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complib/CSPFA(3) -- CSPFA factors a complex symmetric matrix stored in packed form by elimination with symmetric pivoting. To solv
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On Entry AP COMPLEX (N*(N+1)/2) the packed form of a symmetric 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 a block diagonal matrix and the multipliers which were used to obtain it stored in packed form. The factorization can be written A = U*D*TRANS(U) where U is a product of permutation and unit upper triangular matrices , TRANS(U) is the t... |
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complib/cspr(3) -- + A,
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CSPR performs the symmetric rank 1 operation where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form. |
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complib/csprfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefin
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CSPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution. |
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complib/CSPSL(3) -- CSISL solves the complex symmetric system A * X = B using the factors computed by CSPFA.
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On Entry AP COMPLEX(N*(N+1)/2) the output from CSPFA. N INTEGER the order of the matrix A . KVPT INTEGER(N) the pivot vector from CSPFA. B COMPLEX(N) the right hand side vector. On Return B the solution vector X . Error Condition A division by zero may occur if CSPCO has set RCOND .EQ. 0.0 or CSPFA has set INFO .NE. 0 . To compute INVERSE(A) * C where C is a matrix with P columns CALL CSPFA(AP,N,KVPT,INFO) IF (INFO .NE. 0) GO TO ... DO 10 J = 1, P CALL CSPSL(AP,N,KVPT,C(1,J)) 10 CONTINUE LINPACK... |
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complib/cspsv(3) -- X = B,
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CSPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used t... |
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complib/cspsvx(3) -- and X and B are N-by-NRHS matrices
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CSPSVX uses the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric 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/csptrf(3) -- in packed format using the Bunch-Kaufman diagonal pivoting method
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CSPTRF computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method: A = U*D*U**T or A = L*D*L**T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. |
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complib/csptri(3) -- compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U
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CSPTRI computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. |
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complib/csptrs(3) -- solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the
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CSPTRS solves a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. |
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complib/CSROOT(3) -- EISPACK auxiliary routine.
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(yr,yi) = complex sqrt(xr,xi) Branch chosen so that yr .ge. 0.0 and sign(yi) .eq. sign(xi). PPPPaaaaggggeeee 1111 |
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complib/CSROT(3) -- CSROT applies the complex Givens rotation (X) ( C S)(X) (Y) = (-S C)(Y) N times where for I = 0,...,N-1 X = CX
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Argument Description N (integer) number of elements in each vector CX (complex array) beginning of one vector INCX (integer) memory spacing of successive elements of vector CX CY (complex array) beginning of the other vector INCY (integer) memory spacing of successive elements of vector CY C (real) cosine term of the rotation S (real) sine term of the rotation. PPPPaaaaggggeeee 1111 |
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complib/csrscl(3) -- multiplie an n-element complex vector x by the real scalar 1/a
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CSRSCL multiplies an n-element complex vector x by the real scalar 1/a. This is done without overflow or underflow as long as the final result x/a does not overflow or underflow. |
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complib/cstedc(3) -- compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and c
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CSTEDC computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix to tridiagonal form. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like t... |
