Triangular systems: solve, inverse, condition estimation, refinement. More...

Functions/Subroutines
pure subroutine, public	la_slatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
	SLATBS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine STBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_dlatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
	DLATBS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine DTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_qlatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
	QLATBS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine QTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_slatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
	SLATPS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine STPSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_dlatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
	DLATPS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine DTPSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_qlatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
	QLATPS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine QTPSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_slatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
	SLATRS: solves one of the triangular systems A x = sb or A*Tx = sb with scaling to prevent overflow. Here A is an upper or lower triangular matrix, AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine STRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_dlatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
	DLATRS: solves one of the triangular systems A x = sb or A*T x = sb with scaling to prevent overflow. Here A is an upper or lower triangular matrix, AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine DTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_qlatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
	QLATRS: solves one of the triangular systems A x = sb or A*T x = sb with scaling to prevent overflow. Here A is an upper or lower triangular matrix, AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine QTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_slauu2 (uplo, n, a, lda, info)
	SLAUU2: computes the product U * UT or LT * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_dlauu2 (uplo, n, a, lda, info)
	DLAUU2: computes the product U * UT or LT * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_qlauu2 (uplo, n, a, lda, info)
	QLAUU2: computes the product U * UT or LT * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_slauum (uplo, n, a, lda, info)
	SLAUUM: computes the product U * UT or LT * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_dlauum (uplo, n, a, lda, info)
	DLAUUM: computes the product U * UT or LT * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_qlauum (uplo, n, a, lda, info)
	QLAUUM: computes the product U * UT or LT * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_stbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	STBRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by STBTRS or some other means before entering this routine. STBRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_dtbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	DTBRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by DTBTRS or some other means before entering this routine. DTBRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_qtbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	QTBRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by QTBTRS or some other means before entering this routine. QTBRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_stbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
	STBTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_dtbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
	DTBTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_qtbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
	QTBTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_stprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	STPRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by STPTRS or some other means before entering this routine. STPRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_dtprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	DTPRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by DTPTRS or some other means before entering this routine. DTPRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_qtprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	QTPRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by QTPTRS or some other means before entering this routine. QTPRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_stptri (uplo, diag, n, ap, info)
	STPTRI: computes the inverse of a real upper or lower triangular matrix A stored in packed format.

pure subroutine, public	la_dtptri (uplo, diag, n, ap, info)
	DTPTRI: computes the inverse of a real upper or lower triangular matrix A stored in packed format.

pure subroutine, public	la_qtptri (uplo, diag, n, ap, info)
	QTPTRI: computes the inverse of a real upper or lower triangular matrix A stored in packed format.

pure subroutine, public	la_stptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
	STPTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_dtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
	DTPTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_qtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
	QTPTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_strrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	STRRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by STRTRS or some other means before entering this routine. STRRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_dtrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	DTRRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by DTRTRS or some other means before entering this routine. DTRRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_qtrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
	QTRRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by QTRTRS or some other means before entering this routine. QTRRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_strti2 (uplo, diag, n, a, lda, info)
	STRTI2: computes the inverse of a real upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm.

pure subroutine, public	la_dtrti2 (uplo, diag, n, a, lda, info)
	DTRTI2: computes the inverse of a real upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm.

pure subroutine, public	la_qtrti2 (uplo, diag, n, a, lda, info)
	QTRTI2: computes the inverse of a real upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm.

pure subroutine, public	la_strtri (uplo, diag, n, a, lda, info)
	STRTRI: computes the inverse of a real upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

pure subroutine, public	la_dtrtri (uplo, diag, n, a, lda, info)
	DTRTRI: computes the inverse of a real upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

pure subroutine, public	la_qtrtri (uplo, diag, n, a, lda, info)
	QTRTRI: computes the inverse of a real upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

pure subroutine, public	la_strtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
	STRTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_dtrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
	DTRTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_qtrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
	QTRTRS: solves a triangular system of the form A * X = B or A*T X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

subroutine, public	la_stbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
	STBCON: estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_dtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
	DTBCON: estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_qtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
	QTBCON: estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

pure subroutine, public	la_stftri (transr, uplo, diag, n, a, info)
	STFTRI: computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.

pure subroutine, public	la_dtftri (transr, uplo, diag, n, a, info)
	DTFTRI: computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.

pure subroutine, public	la_qtftri (transr, uplo, diag, n, a, info)
	QTFTRI: computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.

subroutine, public	la_stpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
	STPCON: estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_dtpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
	DTPCON: estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_qtpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
	QTPCON: estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_strcon (norm, uplo, diag, n, a, lda, rcond, work, iwork, info)
	STRCON: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_dtrcon (norm, uplo, diag, n, a, lda, rcond, work, iwork, info)
	DTRCON: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_qtrcon (norm, uplo, diag, n, a, lda, rcond, work, iwork, info)
	QTRCON: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

pure subroutine, public	la_clatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
	CLATBS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine CTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_zlatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
	ZLATBS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ZTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_wlatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
	WLATBS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here AT denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine WTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_clatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
	CLATPS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here AT denotes the transpose of A, AH denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine CTPSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_zlatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
	ZLATPS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here AT denotes the transpose of A, AH denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ZTPSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_wlatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
	WLATPS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form. Here AT denotes the transpose of A, AH denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine WTPSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_clatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
	CLATRS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow. Here A is an upper or lower triangular matrix, AT denotes the transpose of A, AH denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine CTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_zlatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
	ZLATRS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow. Here A is an upper or lower triangular matrix, AT denotes the transpose of A, AH denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine ZTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_wlatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
	WLATRS: solves one of the triangular systems A * x = sb, AT x = sb, or AH x = sb, with scaling to prevent overflow. Here A is an upper or lower triangular matrix, AT denotes the transpose of A, AH denotes the conjugate transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine WTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to Ax = 0 is returned.

