version 1.3, 2010/08/06 15:32:20
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version 1.8, 2011/11/21 20:37:08
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SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) |
*> \brief \b DTPSV |
* .. Scalar Arguments .. |
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INTEGER INCX,N |
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CHARACTER DIAG,TRANS,UPLO |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION AP(*),X(*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
* |
* DTPSV solves one of the systems of equations |
* =========== DOCUMENTATION =========== |
* |
* |
* A*x = b, or A'*x = b, |
* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
* |
* |
* where b and x are n element vectors and A is an n by n unit, or |
* Definition: |
* non-unit, upper or lower triangular matrix, supplied in packed form. |
* =========== |
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* |
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* SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INCX,N |
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* CHARACTER DIAG,TRANS,UPLO |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AP(*),X(*) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DTPSV solves one of the systems of equations |
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*> |
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*> A*x = b, or A**T*x = b, |
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*> |
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*> where b and x are n element vectors and A is an n by n unit, or |
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*> non-unit, upper or lower triangular matrix, supplied in packed form. |
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*> |
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*> No test for singularity or near-singularity is included in this |
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*> routine. Such tests must be performed before calling this routine. |
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*> \endverbatim |
* |
* |
* No test for singularity or near-singularity is included in this |
* Arguments: |
* routine. Such tests must be performed before calling this routine. |
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* |
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* Arguments |
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* ========== |
* ========== |
* |
* |
* UPLO - CHARACTER*1. |
*> \param[in] UPLO |
* On entry, UPLO specifies whether the matrix is an upper or |
*> \verbatim |
* lower triangular matrix as follows: |
*> UPLO is CHARACTER*1 |
* |
*> On entry, UPLO specifies whether the matrix is an upper or |
* UPLO = 'U' or 'u' A is an upper triangular matrix. |
*> lower triangular matrix as follows: |
* |
*> |
* UPLO = 'L' or 'l' A is a lower triangular matrix. |
*> UPLO = 'U' or 'u' A is an upper triangular matrix. |
* |
*> |
* Unchanged on exit. |
*> UPLO = 'L' or 'l' A is a lower triangular matrix. |
* |
*> \endverbatim |
* TRANS - CHARACTER*1. |
*> |
* On entry, TRANS specifies the equations to be solved as |
*> \param[in] TRANS |
* follows: |
*> \verbatim |
* |
*> TRANS is CHARACTER*1 |
* TRANS = 'N' or 'n' A*x = b. |
*> On entry, TRANS specifies the equations to be solved as |
* |
*> follows: |
* TRANS = 'T' or 't' A'*x = b. |
*> |
* |
*> TRANS = 'N' or 'n' A*x = b. |
* TRANS = 'C' or 'c' A'*x = b. |
*> |
* |
*> TRANS = 'T' or 't' A**T*x = b. |
* Unchanged on exit. |
*> |
* |
*> TRANS = 'C' or 'c' A**T*x = b. |
* DIAG - CHARACTER*1. |
*> \endverbatim |
* On entry, DIAG specifies whether or not A is unit |
*> |
* triangular as follows: |
*> \param[in] DIAG |
* |
*> \verbatim |
* DIAG = 'U' or 'u' A is assumed to be unit triangular. |
*> DIAG is CHARACTER*1 |
* |
*> On entry, DIAG specifies whether or not A is unit |
* DIAG = 'N' or 'n' A is not assumed to be unit |
*> triangular as follows: |
* triangular. |
*> |
* |
*> DIAG = 'U' or 'u' A is assumed to be unit triangular. |
* Unchanged on exit. |
*> |
* |
*> DIAG = 'N' or 'n' A is not assumed to be unit |
* N - INTEGER. |
*> triangular. |
* On entry, N specifies the order of the matrix A. |
*> \endverbatim |
* N must be at least zero. |
*> |
* Unchanged on exit. |
*> \param[in] N |
* |
*> \verbatim |
* AP - DOUBLE PRECISION array of DIMENSION at least |
*> N is INTEGER |
* ( ( n*( n + 1 ) )/2 ). |
*> On entry, N specifies the order of the matrix A. |
* Before entry with UPLO = 'U' or 'u', the array AP must |
*> N must be at least zero. |
