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complib/zpbtrf(3) -- compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
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ZPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band 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. |
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complib/zpbtrs(3) -- solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky
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ZPBTRS solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF. |
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complib/zpocon(3) -- estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matri
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ZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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complib/zpoequ(3) -- compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its
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ZPOEQU 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.... |
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complib/zporfs(3) -- when the coefficient matrix is Hermitian positive definite,
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ZPORFS 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. |
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complib/zposv(3) -- X = B,
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ZPOSV 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.... |
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complib/zposvx(3) -- compute the solution to a complex system of linear equations A * X = B,
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ZPOSVX 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. |
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complib/zpotf2(3) -- compute the Cholesky factorization of a complex Hermitian positive definite matrix A
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ZPOTF2 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. |
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complib/zpotrf(3) -- compute the Cholesky factorization of a complex Hermitian positive definite matrix A
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ZPOTRF 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. |
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complib/zpotri(3) -- compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**
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ZPOTRI 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 ZPOTRF. |
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complib/zpotrs(3) -- solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky fact
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ZPOTRS 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 ZPOTRF. |
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complib/zppcon(3) -- estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packe
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ZPPCON 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 ZPPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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complib/zppequ(3) -- compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed stora
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ZPPEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage 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.... |
