single_blas_level2(3)

NAME
single_blas_level2

SYNOPSIS

  Functions
subroutine sgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGBMV
subroutine sgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
subroutine sger (M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
subroutine ssbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSBMV
subroutine sspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
subroutine sspr (UPLO, N, ALPHA, X, INCX, AP)
SSPR
subroutine sspr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
SSPR2
subroutine ssymv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSYMV
subroutine ssyr (UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
subroutine ssyr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SSYR2
subroutine stbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBMV
subroutine stbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBSV
subroutine stpmv (UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
subroutine stpsv (UPLO, TRANS, DIAG, N, AP, X, INCX)
STPSV
subroutine strmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
subroutine strsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRSV

Detailed Description

This is the group of real LEVEL 2 BLAS routines.

Function Documentation

  subroutine sgbmv (character TRANS, integer M, integer N, integer KL, integer KU, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)

SGBMV

Purpose:

     SGBMV  performs one of the matrix-vector operations
        y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
     where alpha and beta are scalars, x and y are vectors and A is an
     m by n band matrix, with kl sub-diagonals and ku super-diagonals.

Parameters:
    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                  TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
                  TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.

    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    KL

              KL is INTEGER
               On entry, KL specifies the number of sub-diagonals of the
               matrix A. KL must satisfy  0 .le. KL.

    KU

              KU is INTEGER
               On entry, KU specifies the number of super-diagonals of the
               matrix A. KU must satisfy  0 .le. KU.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry, the leading ( kl + ku + 1 ) by n part of the
               array A must contain the matrix of coefficients, supplied
               column by column, with the leading diagonal of the matrix in
               row ( ku + 1 ) of the array, the first super-diagonal
               starting at position 2 in row ku, the first sub-diagonal
               starting at position 1 in row ( ku + 2 ), and so on.
               Elements in the array A that do not correspond to elements
               in the band matrix (such as the top left ku by ku triangle)
               are not referenced.
               The following program segment will transfer a band matrix
               from conventional full matrix storage to band storage:
                     DO 20, J = 1, N
                        K = KU + 1 - J
                        DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                           A( K + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               ( kl + ku + 1 ).

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
               Before entry, the incremented array X must contain the
               vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
               Before entry, the incremented array Y must contain the
               vector y. On exit, Y is overwritten by the updated vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 187 of file sgbmv.f.

  subroutine sgemv (character TRANS, integer M, integer N, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)

SGEMV

Purpose:

     SGEMV  performs one of the matrix-vector operations
        y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
     where alpha and beta are scalars, x and y are vectors and A is an
     m by n matrix.

Parameters:
    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                  TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
                  TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.

    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry, the leading m by n part of the array A must
               contain the matrix of coefficients.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, m ).

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
               Before entry, the incremented array X must contain the
               vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
               Before entry with BETA non-zero, the incremented array Y
               must contain the vector y. On exit, Y is overwritten by the
               updated vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 158 of file sgemv.f.

  subroutine sger (integer M, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(lda,*) A, integer LDA)

SGER

Purpose:

     SGER   performs the rank 1 operation
        A := alpha*x*y**T + A,
     where alpha is a scalar, x is an m element vector, y is an n element
     vector and A is an m by n matrix.

Parameters:
    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    X

              X is REAL array, dimension at least
               ( 1 + ( m - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the m
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry, the leading m by n part of the array A must
               contain the matrix of coefficients. On exit, A is
               overwritten by the updated matrix.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, m ).

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 132 of file sger.f.

  subroutine ssbmv (character UPLO, integer N, integer K, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)

SSBMV

Purpose:

     SSBMV  performs the matrix-vector  operation
        y := alpha*A*x + beta*y,
     where alpha and beta are scalars, x and y are n element vectors and
     A is an n by n symmetric band matrix, with k super-diagonals.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the band matrix A is being supplied as
               follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      being supplied.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      being supplied.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              K is INTEGER
               On entry, K specifies the number of super-diagonals of the
               matrix A. K must satisfy  0 .le. K.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    A

              A is REAL 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 symmetric matrix, 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 the upper
               triangular part of a symmetric 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 symmetric matrix, 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 the lower
               triangular part of a symmetric 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

    LDA

              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 ).

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the
               vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the
               vector y. On exit, Y is overwritten by the updated vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 186 of file ssbmv.f.

  subroutine sspmv (character UPLO, integer N, real ALPHA, real, dimension(*) AP, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)

SSPMV

Purpose:

     SSPMV  performs the matrix-vector operation
        y := alpha*A*x + beta*y,
     where alpha and beta are scalars, x and y are n element vectors and
     A is an n by n symmetric matrix, supplied in packed form.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the matrix A is supplied in the packed
               array AP as follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      supplied in AP.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      supplied in AP.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    AP

              AP is REAL array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with UPLO = 'U' or 'u', the array AP must
               contain the upper triangular part of the symmetric matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
               and a( 2, 2 ) respectively, and so on.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular part of the symmetric matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
               and a( 3, 1 ) respectively, and so on.