* contain the upper triangular matrix packed sequentially, |
*> \endverbatim |
* column by column, so that AP( 1 ) contains a( 1, 1 ), |
*> |
* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) |
*> \param[in] AP |
* respectively, and so on. |
*> \verbatim |
* Before entry with UPLO = 'L' or 'l', the array AP must |
*> AP is DOUBLE PRECISION array of DIMENSION at least |
* contain the lower triangular matrix packed sequentially, |
*> ( ( n*( n + 1 ) )/2 ). |
* column by column, so that AP( 1 ) contains a( 1, 1 ), |
*> Before entry with UPLO = 'U' or 'u', the array AP must |
* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) |
*> contain the upper triangular matrix packed sequentially, |
* respectively, and so on. |
*> column by column, so that AP( 1 ) contains a( 1, 1 ), |
* Note that when DIAG = 'U' or 'u', the diagonal elements of |
*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) |
* A are not referenced, but are assumed to be unity. |
*> respectively, and so on. |
* Unchanged on exit. |
*> Before entry with UPLO = 'L' or 'l', the array AP must |
* |
*> contain the lower triangular matrix packed sequentially, |
* X - DOUBLE PRECISION array of dimension at least |
*> column by column, so that AP( 1 ) contains a( 1, 1 ), |
* ( 1 + ( n - 1 )*abs( INCX ) ). |
*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) |
* Before entry, the incremented array X must contain the n |
*> respectively, and so on. |
* element right-hand side vector b. On exit, X is overwritten |
*> Note that when DIAG = 'U' or 'u', the diagonal elements of |
* with the solution vector x. |
*> A are not referenced, but are assumed to be unity. |
* |
*> \endverbatim |
* INCX - INTEGER. |
*> |
* On entry, INCX specifies the increment for the elements of |
*> \param[in,out] X |
* X. INCX must not be zero. |
*> \verbatim |
* Unchanged on exit. |
*> X is DOUBLE PRECISION array of dimension at least |
* |
*> ( 1 + ( n - 1 )*abs( INCX ) ). |
* Further Details |
*> Before entry, the incremented array X must contain the n |
* =============== |
*> element right-hand side vector b. On exit, X is overwritten |
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*> with the solution vector x. |
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*> \endverbatim |
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*> |
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*> \param[in] INCX |
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*> \verbatim |
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*> INCX is INTEGER |
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*> On entry, INCX specifies the increment for the elements of |
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*> X. INCX must not be zero. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup double_blas_level2 |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> Level 2 Blas routine. |
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*> |
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*> -- Written on 22-October-1986. |
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*> Jack Dongarra, Argonne National Lab. |
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*> Jeremy Du Croz, Nag Central Office. |
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*> Sven Hammarling, Nag Central Office. |
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*> Richard Hanson, Sandia National Labs. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
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SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) |
* |
* |
* Level 2 Blas routine. |
* -- Reference BLAS level2 routine (version 3.4.0) -- |
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
* |
* |
* -- Written on 22-October-1986. |
* .. Scalar Arguments .. |
* Jack Dongarra, Argonne National Lab. |
INTEGER INCX,N |
* Jeremy Du Croz, Nag Central Office. |
CHARACTER DIAG,TRANS,UPLO |
* Sven Hammarling, Nag Central Office. |
* .. |
* Richard Hanson, Sandia National Labs. |
* .. Array Arguments .. |
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DOUBLE PRECISION AP(*),X(*) |
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* .. |
* |
* |
* ===================================================================== |
* ===================================================================== |
* |
* |
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END IF |
END IF |
ELSE |
ELSE |
* |
* |
* Form x := inv( A' )*x. |
* Form x := inv( A**T )*x. |
* |
* |
IF (LSAME(UPLO,'U')) THEN |
IF (LSAME(UPLO,'U')) THEN |
KK = 1 |
KK = 1 |