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| pure subroutine, public | la_lapack_solve_lu::la_sgtsv (n, nrhs, dl, d, du, b, ldb, info) |
| | SGTSV: solves the equation A*X = B, where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL.
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| pure subroutine, public | la_lapack_solve_lu::la_dgtsv (n, nrhs, dl, d, du, b, ldb, info) |
| | DGTSV: solves the equation A*X = B, where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL.
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| pure subroutine, public | la_lapack_solve_lu::la_qgtsv (n, nrhs, dl, d, du, b, ldb, info) |
| | QGTSV: solves the equation A*X = B, where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL.
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| pure subroutine, public | la_lapack_solve_lu::la_sgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) |
| | SGBSV: computes the solution to a real 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 equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_dgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) |
| | DGBSV: computes the solution to a real 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 equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_qgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) |
| | QGBSV: computes the solution to a real 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 equations A * X = B.
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| subroutine, public | la_lapack_solve_lu::la_sgbsvx (fact, trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | SGBSVX: uses the LU factorization to compute the solution to a real 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.
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| subroutine, public | la_lapack_solve_lu::la_dgbsvx (fact, trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | DGBSVX: uses the LU factorization to compute the solution to a real 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.
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| subroutine, public | la_lapack_solve_lu::la_qgbsvx (fact, trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | QGBSVX: uses the LU factorization to compute the solution to a real 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.
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| pure subroutine, public | la_lapack_solve_lu::la_sgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | SGTSVX: uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N 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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| pure subroutine, public | la_lapack_solve_lu::la_dgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | DGTSVX: uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N 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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| pure subroutine, public | la_lapack_solve_lu::la_qgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | QGTSVX: uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N 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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| subroutine, public | la_lapack_solve_lu::la_dsgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info) |
| | DSGESV: computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. DSGESV first attempts to factorize the matrix in SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with DOUBLE PRECISION normwise backward error quality (see below). If the approach fails the method switches to a DOUBLE PRECISION factorization and solve. The iterative refinement is not going to be a winning strategy if the ratio SINGLE PRECISION performance over DOUBLE PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement. The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
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| subroutine, public | la_lapack_solve_lu::la_qdgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info) |
| | QDGESV: computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. QDGESV first attempts to factorize the matrix in SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with QUAD PRECISION normwise backward error quality (see below). If the approach fails the method switches to a QUAD PRECISION factorization and solve. The iterative refinement is not going to be a winning strategy if the ratio SINGLE PRECISION performance over QUAD PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement. The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by QLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
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| pure subroutine, public | la_lapack_solve_lu::la_sgesv (n, nrhs, a, lda, ipiv, b, ldb, info) |
| | SGESV: computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix 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 = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_dgesv (n, nrhs, a, lda, ipiv, b, ldb, info) |
| | DGESV: computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix 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 = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_qgesv (n, nrhs, a, lda, ipiv, b, ldb, info) |
| | QGESV: computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix 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 = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.
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| subroutine, public | la_lapack_solve_lu::la_sgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | SGESVX: uses the LU factorization to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N 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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| subroutine, public | la_lapack_solve_lu::la_dgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | DGESVX: uses the LU factorization to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N 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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| subroutine, public | la_lapack_solve_lu::la_qgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) |
| | QGESVX: uses the LU factorization to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N 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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| pure subroutine, public | la_lapack_solve_lu::la_cgtsv (n, nrhs, dl, d, du, b, ldb, info) |
| | CGTSV: solves the equation A*X = B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A**T *X = B may be solved by interchanging the order of the arguments DU and DL.
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| pure subroutine, public | la_lapack_solve_lu::la_zgtsv (n, nrhs, dl, d, du, b, ldb, info) |
| | ZGTSV: solves the equation A*X = B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A**T *X = B may be solved by interchanging the order of the arguments DU and DL.
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| pure subroutine, public | la_lapack_solve_lu::la_wgtsv (n, nrhs, dl, d, du, b, ldb, info) |
| | WGTSV: solves the equation A*X = B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A**T *X = B may be solved by interchanging the order of the arguments DU and DL.
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| pure subroutine, public | la_lapack_solve_lu::la_cgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) |
| | 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 equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_zgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) |
| | ZGBSV: 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 equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_wgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) |
| | WGBSV: 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 equations A * X = B.
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| subroutine, public | la_lapack_solve_lu::la_cgbsvx (fact, trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | 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.
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| subroutine, public | la_lapack_solve_lu::la_zgbsvx (fact, trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | ZGBSVX: 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.
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| subroutine, public | la_lapack_solve_lu::la_wgbsvx (fact, trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | WGBSVX: 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.
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| pure subroutine, public | la_lapack_solve_lu::la_cgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | CGTSVX: 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 tridiagonal matrix of order N 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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| pure subroutine, public | la_lapack_solve_lu::la_zgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | ZGTSVX: 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 tridiagonal matrix of order N 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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| pure subroutine, public | la_lapack_solve_lu::la_wgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | WGTSVX: 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 tridiagonal matrix of order N 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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| subroutine, public | la_lapack_solve_lu::la_zcgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, rwork, iter, info) |
| | ZCGESV: computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. ZCGESV first attempts to factorize the matrix in COMPLEX and use this factorization within an iterative refinement procedure to produce a solution with COMPLEX*16 normwise backward error quality (see below). If the approach fails the method switches to a COMPLEX*16 factorization and solve. The iterative refinement is not going to be a winning strategy if the ratio COMPLEX performance over COMPLEX*16 performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement. The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
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| subroutine, public | la_lapack_solve_lu::la_wzgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, rwork, iter, info) |
| | WZGESV: computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. WZGESV first attempts to factorize the matrix in COMPLEX and use this factorization within an iterative refinement procedure to produce a solution with COMPLEX*16 normwise backward error quality (see below). If the approach fails the method switches to a COMPLEX*16 factorization and solve. The iterative refinement is not going to be a winning strategy if the ratio COMPLEX performance over COMPLEX*16 performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement. The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by QLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
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| pure subroutine, public | la_lapack_solve_lu::la_cgesv (n, nrhs, a, lda, ipiv, b, ldb, info) |
| | CGESV: computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix 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 = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_zgesv (n, nrhs, a, lda, ipiv, b, ldb, info) |
| | ZGESV: computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix 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 = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.
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| pure subroutine, public | la_lapack_solve_lu::la_wgesv (n, nrhs, a, lda, ipiv, b, ldb, info) |
| | WGESV: computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix 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 = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.
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| subroutine, public | la_lapack_solve_lu::la_cgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | CGESVX: uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N 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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| subroutine, public | la_lapack_solve_lu::la_zgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | ZGESVX: uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N 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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| subroutine, public | la_lapack_solve_lu::la_wgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) |
| | WGESVX: uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N 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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1.13.2