are used. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A an upper triangular matrix R so that A = CTRANS(R)*R where CTRANS(R) is the conjugate transpose. The strict lower triangle is unaltered. If INFO .NE. 0 , the factorization is not complete. INFO INTEGER = 0 for normal return. = K signals an error condition. The leading minor of order K is... |
|
complib/cporfs(3) -- when the coefficient matrix is Hermitian positive definite,
|
|
CPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and provides error bounds and backward error estimates for the solution. |
|
complib/CPOSL(3) -- CPOSL solves the COMPLEX Hermitian positive definite system A * X = B using the factors computed by CPOCO or C
|
|
On Entry A COMPLEX(LDA, N) the output from CPOCO or CPOFA. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . B COMPLEX(N) the right hand side vector. On Return B the solution vector X . Error Condition A division by zero will occur if the input factor contains a zero on the diagonal. Technically this indicates singularity but it is usually caused by improper subroutine arguments. It will not occur if the subroutines are called correctly and INFO .EQ. 0 . To... |
|
complib/cposv(3) -- X = B,
|
|
CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as A = U**H* U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.... |
|
complib/cposvx(3) -- compute the solution to a complex system of linear equations A * X = B,
|
|
CPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
|
complib/cpotf2(3) -- compute the Cholesky factorization of a complex Hermitian positive definite matrix A
|
|
CPOTF2 computes the Cholesky factorization of a complex Hermitian positive definite matrix A. The factorization has the form A = U' * U , if UPLO = 'U', or A = L * L', if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the unblocked version of the algorithm, calling Level 2 BLAS. |
|
complib/cpotrf(3) -- compute the Cholesky factorization of a complex Hermitian positive definite matrix A
|
|
CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the block version of the algorithm, calling Level 3 BLAS. |
|
complib/cpotri(3) -- compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**
|
|
CPOTRI computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF. |
|
complib/cpotrs(3) -- solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky fact
|
|
CPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF. |
|
complib/CPPCO(3) -- CPPCO factors a complex Hermitian positive definite matrix stored in packed form and estimates the condition o
|
|
On Entry AP COMPLEX (N*(N+1)/2) the packed form of a Hermitian matrix A . The columns of the upper triangle are stored sequentially in a one-dimensional array of length N*(N+1)/2 . See comments below for details. N INTEGER the order of the matrix A . On Return AP an upper triangular matrix R , stored in packed form, so that A = CTRANS(R)*R . If INFO .NE. 0 , the factorization is not complete. RCOND REAL an estimate of the reciprocal condition of A . For the system A*X = B , relative perturbation... |
|
complib/cppcon(3) -- estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packe
|
|
CPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
