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---
:name: clasr
:md5sum: 9edeb6dbb98dd9c3e28985b4bc103c42
:category: :subroutine
:arguments:
- side:
:type: char
:intent: input
- pivot:
:type: char
:intent: input
- direct:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- c:
:type: real
:intent: input
:dims:
- m-1
- s:
:type: real
:intent: input
:dims:
- m-1
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
:substitutions: {}
:fortran_help: " SUBROUTINE CLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CLASR applies a sequence of real plane rotations to a complex matrix\n\
* A, from either the left or the right.\n\
*\n\
* When SIDE = 'L', the transformation takes the form\n\
*\n\
* A := P*A\n\
*\n\
* and when SIDE = 'R', the transformation takes the form\n\
*\n\
* A := A*P**T\n\
*\n\
* where P is an orthogonal matrix consisting of a sequence of z plane\n\
* rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',\n\
* and P**T is the transpose of P.\n\
* \n\
* When DIRECT = 'F' (Forward sequence), then\n\
* \n\
* P = P(z-1) * ... * P(2) * P(1)\n\
* \n\
* and when DIRECT = 'B' (Backward sequence), then\n\
* \n\
* P = P(1) * P(2) * ... * P(z-1)\n\
* \n\
* where P(k) is a plane rotation matrix defined by the 2-by-2 rotation\n\
* \n\
* R(k) = ( c(k) s(k) )\n\
* = ( -s(k) c(k) ).\n\
* \n\
* When PIVOT = 'V' (Variable pivot), the rotation is performed\n\
* for the plane (k,k+1), i.e., P(k) has the form\n\
* \n\
* P(k) = ( 1 )\n\
* ( ... )\n\
* ( 1 )\n\
* ( c(k) s(k) )\n\
* ( -s(k) c(k) )\n\
* ( 1 )\n\
* ( ... )\n\
* ( 1 )\n\
* \n\
* where R(k) appears as a rank-2 modification to the identity matrix in\n\
* rows and columns k and k+1.\n\
* \n\
* When PIVOT = 'T' (Top pivot), the rotation is performed for the\n\
* plane (1,k+1), so P(k) has the form\n\
* \n\
* P(k) = ( c(k) s(k) )\n\
* ( 1 )\n\
* ( ... )\n\
* ( 1 )\n\
* ( -s(k) c(k) )\n\
* ( 1 )\n\
* ( ... )\n\
* ( 1 )\n\
* \n\
* where R(k) appears in rows and columns 1 and k+1.\n\
* \n\
* Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is\n\
* performed for the plane (k,z), giving P(k) the form\n\
* \n\
* P(k) = ( 1 )\n\
* ( ... )\n\
* ( 1 )\n\
* ( c(k) s(k) )\n\
* ( 1 )\n\
* ( ... )\n\
* ( 1 )\n\
* ( -s(k) c(k) )\n\
* \n\
* where R(k) appears in rows and columns k and z. The rotations are\n\
* performed without ever forming P(k) explicitly.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* SIDE (input) CHARACTER*1\n\
* Specifies whether the plane rotation matrix P is applied to\n\
* A on the left or the right.\n\
* = 'L': Left, compute A := P*A\n\
* = 'R': Right, compute A:= A*P**T\n\
*\n\
* PIVOT (input) CHARACTER*1\n\
* Specifies the plane for which P(k) is a plane rotation\n\
* matrix.\n\
* = 'V': Variable pivot, the plane (k,k+1)\n\
* = 'T': Top pivot, the plane (1,k+1)\n\
* = 'B': Bottom pivot, the plane (k,z)\n\
*\n\
* DIRECT (input) CHARACTER*1\n\
* Specifies whether P is a forward or backward sequence of\n\
* plane rotations.\n\
* = 'F': Forward, P = P(z-1)*...*P(2)*P(1)\n\
* = 'B': Backward, P = P(1)*P(2)*...*P(z-1)\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. If m <= 1, an immediate\n\
* return is effected.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. If n <= 1, an\n\
* immediate return is effected.\n\
*\n\
* C (input) REAL array, dimension\n\
* (M-1) if SIDE = 'L'\n\
* (N-1) if SIDE = 'R'\n\
* The cosines c(k) of the plane rotations.\n\
*\n\
* S (input) REAL array, dimension\n\
* (M-1) if SIDE = 'L'\n\
* (N-1) if SIDE = 'R'\n\
* The sines s(k) of the plane rotations. The 2-by-2 plane\n\
* rotation part of the matrix P(k), R(k), has the form\n\
* R(k) = ( c(k) s(k) )\n\
* ( -s(k) c(k) ).\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA,N)\n\
* The M-by-N matrix A. On exit, A is overwritten by P*A if\n\
* SIDE = 'R' or by A*P**T if SIDE = 'L'.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\n\
* =====================================================================\n\
*\n"
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