pure subroutine, public	la_clauu2 (uplo, n, a, lda, info)
	CLAUU2: computes the product U * UH or LH * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_zlauu2 (uplo, n, a, lda, info)
	ZLAUU2: computes the product U * UH or LH * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_wlauu2 (uplo, n, a, lda, info)
	WLAUU2: computes the product U * UH or LH * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_clauum (uplo, n, a, lda, info)
	CLAUUM: computes the product U * UH or LH * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_zlauum (uplo, n, a, lda, info)
	ZLAUUM: computes the product U * UH or LH * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_wlauum (uplo, n, a, lda, info)
	WLAUUM: computes the product U * UH or LH * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_ctbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	CTBRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by CTBTRS or some other means before entering this routine. CTBRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_ztbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	ZTBRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by ZTBTRS or some other means before entering this routine. ZTBRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_wtbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	WTBRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by WTBTRS or some other means before entering this routine. WTBRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_ctbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
	CTBTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_ztbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
	ZTBTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_wtbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
	WTBTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_ctprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	CTPRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by CTPTRS or some other means before entering this routine. CTPRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_ztprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	ZTPRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by ZTPTRS or some other means before entering this routine. ZTPRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_wtprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	WTPRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by WTPTRS or some other means before entering this routine. WTPRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_ctptri (uplo, diag, n, ap, info)
	CTPTRI: computes the inverse of a complex upper or lower triangular matrix A stored in packed format.

pure subroutine, public	la_ztptri (uplo, diag, n, ap, info)
	ZTPTRI: computes the inverse of a complex upper or lower triangular matrix A stored in packed format.

pure subroutine, public	la_wtptri (uplo, diag, n, ap, info)
	WTPTRI: computes the inverse of a complex upper or lower triangular matrix A stored in packed format.

pure subroutine, public	la_ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
	CTPTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_ztptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
	ZTPTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_wtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
	WTPTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_ctrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	CTRRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by CTRTRS or some other means before entering this routine. CTRRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_ztrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	ZTRRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by ZTRTRS or some other means before entering this routine. ZTRRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_wtrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	WTRRFS: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by WTRTRS or some other means before entering this routine. WTRRFS does not do iterative refinement because doing so cannot improve the backward error.

pure subroutine, public	la_ctrti2 (uplo, diag, n, a, lda, info)
	CTRTI2: computes the inverse of a complex upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm.

pure subroutine, public	la_ztrti2 (uplo, diag, n, a, lda, info)
	ZTRTI2: computes the inverse of a complex upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm.

pure subroutine, public	la_wtrti2 (uplo, diag, n, a, lda, info)
	WTRTI2: computes the inverse of a complex upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm.

pure subroutine, public	la_ctrtri (uplo, diag, n, a, lda, info)
	CTRTRI: computes the inverse of a complex upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

pure subroutine, public	la_ztrtri (uplo, diag, n, a, lda, info)
	ZTRTRI: computes the inverse of a complex upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

pure subroutine, public	la_wtrtri (uplo, diag, n, a, lda, info)
	WTRTRI: computes the inverse of a complex upper or lower triangular matrix A. This is the Level 3 BLAS version of the algorithm.

pure subroutine, public	la_ctrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
	CTRTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_ztrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
	ZTRTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

pure subroutine, public	la_wtrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
	WTRTRS: solves a triangular system of the form A * X = B, A*T X = B, or A*H X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular.

subroutine, public	la_ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
	CTBCON: estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_ztbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
	ZTBCON: estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_wtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
	WTBCON: estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

pure subroutine, public	la_ctftri (transr, uplo, diag, n, a, info)
	CTFTRI: computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.

pure subroutine, public	la_ztftri (transr, uplo, diag, n, a, info)
	ZTFTRI: computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.

pure subroutine, public	la_wtftri (transr, uplo, diag, n, a, info)
	WTFTRI: computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.

subroutine, public	la_ctpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
	CTPCON: estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_ztpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
	ZTPCON: estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_wtpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
	WTPCON: estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_ctrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork, info)
	CTRCON: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_ztrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork, info)
	ZTRCON: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

subroutine, public	la_wtrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork, info)
	WTRCON: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Detailed Description

Triangular systems: solve, inverse, condition estimation, refinement.

Function/Subroutine Documentation

◆ la_clatbs()

pure subroutine, public la_lapack_solve_tri_comp::la_clatbs	(	character, intent(in)	uplo,
		character, intent(in)	trans,
		character, intent(in)	diag,
		character, intent(in)	normin,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	kd,
		complex(sp), dimension(ldab,*), intent(in)	ab,
		integer(ilp), intent(in)	ldab,
		complex(sp), dimension(*), intent(inout)	x,
		real(sp), intent(out)	scale,
		real(sp), dimension(*), intent(inout)	cnorm,
		integer(ilp), intent(out)	info )

CLATBS: solves one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, with scaling to prevent overflow, where A is an upper or lower triangular band matrix. Here A**T denotes the transpose of A, x and b are n-element vectors, and s is a scaling factor, usually less than or equal to 1, chosen so that the components of x will be less than the overflow threshold. If the unscaled problem will not cause overflow, the Level 2 BLAS routine CTBSV is called. If the matrix A is singular (A(j,j) = 0 for some j), then s is set to 0 and a non-trivial solution to A*x = 0 is returned.