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y. On exit, Y is overwritten by the updated
               vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 149 of file sspmv.f.

  subroutine sspr (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) AP)

SSPR

Purpose:

     SSPR    performs the symmetric rank 1 operation
        A := alpha*x*x**T + A,
     where alpha is a real scalar, x is an n element vector and A is an
     n by n symmetric matrix, supplied in packed form.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the matrix A is supplied in the packed
               array AP as follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      supplied in AP.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      supplied in AP.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    AP

              AP is REAL array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular part of the symmetric matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
               and a( 2, 2 ) respectively, and so on. On exit, the array
               AP is overwritten by the upper triangular part of the
               updated matrix.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular part of the symmetric matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
               and a( 3, 1 ) respectively, and so on. On exit, the array
               AP is overwritten by the lower triangular part of the
               updated matrix.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 129 of file sspr.f.

  subroutine sspr2 (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(*) AP)

SSPR2

Purpose:

     SSPR2  performs the symmetric rank 2 operation
        A := alpha*x*y**T + alpha*y*x**T + A,
     where alpha is a scalar, x and y are n element vectors and A is an
     n by n symmetric matrix, supplied in packed form.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the matrix A is supplied in the packed
               array AP as follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      supplied in AP.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      supplied in AP.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    AP

              AP is REAL array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular part of the symmetric matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
               and a( 2, 2 ) respectively, and so on. On exit, the array
               AP is overwritten by the upper triangular part of the
               updated matrix.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular part of the symmetric matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
               and a( 3, 1 ) respectively, and so on. On exit, the array
               AP is overwritten by the lower triangular part of the
               updated matrix.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 144 of file sspr2.f.

  subroutine ssymv (character UPLO, integer N, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)

SSYMV

Purpose:

     SSYMV  performs the matrix-vector  operation
        y := alpha*A*x + beta*y,
     where alpha and beta are scalars, x and y are n element vectors and
     A is an n by n symmetric matrix.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the array A is to be referenced as
               follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of A
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of A
                                      is to be referenced.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular part of the symmetric matrix and the strictly
               lower triangular part of A is not referenced.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular part of the symmetric matrix and the strictly
               upper triangular part of A is not referenced.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y. On exit, Y is overwritten by the updated
               vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 154 of file ssymv.f.

  subroutine ssyr (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(lda,*) A, integer LDA)

SSYR

Purpose:

     SSYR   performs the symmetric rank 1 operation
        A := alpha*x*x**T + A,
     where alpha is a real scalar, x is an n element vector and A is an
     n by n symmetric matrix.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the array A is to be referenced as
               follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of A
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of A
                                      is to be referenced.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular part of the symmetric matrix and the strictly
               lower triangular part of A is not referenced. On exit, the
               upper triangular part of the array A is overwritten by the
               upper triangular part of the updated matrix.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular part of the symmetric matrix and the strictly
               upper triangular part of A is not referenced. On exit, the
               lower triangular part of the array A is overwritten by the
               lower triangular part of the updated matrix.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 134 of file ssyr.f.

  subroutine ssyr2 (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(lda,*) A, integer LDA)

SSYR2

Purpose:

     SSYR2  performs the symmetric rank 2 operation
        A := alpha*x*y**T + alpha*y*x**T + A,
     where alpha is a scalar, x and y are n element vectors and A is an n
     by n symmetric matrix.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the array A is to be referenced as
               follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of A
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of A
                                      is to be referenced.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular part of the symmetric matrix and the strictly
               lower triangular part of A is not referenced. On exit, the
               upper triangular part of the array A is overwritten by the
               upper triangular part of the updated matrix.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular part of the symmetric matrix and the strictly
               upper triangular part of A is not referenced. On exit, the
               lower triangular part of the array A is overwritten by the
               lower triangular part of the updated matrix.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 149 of file ssyr2.f.

  subroutine stbmv (character UPLO, character TRANS, character DIAG, integer N, integer K, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)

STBMV

Purpose:

     STBMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular band matrix, with ( k + 1 ) diagonals.

Parameters:
    UPLO

              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.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**T*x.

    DIAG

              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.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              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.

    A

              A is REAL 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.

    LDA

              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 ).

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               transformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 188 of file stbmv.f.

  subroutine stbsv (character UPLO, character TRANS, character DIAG, integer N, integer K, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)

STBSV

Purpose:

     STBSV  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.

Parameters:
    UPLO

              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.

    TRANS

              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.

    DIAG

              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.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              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.

    A

              A is REAL 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.

    LDA

              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 ).

    X

              X is REAL 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.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 191 of file stbsv.f.

  subroutine stpmv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(*) AP, real, dimension(*) X, integer INCX)

STPMV

Purpose:

     STPMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular matrix, supplied in packed form.

Parameters:
    UPLO

              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.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**T*x.

    DIAG

              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.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    AP

              AP is REAL array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
               respectively, and so on.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
               respectively, and so on.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced, but are assumed to be unity.

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               transformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 144 of file stpmv.f.

  subroutine stpsv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(*) AP, real, dimension(*) X, integer INCX)

STPSV

Purpose:

     STPSV  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 matrix, supplied in packed form.
     No test for singularity or near-singularity is included in this
     routine. Such tests must be performed before calling this routine.

Parameters:
    UPLO

              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.

    TRANS

              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.

    DIAG

              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.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    AP

              AP is REAL array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
               respectively, and so on.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
               respectively, and so on.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced, but are assumed to be unity.

    X

              X is REAL 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.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 146 of file stpsv.f.

  subroutine strmv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)

STRMV

Purpose:

     STRMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular matrix.

Parameters:
    UPLO

              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.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**T*x.

    DIAG

              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.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular matrix and the strictly lower triangular part of
               A is not referenced.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular matrix and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced either, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

    X

              X is REAL array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               transformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- 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.

Definition at line 149 of file strmv.f.

  subroutine strsv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)

STRSV

Purpose:

     STRSV  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 matrix.
     No test for singularity or near-singularity is included in this
     routine. Such tests must be performed before calling this routine.

Parameters:
    UPLO

              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.

    TRANS

              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.

    DIAG

              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.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    A

              A is REAL array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular matrix and the strictly lower triangular part of
               A is not referenced.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular matrix and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced either, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

    X

              X is REAL 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.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

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.

Definition at line 151 of file strsv.f.

Author

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