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complib/CPPFA(3) -- CPPFA factors a complex Hermitian positive definite matrix stored in packed form. CPPFA is usually called by C
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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 . INFO INTEGER = 0 for normal return. = K If the leading minor of order K is not positive definite. Packed Storage The following program segment will pack the... |
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complib/cpprfs(3) -- when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward
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CPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution. |
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complib/CPPSL(3) -- CPPSL solves the complex Hermitian positive definite system A * X = B using the factors computed by CPPCO or C
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On Entry AP COMPLEX (N*(N+1)/2) the output from CPPCO or CPPFA. 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 compute INVERSE(A) * C where C is a matrix wi... |
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complib/cppsv(3) -- X = B,
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CPPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format 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/cppsvx(3) -- compute the solution to a complex system of linear equations A * X = B,
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CPPSVX 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 stored in packed format 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/cpptrf(3) -- compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
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CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. 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/cpptri(3) -- compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**
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CPPTRI 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 CPPTRF. |
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complib/cpptrs(3) -- solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using
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CPPTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF. |
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complib/cprod1d(3) -- Compute the product of a 1D Fourier transform with a 1D filter.
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cprod1d and zprod1d compute the product of the Fourier transforms of a complex sequence of N samples with the Fourier transforms of a complex filter. Note, the product of the Fourier transforms of two sequences is equal to the Fourier transform of their convolution. |
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complib/cprod2d(3) -- Compute the product of a 2D Fourier transforms with a 2D filter.
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cprod2d and zprod2d compute the product of the Fourier transforms of 2D complex sequence (size N1xN2) with the Fourier transform of 2D filter. Note, the product of the Fourier transforms of two sequences is equal to the Fourier transform of their convolution. |
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complib/cprod3d(3) -- Compute the product of a 3D Fourier transforms with a 3D filter.
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cprod3d and zprod3d compute the product of the Fourier transforms of 3D complex sequence (size N1xN2xN3) with the Fourier transform of 3D filter. Note, the product of the Fourier transforms of two sequences is equal to the Fourier transform of their convolution. |
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complib/cprodm1d(3) -- Compute the product of Multiple 1D Fourier transforms with Multiple 1D filters.
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cprodm1d and zprodm1d compute the product of the Fourier transforms of P complex sequences of N samples with the Fourier transforms of P complex filters. Note, the product of the Fourier transforms of two sequences is equal to the Fourier transform of their convolution. |
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complib/cptcon(3) -- compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridia
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CPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
