--- rpl/lapack/blas/dtbsv.f 2010/01/26 15:22:45 1.1.1.1 +++ rpl/lapack/blas/dtbsv.f 2018/05/29 06:55:14 1.14 @@ -1,4 +1,199 @@ +*> \brief \b DTBSV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DTBSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular band matrix, with ( k + 1 ) +*> diagonals. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> +*> TRANS = 'N' or 'n' A*x = b. +*> +*> TRANS = 'T' or 't' A**T*x = b. +*> +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension ( LDA, N ) +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date December 2016 +* +*> \ingroup double_blas_level2 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> \endverbatim +*> +* ===================================================================== SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* -- Reference BLAS level2 routine (version 3.7.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* December 2016 +* * .. Scalar Arguments .. INTEGER INCX,K,LDA,N CHARACTER DIAG,TRANS,UPLO @@ -7,139 +202,6 @@ DOUBLE PRECISION A(LDA,*),X(*) * .. * -* Purpose -* ======= -* -* DTBSV solves one of the systems of equations -* -* A*x = b, or A'*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular band matrix, with ( k + 1 ) -* diagonals. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments -* ========== -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A'*x = b. -* -* TRANS = 'C' or 'c' A'*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Further Details -* =============== -* -* Level 2 Blas routine. -* -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. -* * ===================================================================== * * .. Parameters .. @@ -271,7 +333,7 @@ END IF ELSE * -* Form x := inv( A')*x. +* Form x := inv( A**T)*x. * IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1