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complib/cfftm1d(3) -- Multiple 1D, complex-to-complex, Fast Fourier Transforms.
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cfftm1d and zfftm1d compute the complex Fourier transform of P complex sequences of N samples each. The k-th index F(k) of the Transform of an N sample sequence f(i) is equal to: F(k) = Sum ( W^(i*k) * f(i) ), for i =0, ..., (N-1) W = exp( (Sign*2*sqrt(-1)*PI) / N ) The Fourier transforms are computed in-place so the input sequence is overwritten by the Fourier transform output. |
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complib/cfftm1di(3) -- initialize the coefficient array for complex-tocomplex Multiple 1D FFT modules.
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Initialize the coefficient array which is used in the Multiple 1D FFT modules. This array contains the different twiddle factors and the factorization of N into prime numbers. As the FFT modules cfftm1d or zfftm1d only read the coeff array, it may be reused as long as necessary once it has been initialized. In C, if ptr is NULL, cfftm1di or zfftm1di returns a pointer to an allocated buffer. CFFTM1DI should be used to initialize the coefficient array before any call to CFFTM1D ZFFTM1DI should be ... |
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complib/CG(3) -- EISPACK routine. This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine
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On INPUT NM must be set to the row dimension of the two-dimensional array parameters as declared in the calling program dimension statement. N is the order of the matrix A=(AR,AI). AR and AI contain the real and imaginary parts, respectively, of the complex general matrix. MATZ is an integer variable set equal to zero if only eigenvalues are desired. Otherwise it is set to any non-zero integer for both eigenvalues and eigenvectors. On OUTPUT WR and WI contain the real and imaginary parts, respec... |
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complib/cgbbrd(3) -- reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
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CGBBRD reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation: Q' * A * P = B. The routine computes B, and optionally forms Q or P', or computes Q'*C for a given matrix C. |
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complib/CGBCO(3) -- CGBCO factors a complex band matrix by Gaussian elimination and estimates the condition of the matrix. If RCON
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On Entry ABD COMPLEX(LDA, N) contains the matrix in band storage. The columns of the matrix are stored in the columns of ABD and the diagonals of the matrix are stored in rows ML+1 through 2*ML+MU+1 of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. 2*ML + MU + 1 . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. 0 .LE. ML .LT. N . MU INTEGER number of diagonals above the main diago... |
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complib/cgbcon(3) -- general band matrix A, in either the 1-norm or the infinity-norm,
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CGBCON estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGBTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
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complib/CGBDI(3) -- CGBDI computes the determinant of a band matrix using the factors computed by CGBCO or CGBFA. If the inverse i
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On Entry ABD COMPLEX(LDA, N) the output from CGBCo or CGBFA. LDA INTEGER the leading dimension of the array ABD . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. MU INTEGER number of diagonals above the main diagonal. IPVT INTEGER(N) the pivot vector from CGBCO or CGBFA. On Return DET COMPLEX(2) determinant of original matrix. Determinant = DET(1) * 10.0**DET(2) with 1.0 .LE. CABS1(DET(1)) .LT. 10.0 or DET(1) = 0.0 . LINPACK. This version dated... |
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complib/cgbequ(3) -- compute row and column scalings intended to equilibrate an Mby-N band matrix A and reduce its condition number
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CGBEQU computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condi... |
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complib/CGBFA(3) -- CGBFA factors a complex band matrix by elimination. CGBFA is usually called by CGBCO, but it can be called dir
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On Entry ABD COMPLEX(LDA, N) contains the matrix in band storage. The columns of the matrix are stored in the columns of ABD and the diagonals of the matrix are stored in rows ML+1 through 2*ML+MU+1 of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. 2*ML + MU + 1 . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. 0 .LE. ML .LT. N . MU INTEGER number of diagonals above the main diago... |
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complib/cgbrfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provi
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CGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution. |
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complib/CGBSL(3) -- CGBSL solves the complex band system A * X = B or CTRANS(A) * X = B using the factors computed by CGBCO or CGB
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On Entry ABD COMPLEX(LDA, N) the output from CGBCo or CGBFA. LDA INTEGER the leading dimension of the array ABD . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. MU INTEGER number of diagonals above the main diagonal. IPVT INTEGER(N) the pivot vector from CGBCO or CGBFA. B COMPLEX(N) the right hand side vector. JOB INTEGER = 0 to solve A*X = B , = nonzero to solve CTRANS(A)*X = B , where CTRANS(A) is the conjugate transpose. On Return B the sol... |
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complib/cgbsv(3) -- compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N wi
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CGBSV computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of eq... |
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complib/cgbsvx(3) -- system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
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CGBSVX uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
